Home Numerical modeling of the thermoelectric cooler with a complementary equation for heat circulation in air gaps
Article Open Access

Numerical modeling of the thermoelectric cooler with a complementary equation for heat circulation in air gaps

  • En Fang , Xiaojie Wu , Yuesen Yu and Junrui Xiu
Published/Copyright: March 12, 2017
Download Article (PDF)
Open Physics
From the journal Open Physics Volume 15 Issue 1

Abstract

In this paper, a numerical model is developed by combining thermodynamics with heat transfer theory. Taking inner and external multi-irreversibility into account, it is with a complementary equation for heat circulation in air gaps of a steady cooling system with commercial thermoelectric modules operating in refrigeration mode. With two modes concerned, the equation presents the heat flowing through air gaps which forms heat circulations between both sides of thermoelectric coolers (TECs). In numerical modelling, a TEC is separated as two temperature controlled constant heat flux reservoirs in a thermal resistance network. In order to obtain the parameter values, an experimental apparatus with a commercial thermoelectric cooler was built to characterize the performance of a TEC with heat source and sink assembly. At constant power dissipation, steady temperatures of heat source and both sides of the thermoelectric cooler were compared with those in a standard numerical model. The method displayed that the relationship between Φf and the ratio Φc′/Φc was linear as expected. Then, for verifying the accuracy of proposed numerical model, the data in another system were recorded. It is evident that the experimental results are in good agreement with simulation(proposed model) data at different heat transfer rates. The error is small and mainly results from the instabilities of thermal resistances with temperature change and heat flux, heat loss of the device vertical surfaces and measurements.

Keywords: Thermoelectric coolers; Thermoelectric generators; Peltier effect; Refrigeration performance
PACS: 44.05.+e

1 Introduction

The direct energy conversion between heat and electricity based on thermoelectric effects is attractive for many applications as an alternative to traditional methods in power generation and heat transmission [1, 2]. Thermoelectric modules (TEMs) have outstanding advantages such as solid-state, compact, light-weight, containing neither moving parts nor refrigerants, maintenance free, highly reliable and quiet operation, environmental friendly performance, and so on [3, 4]. The use of TEMs for cooling, heating and power generation in a simple and reliable way has been comprehensively discussed in many industrial fields [5]. TEMs can be divided into two types, namely thermoelectric coolers (TECs) and thermoelectric generators (TEGs) [6–8]. Since conventional air cooling techniques for high power electronic packages are reaching the limits in term of cooling capacity, various efforts have been devoted to enhance the cooling design and performance [9]. Among them, the use of TECs, in combination with air cooling or liquid cooling approaches, is gaining more and more attention. The major thermal benefit of this development trend lies in the fact that a negative temperature gradient and thus reduced thermal resistance could be generated from the use of TECs [10, 11].

Bell [12] points out two important pathways that will lead to additional applications of thermoelectric devices. One is to promote the intrinsic efficiencies of TE materials. The other is to improve the way that existing TEMs are currently used by modeling and analyzing of thermoelectric systems [13, 14]. For TECs, the primary mission should be to keep the heat resource working in a certain temperature range. Thermoelectric devices could not be used independently. Heat sources and exchangers should be connected with to dissipate and absorb heat [15]. The commonly used approach is the iterative method as given in [11].

A numerical optimization of a TEC was presented by Xuan [16]. The results indicated that the construction cost of a TEC was closely related to the cooling power density; whereas the running cost was inversely proportional to COP. High efficiency was obtained when the length of the thermo elements was large [17]. In addition, the power generated declined with the cross-sectional area of the thermo elements, whereas efficiency showed the opposite trend [6].

For conduction and convection, the heat only flows from the end at high temperature to low. In electronic devices, the reliability and lifetime of electronic components decrease greatly with temperature rise due to power dissipation. Although a variety of cooling means have been used, such as natural convection, forced air convection and liquid exchangers, heat pipe exchangers, and so on, the electronic components are still often the parts with the highest temperature in electronic devices. The TECs work as heat pumps converting heat flux from the cold end to hot continuously at the expense of electric energy. They can be conveniently controlled by DC power suppliers.

In this paper, a numerical model with the complementary equation is established according to various equations concerning with cooling system and thermoelectric coolers.

2 Numerical model on a cooling system with TECs

A TEC is a solid-state heat pump placed between heat sources and heat sinks. It normally consists of an array of 2N pellets from dissimilar semiconductor materials (p and n type) that make up N thermoelectric couples which are electrically by conducting strips in series and thermally in parallel [18, 19]. The p and n legs are joined by metal interconnects with ohmic contact. The conducting strips of the thermoelectric elements are fixed at a thermal conducting and electrical insulating ceramic plate [20]. The module is packaging by thermally insulating epoxy resin. The thermoelectric elements in most commercial thermoelectric modules are not closely arranged, that is, air gaps exist in the module which lead to heat microcirculations. The heat convection (or conduction) and radiative heat transfer occur between two ceramic plates in the area that the thermoelectric elements do not occupy.

2.1 Assumptions

To simplify the cooling system with TECs, the following assumptions are made:

  1. The numerical model is for a steady-state system;

  2. The TEC is single-stage constructed from N thermoelectric couples which are identical and joined electrically in series and thermally in parallel [6];

  3. All the cooling means such as convection, conduction and radiation are included in the computational domain as a one-dimension thermal resistance varying with heat flux and temperatures in simplification;

  4. Heat transfer at a finite rate, and electrical resistive losses, are necessarily irreversible processes and unavoidable in a thermoelectric device [5];

  5. The ceramic plates work as favorable heat conductors and electrical insulators.

2.2 Standard Model

One-dimensional thermal resistance network of the whole cooling system with a single-stage TEC is shown in Figure 1. The TEC is separated as two temperature controlled constant heat flux reservoirs in thermal resistance network. The positive directions of heat flow expected in the scenario are shown in Figure 1. Presenting the problems in electronic circuit terms helps to understand its functionality, and facilitates the solving of cooling problems without the need for expertise in thermal engineering [21].

