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Numerical analysis on the dynamic response of a plate-and-frame membrane humidifier for PEMFC vehicles under various operating conditions

  • Sungho Yun , Dowon Cha , Kang Sub Song , Seong Ho Hong , Sang Hun Lee , Wonseok Yang and Yongchan Kim EMAIL logo
Published/Copyright: October 25, 2018
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Open Physics
From the journal Open Physics Volume 16 Issue 1

Abstract

PEMFC needs to be maintained at an appropriate temperature and humidity in a rapidly changing environment for automobile applications. In this study, a pseudo-multi-dimensional dynamic model for predicting the heat and mass transfer performance of a plate-and-frame membrane humidifier for PEMFC vehicles is developed. Based on the developed model, the variations in the temperature and relative humidity at the dry air outlet are investigated according to the air flow acceleration. Moreover, the dynamic response is analyzed as a function of the amplitude and period of the sinusoidal air flow rate at actual operating conditions. The effects of heat transfer on the dynamic response are more dominant than those of mass transfer. The settling time of the temperature and relative humidity at the dry air outlet decrease with the increase in air flow acceleration. In addition, the variations in the temperature and relative humidity at the dry air outlet increase with the increases in the amplitude and period of the sinusoidal air flow rate.

Keywords: Dynamic response; Heat and mass transfer; Numerical model; PEMFC; Plate-and-frame membrane humidifier
PACS: 44.05.+e; 44.27.+g; 88.30.gg; 88.30.pd

Nomenclature

Aamp amplitude (g s−1)

Afr fractional area (m2)

av water activity (-)

Bperi period (s)

C heat capacity ratio (J s−1K−1)

cp heat capacity (J kg−1K−1)

Dg water diffusivity in the gas phase (m2 s−1)

Dh hydraulic diameter (m)

Dw water diffusivity (kg m−1s−1)

h convective heat transfer coefficient (W m−2K−1)

hm convective mass transfer coefficient (kg m−2s−1)

k thermal conductivity (W m−1K−1)

Le Lewis number (-)

m˙ mass flow rate (kg s−1)

Nu Nusselt number (-)

P pressure (bar)

U overall heat transfer coefficient (W m−2K−1)

V velocity (m s−1)

S perimeter (m)

Sh Sherwood number (-)

Greek symbols

Δ difference (-)

δ thickness (m)

λ water content (-)

ρ density (kg m−3)

φ relative humidity (%)

Subscripts

d dry air

global global value

in inlet

m membrane

max maximum value

min minimum value

out outlet

p plate

sat saturation

v vapor

w wet air

Acronyms

MFF mass flow rate factor

PEMFC proton exchange membrane fuel cells

1 Introduction

Proton exchange membrane fuel cells (PEMFCs) can be utilized in the power supply for portable systems, stationary systems, vehicles, spacecraft, and other special applications owing to their high power density, high efficiency, and modular nature [1, 2]. In particular, owing to their lower operating temperature, higher power density, and shorter start-up time, various studies on PEMFC vehicles are occurring in major automobile companies [3, 4, 5]. However, the PEMFC need to be maintained at an appropriate temperature and humidity in the rapidly changing environment associated with automobile applications [6].

Studies involving various types of humidifiers have been conducted in order to control the temperature and relative humidity of the supply air [7, 8, 9, 10]. Extensive studies have been also conducted on bubbling, water spray, enthalpy wheel, and membrane humidifiers. From these types, membrane humidifiers are the most suitable for PEMFC vehicles due to their fast response and simplicity. Recently, case studies have been carried out to apply membrane humidifiers to PEMFC systems [11, 12, 13, 14]. Membrane humidifiers are categorized as either shell-and-tube or plate-and-frame membrane humidifiers depending on the shape [15, 16]. Park [17] presented a dynamic model of a shell-and-tube membrane humidifier. Kang [18] investigated the performance of a shell-and-tube membrane humidifier for PEMFC vehicles. However, the shell-and-tube membrane humidifier has the disadvantages of a bulky volume and difficulty in mass production. Accordingly, studies on the plate-and-frame membrane humidifier are underway to overcome these drawbacks.