Figure 1 One-dimension thermal resistance network of a cooling system with a single-stage TEC
Figure 1

One-dimension thermal resistance network of a cooling system with a single-stage TEC

According to the non-equilibrium thermodynamics, the inner effects of the thermoelectric elements include Seebeck effect, Fourier effect, Joule effect and Thomson effect. The increment rate of inner energy of the infinitesimal is zero at steady-state, so one can obtain the energy conservation equation as follows:

Φc=NαITc−12I2R−K(Th−Tc)Φh=Φc+NαI(Th−Tc)+I2RΦh=Th−TaRhΦc=Ploss−Tj−TaR′Tj−Tc=ΦcRc(1)

2.3 Proposed Model with complementary equation

In standard models, the heat flux Φc′ absorbed by the semiconductor nodes is assumed to be of an equivalent amount to that flows through the cold side Φc. But in fact, due to the existences of constriction thermal resistance, they are not equal. Comparing the heat flow in TECs against the air flow in an unsealed duct with two exhaust fans, two modes are maintained in Figure 2.

Figure 2 Two modes of heat flow in TECs
Figure 2

Two modes of heat flow in TECs

Thus,

Φc=Φc′+Φf+Φl(2)

Where, Φf is the heat flowing through air gaps which forms heat circulations between both sides of TECs. It should be a piecewise function depending on the relationship of Φc and Φc′.Φl is the leakage heat through the thermal insulation material. The conduction properties and insulation characteristics of the materials should have significant effect on Φf. It is also related to the thickness of ceramic plates and conduction trips, the area ratio of N(Sn +Sp)/S, and so on. As these parameters vary little in a certain range, in view of the air flow in an unsealed duct with two exhaust fans, the piecewise function is proposed to be linear. And the positive directions of heat flow are defined as in Figure 2(a).

Φf=δ1Φc′Φc+Φp1,Φc≥(Φc′+Φl)δ2Φc′Φc+Φp2,Φc<(Φc′+Φl)(3)

While Φc≥(Φc′+Φl),Φf≥0 and vice versa. As mentioned before, with the complementary equation for the heat flowing through air gaps, the model is proposed as,

Φc−Φc′−Φl=δ1Φc′Φc+Φp1,Φc≥(Φc′+Φl)δ2Φc′Φc+Φp2,Φc<(Φc′+Φl)Φc′=NαITc−12I2R−K(Th−Tc)Φh=Φc+NαI(Th−Tc)+I2RΦhRh=Th−TaΦc=Ploss−Tj−TaR′Tj−Tc=ΦcRc(4)

The proposed numerical model may be applied to the calculation of characteristic parameters, temperature prediction and further optimization study for thermoelectric coolers. The simulation results can be used as feasibility and effectiveness reference by employing component package and device cooling.

3 Experimental setup

3.1 System characterization with TEC in refrigeration

In order to realize the output performance following control of this case study, a cooling process with a TEC was considered where film resistor temperature sensors were located at different places, as shown in Figure 3.

Figure 3 Setup to measure the temperatures of heat source and TEC
Figure 3

Setup to measure the temperatures of heat source and TEC

A sandwiched structure (from top to bottom) of thermal insulation layer/patch heater/thermal silicone grease/copper plate/thermal silicone grease/TEC/thermal silicone grease/heat sink was introduced. The CH-J404020 is one of the patch heater modules available from Company MCH, which was attached to a copper plate on the cold side of the TEC. The TEC 12706AJ (N = 127) is manufactured by Wanhao Technology. A water cooled exchanger was used to absorb the heat from the hot side of TEC. The coolant (water) was supplied from a water-circulating chiller. In order to reduce thermal contact resistance, a thermal interface material, thermal silicone grease (Aobaili ABL3601) was smeared uniformly on every contact surface. Figure 4 shows the schematic diagram of the experimental cooling system. The assembly was insulated with heat-insulated foam to minimize the parasitic heat load from the ambient except for the heat sink and is held under compression between four aluminum latches for proper contact between surfaces at a constant pressure. Temperatures on the heater (Tj), cold side (Tc) and hot side (Th) of the TEC, as well as the ambient temperature (Ta), are measured using film resistor temperature sensors which are held in place with thermally conductive silicone grease. The sensors have an uncertainty of ± 0.5 K. Two programmable DC power supplies (Chroma 62100H-450) are employed for heater and TEC, respectively. The voltage across and current through the patch heater are measured to determine the heat dissipation in the cooling system. The uncertainty in the measurements of voltage and current are ± 1 mV and ± 1 mA, respectively.

Figure 4 Schematic diagram of the experimental setup of water cooling system The programmable DC supply for TEC worked as a constant current power
Figure 4

Schematic diagram of the experimental setup of water cooling system The programmable DC supply for TEC worked as a constant current power

The programmable DC supply for TEC worked as a constant current power supply, while the other one as a constant voltage source for patch heater (Uheater = 20V). All the temperatures at different currents of the TEC with this water cooled exchanger were recorded.

Then, the programmable DC supply for TEC worked as a constant current power supply (ITEC = 0.5A), while the other one as a constant voltage source for patch heater. By replacing the water cooled exchanger with aluminum radiator, the experimental temperatures at different heat transfer rate with aluminum heat sink were also recorded.

3.2 System characterization with TEM for thermal conduction

Before the system performance testing, a performance characterization should be achieved by means of testing the parameters, such as the equivalent thermal resistance of contact thermal resistance, constriction thermal resistance and convection thermal resistance, and so on.

Firstly, the patch heater was encapsulated bilateral symmetry by thermal insulation layers.

R′=2(Tj−Ta)Ploss

Temperatures of the patch heater above ambient at different applied heat load are presented in Figure 5. The thermal resistance of insulation layer is 59.11 K/W as slope. The value of R-square in Figure 5 is 0.9966 which imply the accuracy of the fitting lines that explain our measurement results are more than 99%. Due to high insulation capability of the layer, the thermal resistance value changes little with the heat flux and temperature.

Figure 5 Temperatures of the patch heater above ambient at different applied heat load
Figure 5

Temperatures of the patch heater above ambient at different applied heat load

Then, the test apparatus mentioned before were tested. The TEM was treated as a conduction module without being powered. As the assembly was insulated with heat-insulated foam, little heat dissipated from vertical sides to ambient, that is to say, Φc ≈ Φh.

Φc=Φh=Ploss−Tj−TaR′Rc=Tj−TcΦcRh=Th−TaΦhK=ΦcTc−Th

The tested temperature differences of (Tj − Tc), (Tc − Th) and (Th − Ta) are plotted against the applied heat load in Figure 6. The equivalent thermal resistance Rc and Rh could be obtained by curve fitting. Hence the slope of the linear fit in Figure 6(a) provides the thermal interface resistance and constriction resistance. In Figure 6(b), the thermal conductivity of the module is characterized. Figure 6(c) and (d) represent the combined heat sink and water cooled exchanger with parasitic resistance in parallel, respectively.

Figure 6 Tested temperatures and corresponding thermal resistance/conductivity against the applied heat load
Figure 6

Tested temperatures and corresponding thermal resistance/conductivity against the applied heat load

4 Results

A total of 51 samples was collected and then analyzed for modeling. Figure 7 shows the measured and simulated (standard model) curves of temperatures versus current of the TEC at the same power dissipation with water cooling system. Based on the standard model without the microcirculation heat Φf and leakage heat Φl, the theoretical results in Figure 7(a) and (b) are quite different from those in experiments. It shows the necessity of proposing an accurate model to predict the temperature behavior of TECs. In Figure 7(c), the results of the experiment and simulation were highly consistent due to the accuracy of Rh and Φh.

Figure 7 Temperatures for different currents of the TEC with water cooled exchanger at Uheater = 20V
Figure 7

Temperatures for different currents of the TEC with water cooled exchanger at Uheater = 20V

Figure 8 shows the linear relationship between the temperature differences and current of TEC with water cooled exchanger at constant power dissipation. The temperature differences decrease from positive to negative with TEC current increasing. While the current of TEC remains about 4.4A, the experimental junction temperature is the same as the predicted one. The maximum absolute value of temperature difference in test range is 11.55 K.

Figure 8 Temperature differences between experimental and theoretical Tj for different currents of the TEC with the water cooled exchanger
Figure 8

Temperature differences between experimental and theoretical Tj for different currents of the TEC with the water cooled exchanger

In view of the proposed model in formula (4), based on the measured temperatures, the heat flows in every thermal path are calculated. The factor (Φf + Φl) is shown in Figure 9.

Figure 9 Calculated Φf + Φl for different Φc′ $\varPhi_{{\text c}}' $
Figure 9

Calculated Φf + Φl for different Φc′

In this case, the method of least squares nonlinear regression and subsection function are introduced to deal with data. As mentioned before, Φf should be a piecewise function of Φc′ at constant Φc,

Φf+Φl=−0.88279Φc′+15.52372,Φc≥(Φc′+Φl)−1.57414Φc′+29.33509,Φc<(Φc′+Φl)(5)

In the proposed model, there is a turning point from which Φf changes from positive to negative with increasing Φc′. Compared to the segmental fitting equations, the intersection point (19.98, −2.11) is the turning point of subsection.

Thus, at the turning point for this experimental system, Φf = 0W, Φc′ =19.98W, Φl = −2.11W and Φc = Φc′ + Φl = 17.87W.

Φf=−15.78Φc′Φc+17.63,Φc≥(Φc′+Φl)−28.13Φc′Φc+31.45,Φc<(Φc′+Φl)(6)

Then the water cooled exchanger was replaced with aluminum radiator. The differences between experimental and calculated (proposed model) temperatures at different heat transfer rate are shown in Figure 10.

Figure 10 Temperatures for different heat transfer rate with aluminum heat sink at iTEC =0.5A
Figure 10

Temperatures for different heat transfer rate with aluminum heat sink at iTEC =0.5A

In Figure 10, the prediction temperatures are very consistent with that observed in test at constant current of TEC (iTEC = 0.5A). There is a maximum difference between theoretical and experimental junction temperatures up to 4K when experimental Tj reaches 364.6 K.

5 Discussion and conclusion

Electricity is consumed by thermoelectric effect with Φc′ to maintain system balance. But in fact, there are lots of air gaps between semiconductor legs which lead to the appearance of heat microcirculations between both sides of TEMs. Due to the constriction resistance, conducting strips and air gaps, there is a difference between thermal power absorbed by the semiconductor nodes and the heat fluxing through the ceramic plate on the cold side, which leads to the error between theoretical and experimental Tj as in Figure 7.

High precision of the model can be obtained by the introduction of a correct function Φc=Φc′+Φf+Φl. And the heat flowing through air gaps Φf can be treated as a linear piecewise function of Φc′/Φc. The coefficient δ is related to the thickness of ceramic plates and conduction trips, the area ratio of N(Sn +Sp)/S, the conduction properties and insulation characteristics of materials, and so on. The linear relationship is approximate because there are factors (such as heat convections and radiative heat transfer) which caused inaccuracy in thermal resistance measurements.

For the prediction model of junction temperature, it is very difficult to obtain accurate thermal resistance values, which varies with ambient temperature, heat flux, device layout and other factors in the cooling system with TECs. The way to obtain the thermal resistance values by theoretical analysis can be achieved in other papers. In order to verify the validity of the proposed model, thermal resistance values with experimental method are adopted. Figure 6 illustrates temperature distribution in heat flow path including TEC (Tj, Th, Tc and Ta) related to applied heat load. The results show that Rc decreases with the increase of heat flux according to exponential decay. And the thermal conductivity K increases as the reciprocal of according thermal resistance.

The model is derived basing on the structure of the TEMs, so it can be used also in TEGs. In TEGs, there are initiative heat absorptions to generate power. The correction function Φf works only in one mode Φc≥Φc′, and remains linear to Φc as in TECs.

It is worth mentioning that in most research articles on TEMs, the thermal conductivity is only effected by semiconductor materials, K=λAx/L=λNAxN/LN+λPAxP/LPρNLN/AxN. In this case, the thermal conductivity K, representing the heat transferring from the hot surface to cold through conduction element (not only semiconductor materials but also devices within the package) due to the temperature difference, should be considered. In fact, the thermal conductivity with only semiconductor materials caused a significant error between theoretical and experimental data. The total thermal conductivity tested by experiments is more than one hundred times than the theoretical value of semiconductor materials.