Zhang [19] proposed an effectiveness-correlation model for a plate-and-frame membrane humidifier, in order to analyze the heat and mass transfer processes in an enthalpy exchanger. Several studies verified the effectiveness-correlation model for the enthalpy exchanger [20, 21, 22]. Kadylak [23] discussed limitations on the application of the effectiveness-correlation model to the plate-and-frame membrane humidifier. Kadylak [24] also experimentally validated the developed effectiveness-correlation model with a plate-and-frame membrane. However, the effectiveness-correlation model showed some limitations for analyzing the dynamic response of a plate-and-frame membrane humidifier. Accordingly, there is a need to develop a novel model for predicting the dynamic response of a plate-and-frame membrane humidifier for PEMFC vehicles under actual operating conditions. In particular, the temperature variations due to air entering the plate-and-frame membrane humidifier according to the air flow rate need to be considered.

Numerical and experimental studies analyzing the phenomena in the plate-and-frame membrane humidifier have also been carried out. Yu [25] proposed a static model for a counter flow plate-and-frame membrane humidifier. Ahluwalia [26] conducted static and dynamic tests on a plate-and-frame membrane humidifier. Even though these studies developed a finite-difference model, the heat transfer, which is a main dynamic mechanism in the plate-and-frame humidifier, was not considered in the plate. Moreover, in the existing studies, a multi-dimensional dynamic model was not applied for a plate-and-frame membrane humidifier, which has multi-dimensional structures stacked with multiple membranes and plates for PEMFC vehicles [17, 27].

In this study, a pseudo-multi-dimensional dynamic model was developed for predicting the dynamic response of a plate-and-frame membrane humidifier with a plate domain. This model incorporated one-dimensional heat transfer in the plate, one-dimensional heat and mass transfer in the membrane, and one-dimensional thermo-fluid channel in the plate-and-frame membrane humidifier. Based on the proposed model, the dynamic response of the plate-and-frame membrane humidifier for PEMFC vehicleswas analyzed under various operating conditions. The variations in the temperature and relative humidity at the dry air outlet were investigated in accordance with air flow acceleration. The temperature changes in the membrane and plate were also examined to evaluate the overshoot and settling time. Moreover, the dynamic response of the plate-and-frame membrane humidifier was analyzed as a function of the amplitude and period of the sinusoidal air flow rate under actual operating conditions.

2 Numerical model

As shown in Figure 1, the plate-and-frame membrane humidifier has multiple membranes and plates. It is a heat and mass exchanger with a water-permeable polymer membrane installed in between dry and wet air. Table 1 shows geometric configurations of the computational model and humidifier. The channel width, channel height, and channel length were determined from the tested plate-and-frame membrane humidifier in the previous study [25]. In addition, the number of channels in the plate and number of plates were designed to satisfy the rated capacity of 100 kW in a PEMFC system. Figure 2 shows the computational domain of the plate-and-frame membrane humidifier. In the numerical analysis, the wet air and dry air were discretized in their individual flow directions.

Figure 1 Schematic of the plate-and-frame membrane humidifier
Figure 1

Schematic of the plate-and-frame membrane humidifier

Figure 2 Computational domain of the plate-and-frame membrane humidifier
Figure 2

Computational domain of the plate-and-frame membrane humidifier

Table 1

Geometric parameters of the plate-and-frame membrane humidifier

ParametersValue
Channel width0.003 m
Channel height0.003 m
Channel length0.322 m
Number of channels in the plate34
Number of plates90
Plate thickness0.001 m
Membrane thickness (Nafion@)5.1×10−5 m

The numerical model has been developed based on the following assumptions [15, 18]: (1) the flow in the air channel is incompressible and laminar; (2) phase change is ignored; (3) physical properties are constant along the length of the humidifier; (4) the velocity is constant in the axial direction and the velocity profile is fully developed; and (5) the vapor diffusion in the membrane occurs only in the normal direction. Algebraic heat and mass transfer equations were solved simultaneously by using the Gauss-Seidel method based on an upwind finite-difference scheme in Visual Fortran 6.0.

2.1 Heat transfer

The plate-and-frame membrane humidifier consists of the wet air, dry air, membrane, and plate domains. The wet air domain contains humid air flow discharged from the PEMFC, whereas the dry air domain includes a dry air flow path in which the ambient air flows into an air humidifier using an air blower. In these domains, the forced convective heat transfer is dominant. On the other hand, the conduction heat transfer is dominant in the plate and membrane domains.

The energy balance equations for the wet air, membrane, dry air, and plate domains in the plate-and-frame membrane humidifier are expressed by Eqs. (1), 2, 3(4) [28, 29], respectively:

(1)CwdTwdx−UwSw(Tw−Tm)−UdSd(Tp−Td)=−CwVw∂Tw∂t
(2)UdSd(Tm−Td)−UwSw(Tw−Tm)=−cp,mρmδmSm∂Tm∂t
(3)CddTddx+UwSw(Tw−Tm)+UdSd(Tm−Td)=−CdVd∂Td∂t
(4)UdSd(Tp−Td)−UwSw(Tw−Tp)=−cp,pρpδpSp∂Tp∂t

where U is the overall heat transfer coefficient, S is the perimeter, and δ is the thickness. The heat capacity ratio (C) is given as:

(5)Cw=cp,wρwAfr,wVw
(6)Cd=cp,dρdAfr,dVd

As given in Eq. (7), the convective heat transfer coefficient is constant in the fully developed laminar flow [28]:

(7)Nu=3.61
(8)Nu=hDhk

where Dh is the hydraulic diameter and k is the thermal conductivity.

2.2 Mass transfer

The mass balance equations for the wet air, membrane, and dry air domains are given by Eqs. (9), 10, (11), respectively:

(9)Vwdωwdx−hM,wSw(ωw−ωmw)=−∂ωw∂t
(10)∂∂zDw∂ωm∂z=dωmdt
(11)Vddωddx+hM,dSd(ωmd−ωd)=−∂ωd∂t

where ω is the absolute humidity and hM is the mass transfer coefficient. In addition, the diffusion coefficient (Dw) is given as [30]:

(12)Dw=3.1⋅10−3λ(−1+e−2436/T):0<λ≤3
(13)Dw=4.17⋅10−4λ(1+161e−λ)e−2436/T:3≤λ<17

As given in Eqs. (14) and (15), the water content (λ) is determined by the water activity (av) [30]:

(14)λ=0.3+10.8⋅av−16⋅av2+14.1⋅av3
(15)av=xvppsat,v

As given in Eqs. (16) and (17), the mass transfer coefficient (hM) can be obtained from the relationship between Sherwood number and Nusselt number [15]:

(16)Sh=hMDhDg
(17)Sh=NuLe−1/3

where Lewis number represents the ratio of the thermal diffusivity to the mass diffusivity.

The relationship between the relative humidity and the absolute humidity is estimated by Eq. (18).

(18)φ=ωP(0.622+ω)Psat,v

As given in Eq. (19), the saturation vapor pressure is calculated by Hyland-Wexler equation [31]:

(19)Psat,v=exp∑i=−13hiTi+h4ln⁡T

where h−1 = –0.580 × 104, h0 = 0.139 × 10, h1 = –0.486 × 10−1, h2 = 0.418 × 10−4, h3 = –0.145 × 10−7, and h4 = 0.655, which are valid for temperatures between 0∘C and 200∘C.