References

[1] Simons R.E., Chu R.C., Application of thermoelectric cooling to electronic equipment: a review and analysis, 16th Annu. IEEE Semiconductor Thermal Meas. Manag. Symp., 2000, 1-9.10.1109/STHERM.2000.837055Search in Google Scholar

[2] Hsu C.T., Huang G.Y., Chu H.S., Yu B., Yao D.J., Experiments and simulations on low-temperature waste heat harvesting system by thermoelectric power generators, Appl. Energy, 2011, 88, 1291-1297.10.1016/j.apenergy.2010.10.005Search in Google Scholar

[3] Kane A., Verma V., Singh B., Temperature Dependent Analysis of Thermoelectric Module using Matlab/SIMULINK, IEEE Int. Conf.Power Energy, 2012, 632-637.10.1109/PECon.2012.6450291Search in Google Scholar

[4] Zebarjadi M., Esfarjani K., Dresselhaus M.S., Ren Z.F., Chen G., Perspectives on thermoelectrics: from fundamentals to device applications, Energy & Environ. Sci., 2012, 5, 5147-5162.10.1039/C1EE02497CSearch in Google Scholar

[5] Meng F., Chen L., Sun F., A numerical model and comparative investigation of a thermoelectric generator with multi-irreversibilities, Energy, 2011, 36, 3513-3522.10.1016/j.energy.2011.03.057Search in Google Scholar

[6] Wang C., Hung C., Chen W., Design of heat sink for improving the performance of thermoelectric generator using two-stage optimization, Energy, 2012, 39, 236-245.10.1016/j.energy.2012.01.025Search in Google Scholar

[7] Wen S., Zhang G., Dan Y., Wang D., Model output following control for an aluminum plate cooling process with a Peltier device, Int. Conf. Adv. Mechatronic Syst., 2012, 452-457.Search in Google Scholar

[8] Wang D., Zhang L., Zhang G., Yang K., Cooling control of aluminum plate with a Peltier device thermal process by using a robust right coprime factorization approach, 10th World Congr. Intelligent Control Automation, 2012, 1115-1119.10.1109/WCICA.2012.6358047Search in Google Scholar

[9] Deng M., Yanou A., Tokuda Y., Wang A., Robust fault tolerant thermal control system design of an aluminum plate with Peltier device, Int. Conf. Adv. Mechatronic Syst., 2012, 223-228.Search in Google Scholar

[10] Nandini K.K., Muralidhara, Peltier based cabinet cooling system using heat pipe and liquid based heat sink, Nat. Conf. Challenges Res. & Technol. in the Coming Decades, 2013, 1-5.10.1049/cp.2013.2536Search in Google Scholar

[11] Zhang H.Y., Mui Y.C., Tarin M., Analysis of thermoelectric cooler performance for high power electronic packages, Appl. Thermal Eng., 2010, 30, 561-568.10.1016/j.applthermaleng.2009.10.020Search in Google Scholar

[12] Bell L.E., Cooling, heating, generating power, and recovering waste heat with thermoelectric systems, Sci., 2008, 321, 1457-1461.10.1126/science.1158899Search in Google Scholar PubMed

[13] Gou X., Xiao H., Yang S., Modeling, experimental study and optimization on low-temperature waste heat thermoelectric generator system, Appl. Energy, 2010, 87, 3131-3136.10.1016/j.apenergy.2010.02.013Search in Google Scholar

[14] Takahashi K., Wen S., Sanada M., Deng M., Nonlinear cooling control for a Peltier actuated aluminum plate thermal system by considering radiation heat transfer, Int. Conf. Adv. Mechatronic Syst., 2012, 18-23.10.1109/ICAMechS.2013.6681839Search in Google Scholar

[15] Aranguren P., Astrain D., Perez M.G., Computational and experimental study of a complete heat dissipation system using water as heat carrier placed on a thermoelectric generator, Energy, 2014, 346-358.10.1016/j.energy.2014.06.094Search in Google Scholar

[16] Xuan X.C., Optimum design of a thermoelectric device, Semiconductor Sci. & Technol., 2002, 17, 114-119.10.1088/0268-1242/17/2/304Search in Google Scholar

[17] Riffat S.B., Ma X., Improving the coeflcient of performance of thermoelectric cooling systems: a review, Int. J. Energy Res., 2004, 28, 753-768.10.1002/er.991Search in Google Scholar

[18] Lineykin S., Ben-Yaakov S., Modeling and Analysis of Thermoelectric Modules, IEEE Trans. Ind. Appl., 2007, 43, 505-512.10.1109/APEC.2005.1453336Search in Google Scholar

[19] Rabari R., Mahmud S., Dutta A., Biglarbegian M., Effect of convection heat transfer on performance of waste heat thermoelectric generator, Heat Transfer Eng., 2015, 36, 1458-1471.10.1080/01457632.2015.1010925Search in Google Scholar

[20] Hsiao Y.Y., Chang W.C., Chen S.L., A mathematic model of thermoelectric module with applications on waste heat recovery from automobile engine, Energy, 2010, 35, 1447-1454.10.1016/j.energy.2009.11.030Search in Google Scholar

[21] Hodes M., On one-dimensional analysis of thermoelectric modules (TEMs), IEEE Trans. Compon. Packag. Technol., 2005, 28, 218-229.10.1109/TCAPT.2005.848532Search in Google Scholar

Received: 2016-10-13
Accepted: 2016-11-14
Published Online: 2017-3-12

© 2017 E. Fang et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Articles in the same Issue

  1. Regular Articles
  2. Analysis of a New Fractional Model for Damped Bergers’ Equation
  3. Regular Articles
  4. Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem
  5. Regular Articles
  6. Semi- analytic numerical method for solution of time-space fractional heat and wave type equations with variable coefficients
  7. Regular Articles
  8. Investigation of a curve using Frenet frame in the lightlike cone
  9. Regular Articles
  10. Construction of complex networks from time series based on the cross correlation interval
  11. Regular Articles
  12. Nonlinear Schrödinger approach to European option pricing
  13. Regular Articles
  14. A modified cubic B-spline differential quadrature method for three-dimensional non-linear diffusion equations
  15. Regular Articles
  16. A new miniaturized negative-index meta-atom for tri-band applications
  17. Regular Articles
  18. Seismic stability of the survey areas of potential sites for the deep geological repository of the spent nuclear fuel
  19. Regular Articles
  20. Distributed containment control of heterogeneous fractional-order multi-agent systems with communication delays
  21. Regular Articles
  22. Sensitivity analysis and economic optimization studies of inverted five-spot gas cycling in gas condensate reservoir
  23. Regular Articles
  24. Quantum mechanics with geometric constraints of Friedmann type
  25. Regular Articles
  26. Modeling and Simulation for an 8 kW Three-Phase Grid-Connected Photo-Voltaic Power System
  27. Regular Articles
  28. Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers
  29. Regular Articles
  30. Analysis of Drude model using fractional derivatives without singular kernels
  31. Regular Articles
  32. An unsteady MHD Maxwell nanofluid flow with convective boundary conditions using spectral local linearization method
  33. Regular Articles
  34. New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method
  35. Regular Articles
  36. Quantum mechanical calculation of electron spin
  37. Regular Articles
  38. CO2 capture by polymeric membranes composed of hyper-branched polymers with dense poly(oxyethylene) comb and poly(amidoamine)
  39. Regular Articles
  40. Chain on a cone
  41. Regular Articles
  42. Multi-task feature learning by using trace norm regularization
  43. Regular Articles
  44. Superluminal tunneling of a relativistic half-integer spin particle through a potential barrier
  45. Regular Articles
  46. Neutrosophic triplet normed space
  47. Regular Articles
  48. Lie algebraic discussion for affinity based information diffusion in social networks
  49. Regular Articles
  50. Radiation dose and cancer risk estimates in helical CT for pulmonary tuberculosis infections
  51. Regular Articles
  52. A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives
  53. Regular Articles
  54. Some new remarks on MHD Jeffery-Hamel fluid flow problem
  55. Regular Articles
  56. Numerical investigation of magnetohydrodynamic slip flow of power-law nanofluid with temperature dependent viscosity and thermal conductivity over a permeable surface
  57. Regular Articles
  58. Charge conservation in a gravitational field in the scalar ether theory
  59. Regular Articles
  60. Measurement problem and local hidden variables with entangled photons
  61. Regular Articles
  62. Compression of hyper-spectral images using an accelerated nonnegative tensor decomposition
  63. Regular Articles
  64. Fabrication and application of coaxial polyvinyl alcohol/chitosan nanofiber membranes
  65. Regular Articles
  66. Calculating degree-based topological indices of dominating David derived networks
  67. Regular Articles
  68. The structure and conductivity of polyelectrolyte based on MEH-PPV and potassium iodide (KI) for dye-sensitized solar cells
  69. Regular Articles
  70. Chiral symmetry restoration and the critical end point in QCD
  71. Regular Articles
  72. Numerical solution for fractional Bratu’s initial value problem
  73. Regular Articles
  74. Structure and optical properties of TiO2 thin films deposited by ALD method
  75. Regular Articles
  76. Quadruple multi-wavelength conversion for access network scalability based on cross-phase modulation in an SOA-MZI
  77. Regular Articles
  78. Application of ANNs approach for wave-like and heat-like equations
  79. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  80. Study on node importance evaluation of the high-speed passenger traffic complex network based on the Structural Hole Theory
  81. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  82. A mathematical/physics model to measure the role of information and communication technology in some economies: the Chinese case
  83. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  84. Numerical modeling of the thermoelectric cooler with a complementary equation for heat circulation in air gaps
  85. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  86. On the libration collinear points in the restricted three – body problem
  87. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  88. Research on Critical Nodes Algorithm in Social Complex Networks
  89. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  90. A simulation based research on chance constrained programming in robust facility location problem
  91. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  92. A mathematical/physics carbon emission reduction strategy for building supply chain network based on carbon tax policy
  93. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  94. Mathematical analysis of the impact mechanism of information platform on agro-product supply chain and agro-product competitiveness
  95. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  96. A real negative selection algorithm with evolutionary preference for anomaly detection
  97. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  98. A privacy-preserving parallel and homomorphic encryption scheme
  99. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  100. Random walk-based similarity measure method for patterns in complex object
  101. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  102. A Mathematical Study of Accessibility and Cohesion Degree in a High-Speed Rail Station Connected to an Urban Bus Transport Network
  103. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  104. Design and Simulation of the Integrated Navigation System based on Extended Kalman Filter
  105. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  106. Oil exploration oriented multi-sensor image fusion algorithm
  107. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  108. Analysis of Product Distribution Strategy in Digital Publishing Industry Based on Game-Theory
  109. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  110. Expanded Study on the accumulation effect of tourism under the constraint of structure
  111. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  112. Unstructured P2P Network Load Balance Strategy Based on Multilevel Partitioning of Hypergraph
  113. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  114. Research on the method of information system risk state estimation based on clustering particle filter
  115. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  116. Demand forecasting and information platform in tourism
  117. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  118. Physical-chemical properties studying of molecular structures via topological index calculating
  119. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  120. Local kernel nonparametric discriminant analysis for adaptive extraction of complex structures
  121. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  122. City traffic flow breakdown prediction based on fuzzy rough set
  123. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  124. Conservation laws for a strongly damped wave equation
  125. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  126. Blending type approximation by Stancu-Kantorovich operators based on Pólya-Eggenberger distribution
  127. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  128. Computing the Ediz eccentric connectivity index of discrete dynamic structures
  129. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  130. A discrete epidemic model for bovine Babesiosis disease and tick populations
  131. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  132. Study on maintaining formations during satellite formation flying based on SDRE and LQR
  133. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  134. Relationship between solitary pulmonary nodule lung cancer and CT image features based on gradual clustering
  135. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  136. A novel fast target tracking method for UAV aerial image
  137. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  138. Fuzzy comprehensive evaluation model of interuniversity collaborative learning based on network
  139. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  140. Conservation laws, classical symmetries and exact solutions of the generalized KdV-Burgers-Kuramoto equation
  141. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  142. After notes on self-similarity exponent for fractal structures
  143. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  144. Excitation probability and effective temperature in the stationary regime of conductivity for Coulomb Glasses
  145. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  146. Comparisons of feature extraction algorithm based on unmanned aerial vehicle image
  147. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  148. Research on identification method of heavy vehicle rollover based on hidden Markov model
  149. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  150. Classifying BCI signals from novice users with extreme learning machine