2.3 Air blower

As shown in Figure 3, the air supply system for PEMFC vehicles is composed of an air blower and a humidifier. The numerical model considers the temperature and pressure changes of the air when it passes through the air blower. The pressure ratio is determined by the blower map, with the air flow mass flow rate factor (MFF) as given in Eq. (20) [32, 33]:

Figure 3 Schematic of the air supply system for PEMFC vehicles
Figure 3

Schematic of the air supply system for PEMFC vehicles

(20)MFF=m˙Tair,ambientPair,ambient

The temperature at the dry air inlet is calculated by Eq. (21):

(21)Tdry,inlet=Tair,ambient+Tair,ambientηblowerPdry,inletPair,ambientγ−1γ

where ηblower is the blower efficiency.

2.4 Boundary conditions

For PEMFC vehicles, the operating conditions continuously change as the load changes. The required air flow rate for the PEMFC varies continuously corresponding to the current. Moreover, the air supplied to the PEMFC must be humidified. The dynamic response of the humidifier at various air flow rates needs to be analyzed to develop a control strategy to maintain the air temperature and relative humidity. The dry air entering into the plate-and-frame membrane humidifier was conditioned according to the air flow acceleration and sinusoidal air flow rate. The high acceleration of the air flow rate means a rapid increase in the velocity at the driving condition. The air flow rate was calculated based on the amount of the air required in the PEMFC. The baseline operating conditions in the humidifier are summarized in Table 2. The operating conditions were determined from experimental conditions used in the previous studies [24, 25]. The temperature at the dry air inlet varied in the range of 33.9–59.3∘C under the simulation conditions. Transport properties including the thermal conductivity, heat capacity, and water diffusivity in the gas phase are shown in Table 3.

Table 2

Operating conditions

ParametersValue
Ambient air pressure101.35 kPa
Ambient air temperature20∘C
Ambient air relative humidity0.01%
Wet air temperature80∘C
Wet air relative humidity100%
Air flow rate50 g s−1–100
g s−1
Air velocity in the channel1.5 m s−1–3
m s−1
Table 3

Transport properties

ParametersValue
Membrane [34, 35]
Thermal conductivity0.95
W m−1K−1
Heat capacity4188
J kg−1K−1
Plate [36]
Thermal conductivity200
W m−1K−1
Heat capacity719 J kg−1K−1
Air [15]
Heat capacity1006
J kg−1K−1
Water diffusivity in the gas phase0.0000282
m2 s−1

3 Results and discussion

3.1 Effects of air flow acceleration

Figure 4 shows the variations in the air flow rate, temperature, absolute humidity, and relative humidity at the dry air outlet in response to the air flow acceleration. The difference between the peak and steady state values was defined as the overshoot or undershoot during the air flow change. The settling time was defined as the time required to reach 99% of the steady state value after the air flow rate change. As shown in Figure 4(a), the increasing slope of the air flow rate with respect to time increased with the increase in air flow acceleration from 0.05 to 1.0 m s−2. As shown in Figure 4(b), for all air flow accelerations, the temperature at the dry air outlet decreased rapidly and reached the minimum value. After the undershoot, the temperature at the dry air outlet started to increase and then gradually approached the steady state value. However, as the air flow acceleration increased, the undershoot occurred earlier, owing to slow temperature change in the membrane and plate with low thermal diffusivity. Moreover, after the undershoot, the settling time decreased with the increase in air flow acceleration, because the inlet condition reached the steady state value quickly.

Figure 4 Variations of (a) air flow rate (b) temperature, (c) absolute humidity, and (d) relative humidity at the dry air outlet in response to change in air flow acceleration
Figure 4

Variations of (a) air flow rate (b) temperature, (c) absolute humidity, and (d) relative humidity at the dry air outlet in response to change in air flow acceleration

As shown in Figure 4(c), the undershoot of the absolute humidity at the dry air outlet occurred early, and the settling time decreased with the increase in air flow acceleration. In the plate-and-frame membrane humidifier, as shown in Figures 4(b) and 4(c), the mass transfer was faster than the heat transfer, because the settling time of the absolute humidity was shorter than that of the temperature. The plate where the heat transfer mainly occurred was about 20 times thicker than the membrane where the mass transfer mainly occurred.