  151. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  152. Topics on data transmission problem in software definition network
  153. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  154. Statistical inferences with jointly type-II censored samples from two Pareto distributions
  155. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  156. Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme
  157. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  158. Analysis on trust influencing factors and trust model from multiple perspectives of online Auction
  159. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  160. Coupling of two-phase flow in fractured-vuggy reservoir with filling medium
  161. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  162. Production decline type curves analysis of a finite conductivity fractured well in coalbed methane reservoirs
  163. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  164. Flow Characteristic and Heat Transfer for Non-Newtonian Nanofluid in Rectangular Microchannels with Teardrop Dimples/Protrusions
  165. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  166. The size prediction of potential inclusions embedded in the sub-surface of fused silica by damage morphology
  167. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  168. Research on carbonate reservoir interwell connectivity based on a modified diffusivity filter model
  169. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  170. The method of the spatial locating of macroscopic throats based-on the inversion of dynamic interwell connectivity
  171. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  172. Unsteady mixed convection flow through a permeable stretching flat surface with partial slip effects through MHD nanofluid using spectral relaxation method
  173. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  174. A volumetric ablation model of EPDM considering complex physicochemical process in porous structure of char layer
  175. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  176. Numerical simulation on ferrofluid flow in fractured porous media based on discrete-fracture model
  177. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  178. Macroscopic lattice Boltzmann model for heat and moisture transfer process with phase transformation in unsaturated porous media during freezing process
  179. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  180. Modelling of intermittent microwave convective drying: parameter sensitivity
  181. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  182. Simulating gas-water relative permeabilities for nanoscale porous media with interfacial effects
  183. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  184. Simulation of counter-current imbibition in water-wet fractured reservoirs based on discrete-fracture model
  185. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  186. Investigation effect of wettability and heterogeneity in water flooding and on microscopic residual oil distribution in tight sandstone cores with NMR technique
  187. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  188. Analytical modeling of coupled flow and geomechanics for vertical fractured well in tight gas reservoirs
  189. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  190. Special Issue: Ever New "Loopholes" in Bell’s Argument and Experimental Tests
  191. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  192. The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′s assuming merely that they exist
  193. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  194. Erratum to: The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′s assuming merely that they exist
  195. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  196. Rhetoric, logic, and experiment in the quantum nonlocality debate
  197. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  198. What If Quantum Theory Violates All Mathematics?
  199. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  200. Relativity, anomalies and objectivity loophole in recent tests of local realism
  201. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  202. The photon identification loophole in EPRB experiments: computer models with single-wing selection
  203. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  204. Bohr against Bell: complementarity versus nonlocality
  205. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  206. Is Einsteinian no-signalling violated in Bell tests?
  207. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  208. Bell’s “Theorem”: loopholes vs. conceptual flaws
  209. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  210. Nonrecurrence and Bell-like inequalities
  211. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  212. Three-dimensional computer models of electrospinning systems
  213. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  214. Electric field computation and measurements in the electroporation of inhomogeneous samples
  215. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  216. Modelling of magnetostriction of transformer magnetic core for vibration analysis
  217. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  218. Comparison of the fractional power motor with cores made of various magnetic materials
  219. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  220. Dynamics of the line-start reluctance motor with rotor made of SMC material
  221. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  222. Inhomogeneous dielectrics: conformal mapping and finite-element models
  223. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  224. Topology optimization of induction heating model using sequential linear programming based on move limit with adaptive relaxation
  225. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  226. Detection of inter-turn short-circuit at start-up of induction machine based on torque analysis
  227. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  228. Current superimposition variable flux reluctance motor with 8 salient poles
  229. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  230. Modelling axial vibration in windings of power transformers
  231. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  232. Field analysis & eddy current losses calculation in five-phase tubular actuator
  233. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  234. Hybrid excited claw pole generator with skewed and non-skewed permanent magnets
  235. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  236. Electromagnetic phenomena analysis in brushless DC motor with speed control using PWM method
  237. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  238. Field-circuit analysis and measurements of a single-phase self-excited induction generator
  239. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  240. A comparative analysis between classical and modified approach of description of the electrical machine windings by means of T0 method
  241. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  242. Field-based optimal-design of an electric motor: a new sensitivity formulation
  243. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  244. Application of the parametric proper generalized decomposition to the frequency-dependent calculation of the impedance of an AC line with rectangular conductors
  245. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  246. Virtual reality as a new trend in mechanical and electrical engineering education
  247. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  248. Holonomicity analysis of electromechanical systems
  249. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  250. An accurate reactive power control study in virtual flux droop control
  251. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  252. Localized probability of improvement for kriging based multi-objective optimization
  253. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  254. Research of influence of open-winding faults on properties of brushless permanent magnets motor
  255. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  256. Optimal design of the rotor geometry of line-start permanent magnet synchronous motor using the bat algorithm
  257. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  258. Model of depositing layer on cylindrical surface produced by induction-assisted laser cladding process
  259. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  260. Detection of inter-turn faults in transformer winding using the capacitor discharge method
  261. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  262. A novel hybrid genetic algorithm for optimal design of IPM machines for electric vehicle
  263. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  264. Lamination effects on a 3D model of the magnetic core of power transformers
  265. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  266. Detection of vertical disparity in three-dimensional visualizations
  267. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  268. Calculations of magnetic field in dynamo sheets taking into account their texture
  269. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  270. 3-dimensional computer model of electrospinning multicapillary unit used for electrostatic field analysis
  271. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  272. Optimization of wearable microwave antenna with simplified electromagnetic model of the human body
  273. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  274. Induction heating process of ferromagnetic filled carbon nanotubes based on 3-D model
  275. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  276. Speed control of an induction motor by 6-switched 3-level inverter
https://doi.org/10.1515/phys-2017-0004
Keywords for this article
Thermoelectric coolers; Thermoelectric generators; Peltier effect; Refrigeration performance
Creative Commons
BY-NC-ND 3.0

Articles in the same Issue

  1. Regular Articles
  2. Analysis of a New Fractional Model for Damped Bergers’ Equation
  3. Regular Articles
  4. Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem
  5. Regular Articles
  6. Semi- analytic numerical method for solution of time-space fractional heat and wave type equations with variable coefficients
  7. Regular Articles
  8. Investigation of a curve using Frenet frame in the lightlike cone
  9. Regular Articles
  10. Construction of complex networks from time series based on the cross correlation interval
  11. Regular Articles
  12. Nonlinear Schrödinger approach to European option pricing
  13. Regular Articles
  14. A modified cubic B-spline differential quadrature method for three-dimensional non-linear diffusion equations
  15. Regular Articles
  16. A new miniaturized negative-index meta-atom for tri-band applications
  17. Regular Articles
  18. Seismic stability of the survey areas of potential sites for the deep geological repository of the spent nuclear fuel
  19. Regular Articles
  20. Distributed containment control of heterogeneous fractional-order multi-agent systems with communication delays
  21. Regular Articles
  22. Sensitivity analysis and economic optimization studies of inverted five-spot gas cycling in gas condensate reservoir
  23. Regular Articles
  24. Quantum mechanics with geometric constraints of Friedmann type
  25. Regular Articles
  26. Modeling and Simulation for an 8 kW Three-Phase Grid-Connected Photo-Voltaic Power System
  27. Regular Articles
  28. Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers
  29. Regular Articles
  30. Analysis of Drude model using fractional derivatives without singular kernels
  31. Regular Articles
  32. An unsteady MHD Maxwell nanofluid flow with convective boundary conditions using spectral local linearization method
  33. Regular Articles
  34. New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method
  35. Regular Articles
  36. Quantum mechanical calculation of electron spin
  37. Regular Articles
  38. CO2 capture by polymeric membranes composed of hyper-branched polymers with dense poly(oxyethylene) comb and poly(amidoamine)
  39. Regular Articles
  40. Chain on a cone
  41. Regular Articles
  42. Multi-task feature learning by using trace norm regularization
  43. Regular Articles
  44. Superluminal tunneling of a relativistic half-integer spin particle through a potential barrier
  45. Regular Articles
  46. Neutrosophic triplet normed space
  47. Regular Articles
  48. Lie algebraic discussion for affinity based information diffusion in social networks
  49. Regular Articles
  50. Radiation dose and cancer risk estimates in helical CT for pulmonary tuberculosis infections
  51. Regular Articles
  52. A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives
  53. Regular Articles
  54. Some new remarks on MHD Jeffery-Hamel fluid flow problem
  55. Regular Articles
  56. Numerical investigation of magnetohydrodynamic slip flow of power-law nanofluid with temperature dependent viscosity and thermal conductivity over a permeable surface
  57. Regular Articles
  58. Charge conservation in a gravitational field in the scalar ether theory
  59. Regular Articles
  60. Measurement problem and local hidden variables with entangled photons
  61. Regular Articles
  62. Compression of hyper-spectral images using an accelerated nonnegative tensor decomposition
  63. Regular Articles
  64. Fabrication and application of coaxial polyvinyl alcohol/chitosan nanofiber membranes
  65. Regular Articles
  66. Calculating degree-based topological indices of dominating David derived networks
  67. Regular Articles
  68. The structure and conductivity of polyelectrolyte based on MEH-PPV and potassium iodide (KI) for dye-sensitized solar cells
  69. Regular Articles
  70. Chiral symmetry restoration and the critical end point in QCD
  71. Regular Articles
  72. Numerical solution for fractional Bratu’s initial value problem
  73. Regular Articles
  74. Structure and optical properties of TiO2 thin films deposited by ALD method
  75. Regular Articles
  76. Quadruple multi-wavelength conversion for access network scalability based on cross-phase modulation in an SOA-MZI
  77. Regular Articles
  78. Application of ANNs approach for wave-like and heat-like equations
  79. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  80. Study on node importance evaluation of the high-speed passenger traffic complex network based on the Structural Hole Theory
  81. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  82. A mathematical/physics model to measure the role of information and communication technology in some economies: the Chinese case
  83. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  84. Numerical modeling of the thermoelectric cooler with a complementary equation for heat circulation in air gaps
  85. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  86. On the libration collinear points in the restricted three – body problem
  87. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  88. Research on Critical Nodes Algorithm in Social Complex Networks
  89. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  90. A simulation based research on chance constrained programming in robust facility location problem
  91. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  92. A mathematical/physics carbon emission reduction strategy for building supply chain network based on carbon tax policy
  93. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  94. Mathematical analysis of the impact mechanism of information platform on agro-product supply chain and agro-product competitiveness
  95. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  96. A real negative selection algorithm with evolutionary preference for anomaly detection
  97. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  98. A privacy-preserving parallel and homomorphic encryption scheme
  99. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  100. Random walk-based similarity measure method for patterns in complex object
  101. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  102. A Mathematical Study of Accessibility and Cohesion Degree in a High-Speed Rail Station Connected to an Urban Bus Transport Network
  103. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  104. Design and Simulation of the Integrated Navigation System based on Extended Kalman Filter
  105. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  106. Oil exploration oriented multi-sensor image fusion algorithm
  107. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  108. Analysis of Product Distribution Strategy in Digital Publishing Industry Based on Game-Theory
  109. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  110. Expanded Study on the accumulation effect of tourism under the constraint of structure
  111. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  112. Unstructured P2P Network Load Balance Strategy Based on Multilevel Partitioning of Hypergraph
  113. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  114. Research on the method of information system risk state estimation based on clustering particle filter
  115. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  116. Demand forecasting and information platform in tourism
  117. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  118. Physical-chemical properties studying of molecular structures via topological index calculating
  119. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  120. Local kernel nonparametric discriminant analysis for adaptive extraction of complex structures
  121. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  122. City traffic flow breakdown prediction based on fuzzy rough set
  123. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  124. Conservation laws for a strongly damped wave equation
  125. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  126. Blending type approximation by Stancu-Kantorovich operators based on Pólya-Eggenberger distribution
  127. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  128. Computing the Ediz eccentric connectivity index of discrete dynamic structures
  129. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  130. A discrete epidemic model for bovine Babesiosis disease and tick populations
  131. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  132. Study on maintaining formations during satellite formation flying based on SDRE and LQR
  133. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  134. Relationship between solitary pulmonary nodule lung cancer and CT image features based on gradual clustering
  135. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  136. A novel fast target tracking method for UAV aerial image
  137. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  138. Fuzzy comprehensive evaluation model of interuniversity collaborative learning based on network
  139. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  140. Conservation laws, classical symmetries and exact solutions of the generalized KdV-Burgers-Kuramoto equation
  141. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  142. After notes on self-similarity exponent for fractal structures
  143. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  144. Excitation probability and effective temperature in the stationary regime of conductivity for Coulomb Glasses
  145. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  146. Comparisons of feature extraction algorithm based on unmanned aerial vehicle image
  147. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  148. Research on identification method of heavy vehicle rollover based on hidden Markov model
  149. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  150. Classifying BCI signals from novice users with extreme learning machine