The temperature and relative humidity at the dry air outlet are important parameters for the optimal control of PEMFC vehicles [37]. As shown in Figure 4(d), the settling time of the relative humidity at the dry air outlet decreased with the increase in the air flow acceleration because the relative humidity was affected by the absolute humidity and temperature. As the air flow acceleration increased, the relative humidity at the dry air outlet decreased rapidly, owing to the initial decrease in the absolute humidity. The relative humidity then approached the steady state value quickly, corresponding to the variation in temperature at the dry air outlet. Accordingly, higher air flow acceleration is more advantageous for PEMFC control owing to its fast responsiveness.

Figure 5 shows the effect of air flow acceleration on the average temperatures of the plate and membrane during the mass flow rate change. The average temperatures of the plate and membrane slowly increased with time, but the settling time of the plate with a larger heat capacity was longer than that of the membrane. At an air flow acceleration of 0.05 m s−2, the average temperatures of the plate and membrane gradually and similarly increased, corresponding to the increase in the inlet temperature, owing to the gradual increase in the air flow rate. However, during 0 to 10 s with the rapid increase in the air flow rate, the average temperatures of the plate and membrane at an air flow acceleration of 1.0 m s−2 increased more slowly than those at an air flow acceleration of 0.05 ms−2. The delay in heat transfer between the dry air and plate increased with the rapid increase in air flow acceleration. However, after 10 s, the average temperatures of the plate and membrane increased rapidly, owing to the dominant influence of the increased temperature at the dry air inlet. Therefore, the undershoot and settling time of the temperature at the dry air outlet were affected by the temperature of the plate and membrane during the air flow rate change.

Figure 5 Effect of the air flow acceleration on plate and membrane average temperatures during mass flow rate change
Figure 5

Effect of the air flow acceleration on plate and membrane average temperatures during mass flow rate change

Figure 6 shows variations in the dry air temperature and relative humidity of the dry air versus fractional distance in the air flow direction at an air flow acceleration of 1.0 m s−2. When the dry air temperature was lower than the initial value (0 s), the undershoot was observed at the fractional distance in the air flow direction. Before 1 s, the undershoot of the dry air temperature was observed at the fractional distance between 0.6 and 1, because the effect of the air flow rate was larger than that of the inlet temperature. However, after 1 s, the dry air temperature increased above the initial temperature, owing to the increase in the effect of the increased inlet temperature. Before 0.5 s, the dry air relative humidity was close to the initial value at the fractional distance between 0.8 and 1, because the dry air temperature was lower than the initial value at the same time. However, after 0.5 s, the dry air relative humidity decreased with time for all fractional distances under the increased dry air temperature condition.

Figure 6 Profiles of (a) dry air temperature and (b) dry air relative humidity during mass flow change at 1.0 m s−2
Figure 6

Profiles of (a) dry air temperature and (b) dry air relative humidity during mass flow change at 1.0 m s−2

3.2 Effects of amplitude of sinusoidal air flow rate

As the PEMFC vehicle accelerates, the air flow rate increases because the PEMFC needs a large number of reactants instantaneously to raise the power. Accordingly, in actual driving conditions, the air flow rate varies corresponding to continuous periodic change between air flow acceleration and deceleration. In this study, when the air flow rate changed according to the sinusoidal function, the variations in the temperature and relative humidity were analyzed. The sinusoidal air flow rate is given by Eq. (22).

(22)m˙air,in=Aampsin2πtBperi+75

where Aamp is the amplitude and Bperi is the period.

The global maximum and minimum temperatures and relative humidities are defined as the maximum and minimum values within one period, respectively. In addition, the local maximum and minimum temperatures and relative humidities are defined as the saddle points between these two values, respectively. The temperature and relative humidity differences between the global maximum and minimum values are given by Eqs. (23) and (24), respectively.