  151. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  152. Topics on data transmission problem in software definition network
  153. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  154. Statistical inferences with jointly type-II censored samples from two Pareto distributions
  155. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  156. Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme
  157. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  158. Analysis on trust influencing factors and trust model from multiple perspectives of online Auction
  159. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  160. Coupling of two-phase flow in fractured-vuggy reservoir with filling medium
  161. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  162. Production decline type curves analysis of a finite conductivity fractured well in coalbed methane reservoirs
  163. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  164. Flow Characteristic and Heat Transfer for Non-Newtonian Nanofluid in Rectangular Microchannels with Teardrop Dimples/Protrusions
  165. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  166. The size prediction of potential inclusions embedded in the sub-surface of fused silica by damage morphology
  167. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  168. Research on carbonate reservoir interwell connectivity based on a modified diffusivity filter model
  169. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  170. The method of the spatial locating of macroscopic throats based-on the inversion of dynamic interwell connectivity
  171. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  172. Unsteady mixed convection flow through a permeable stretching flat surface with partial slip effects through MHD nanofluid using spectral relaxation method
  173. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  174. A volumetric ablation model of EPDM considering complex physicochemical process in porous structure of char layer
  175. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  176. Numerical simulation on ferrofluid flow in fractured porous media based on discrete-fracture model
  177. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  178. Macroscopic lattice Boltzmann model for heat and moisture transfer process with phase transformation in unsaturated porous media during freezing process
  179. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  180. Modelling of intermittent microwave convective drying: parameter sensitivity
  181. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  182. Simulating gas-water relative permeabilities for nanoscale porous media with interfacial effects
  183. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  184. Simulation of counter-current imbibition in water-wet fractured reservoirs based on discrete-fracture model
  185. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  186. Investigation effect of wettability and heterogeneity in water flooding and on microscopic residual oil distribution in tight sandstone cores with NMR technique
  187. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  188. Analytical modeling of coupled flow and geomechanics for vertical fractured well in tight gas reservoirs
  189. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  190. Special Issue: Ever New "Loopholes" in Bell’s Argument and Experimental Tests
  191. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  192. The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′s assuming merely that they exist
  193. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  194. Erratum to: The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′s assuming merely that they exist
  195. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  196. Rhetoric, logic, and experiment in the quantum nonlocality debate
  197. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  198. What If Quantum Theory Violates All Mathematics?
  199. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  200. Relativity, anomalies and objectivity loophole in recent tests of local realism
  201. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  202. The photon identification loophole in EPRB experiments: computer models with single-wing selection
  203. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  204. Bohr against Bell: complementarity versus nonlocality
  205. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  206. Is Einsteinian no-signalling violated in Bell tests?
  207. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  208. Bell’s “Theorem”: loopholes vs. conceptual flaws
  209. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  210. Nonrecurrence and Bell-like inequalities
  211. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  212. Three-dimensional computer models of electrospinning systems
  213. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  214. Electric field computation and measurements in the electroporation of inhomogeneous samples
  215. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  216. Modelling of magnetostriction of transformer magnetic core for vibration analysis
  217. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  218. Comparison of the fractional power motor with cores made of various magnetic materials
  219. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  220. Dynamics of the line-start reluctance motor with rotor made of SMC material
  221. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  222. Inhomogeneous dielectrics: conformal mapping and finite-element models
  223. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  224. Topology optimization of induction heating model using sequential linear programming based on move limit with adaptive relaxation
  225. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  226. Detection of inter-turn short-circuit at start-up of induction machine based on torque analysis
  227. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  228. Current superimposition variable flux reluctance motor with 8 salient poles
  229. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  230. Modelling axial vibration in windings of power transformers
  231. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  232. Field analysis & eddy current losses calculation in five-phase tubular actuator
  233. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  234. Hybrid excited claw pole generator with skewed and non-skewed permanent magnets
  235. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  236. Electromagnetic phenomena analysis in brushless DC motor with speed control using PWM method
  237. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  238. Field-circuit analysis and measurements of a single-phase self-excited induction generator
  239. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  240. A comparative analysis between classical and modified approach of description of the electrical machine windings by means of T0 method
  241. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  242. Field-based optimal-design of an electric motor: a new sensitivity formulation
  243. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  244. Application of the parametric proper generalized decomposition to the frequency-dependent calculation of the impedance of an AC line with rectangular conductors
  245. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  246. Virtual reality as a new trend in mechanical and electrical engineering education
  247. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  248. Holonomicity analysis of electromechanical systems
  249. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  250. An accurate reactive power control study in virtual flux droop control
  251. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  252. Localized probability of improvement for kriging based multi-objective optimization
  253. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  254. Research of influence of open-winding faults on properties of brushless permanent magnets motor
  255. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  256. Optimal design of the rotor geometry of line-start permanent magnet synchronous motor using the bat algorithm
  257. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  258. Model of depositing layer on cylindrical surface produced by induction-assisted laser cladding process
  259. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  260. Detection of inter-turn faults in transformer winding using the capacitor discharge method
  261. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  262. A novel hybrid genetic algorithm for optimal design of IPM machines for electric vehicle
  263. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  264. Lamination effects on a 3D model of the magnetic core of power transformers
  265. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  266. Detection of vertical disparity in three-dimensional visualizations
  267. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  268. Calculations of magnetic field in dynamo sheets taking into account their texture
  269. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  270. 3-dimensional computer model of electrospinning multicapillary unit used for electrostatic field analysis
  271. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  272. Optimization of wearable microwave antenna with simplified electromagnetic model of the human body
  273. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  274. Induction heating process of ferromagnetic filled carbon nanotubes based on 3-D model
  275. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  276. Speed control of an induction motor by 6-switched 3-level inverter
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 10.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/phys-2017-0004/html
Scroll to top button