(23)ΔTglobal=Tmax,global−Tmin,global
(24)Δφglobal=φmax,global−φmin,global

Figure 7 shows the variations in the temperature and relative humidity at the dry air outlet in response to amplitude change with a period of 20 s. ΔTglobal,air increased with the increase in the amplitude of the air flow rate because the variation in the temperature at the dry air inlet increased. In addition, while the variations in the temperature at the dry air outlet repeatedly increased and decreased at the amplitude of 10 g s−1, the local maximum and minimum values occurred at amplitudes of 17.5 and 25 g s−1, respectively. Overall, the nonlinearity in the temperature at the dry air outlet increased with the increase in the amplitude. Moreover, Δφglobal,air increased with the increase in the amplitude of the relative humidity owing to the effect of ΔTglobal,air. Under the repeated air flow acceleration and deceleration conditions, the decrease in the amplitude is advantageous for controlling the PEMFC owing to the decrease in the temperature and relative humidity.

Figure 7 Variations of (a) temperature and (b) relative humidity at the dry air outlet with increase in the amplitude of the sinusoidal air flow rate from 10 to 25 g s−1
Figure 7

Variations of (a) temperature and (b) relative humidity at the dry air outlet with increase in the amplitude of the sinusoidal air flow rate from 10 to 25 g s−1

3.3 Effects of period of sinusoidal air flow rate

Figure 8 shows the variations in the temperature and relative humidity at the dry air outlet in response to the period change at an amplitude of 25 g s−1. The local maximum and minimum temperatures at the dry air outlet were observed not only at a period of 10 s, but also at a period of 40 s. Even though the air flow acceleration decreased with the increase in the period, the nonlinearity in the temperature at the dry air outlet was not reduced by the increased period. Therefore, to reduce the nonlinearity with the sinusoidal air flow rate, it would be better to decrease the amplitude rather than to increase the period. In addition, ΔTglobal,air for a 10 s period decreased more substantially than that for a 40 s period, because the delay in heat transfer increased with the increase in the air flow acceleration and deceleration. Moreover, Δφglobal,air for a 10 s period decreased more substantially than that for a 40 s period, owing to increases in the delay in heat and mass transfer.

Figure 8 Variations of (a) temperature and (b) relative humidity at the dry air outlet with increase in the period of the sinusoidal air flow rate from 10 to 40 s
Figure 8

Variations of (a) temperature and (b) relative humidity at the dry air outlet with increase in the period of the sinusoidal air flow rate from 10 to 40 s

Figure 9 shows the variation in the average temperature of the plate in response to the period change. ΔTglobal,plate decreased with the decrease in the period because the variation in the temperature of the plate was delayed at a larger heat capacity. The slow temperature change in the plate affected the maximum and minimum values of the dry air temperature and relative humidity in accordance with the period. As the period in the air flow rate decreased, the variations in the temperature and relative humidity at the dry air outlet also decreased owing to the influence between the plate and dry air. Therefore, to control the performance of the PEMFC under the repeated air flow acceleration and deceleration conditions, it would be preferable to decrease the period.

Figure 9 Effect of the period of the sinusoidal air flow rate on average plate temperature
Figure 9

Effect of the period of the sinusoidal air flow rate on average plate temperature

3.4 Model validation

The numerical model was validated by comparing the predictions with the experimental data in a plate-and-frame membrane humidifier reported by Yu [25]. The simulations were conducted using the developed numerical model at the same experimental conditions. As shown in Figure 10, the predicted mass flux and heat flux were compared with the experimental data at various dry air velocities. The predicted results showed a good agreement with the measured data within a deviation of ±9%.

Figure 10 Comparison of the predictions with the measured data by Yu [25]
Figure 10

Comparison of the predictions with the measured data by Yu [25]

4 Conclusions

In this study, a pseudo-multi-dimensional dynamic model of a plate-and-frame membrane humidifier for PEMFC vehicles was developed in order to predict the heat and mass transfer performance under dynamic operating conditions. The numerical model was validated with experimental data. Based on the model developed, variations in the temperature and relative humidity at the dry air outlet in the plate-and-frame membrane humidifier were analyzed according to the air flow acceleration. The effects of heat transfer on the dynamic response of the plate-and-frame membrane humidifier are more dominant than those of mass transfer. The increased air flow acceleration was advantageous for the PEMFC control, due to its fast responsiveness. The dynamic response was also analyzed as a function of the amplitude and period of the sinusoidal air flow rate. Decreases in the amplitude and period of the air flow rate were advantageous for the PEMFC control owing to the decrease in the temperature and relative humidity difference between the maximum and minimum values. This study has some limitations on the consideration of the temperature and humidity variations at the humidifier inlet because the dynamic reaction in the PEMFC is not solved. Accordingly, further research is required on the dynamic response of PEMFC vehicle systems combining the plate-and-frame membrane humidifier and PEMFC under actual driving conditions.

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Acknowledgement

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIP) (No. 2017R1A2B2003416).

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Received: 2017-09-18
Accepted: 2018-07-04
Published Online: 2018-10-25

© 2018 S. Yun et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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  10. Feynman diagrams and rooted maps
  11. New type of chaos synchronization in discrete-time systems: the F-M synchronization
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  13. A note on the uniqueness of 2D elastostatic problems formulated by different types of potential functions
  14. On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics
  15. Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications
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  125. Face recognition method based on GA-BP neural network algorithm
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  129. Optimization design of reconfiguration algorithm for high voltage power distribution network based on ant colony algorithm
  130. Feasibility simulation of aseismic structure design for long-span bridges
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  137. Numerical analysis on the dynamic response of a plate-and-frame membrane humidifier for PEMFC vehicles under various operating conditions
  138. Energy converting layers for thin-film flexible photovoltaic structures
  139. Effect of convection heat transfer on thermal energy storage unit
https://doi.org/10.1515/phys-2018-0081
Keywords for this article
Dynamic response; Heat and mass transfer; Numerical model; PEMFC; Plate-and-frame membrane humidifier
Creative Commons
BY-NC-ND 4.0

Articles in the same Issue

  1. Regular Articles
  2. A modified Fermi-Walker derivative for inextensible flows of binormal spherical image
  3. Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics
  4. Three-dimensional atom localization via probe absorption in a cascade four-level atomic system
  5. Determination of the energy transitions and half-lives of Rubidium nuclei
  6. Three phase heat and mass transfer model for unsaturated soil freezing process: Part 1 - model development
  7. Three phase heat and mass transfer model for unsaturated soil freezing process: Part 2 - model validation
  8. Mathematical model for thermal and entropy analysis of thermal solar collectors by using Maxwell nanofluids with slip conditions, thermal radiation and variable thermal conductivity
  9. Constructing analytic solutions on the Tricomi equation
  10. Feynman diagrams and rooted maps
  11. New type of chaos synchronization in discrete-time systems: the F-M synchronization
  12. Unsteady flow of fractional Oldroyd-B fluids through rotating annulus
  13. A note on the uniqueness of 2D elastostatic problems formulated by different types of potential functions
  14. On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics
  15. Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications
  16. Siewert solutions of transcendental equations, generalized Lambert functions and physical applications
  17. Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction
  18. A new three-dimensional chaotic flow with one stable equilibrium: dynamical properties and complexity analysis
  19. Dynamics of a dry-rebounding drop: observations, simulations, and modeling
  20. Modeling the initial mechanical response and yielding behavior of gelled crude oil
  21. Lie symmetry analysis and conservation laws for the time fractional simplified modified Kawahara equation
  22. Solitary wave solutions of two KdV-type equations
  23. Applying industrial tomography to control and optimization flow systems
  24. Reconstructing time series into a complex network to assess the evolution dynamics of the correlations among energy prices
  25. An optimal solution for software testing case generation based on particle swarm optimization
  26. Optimal system, nonlinear self-adjointness and conservation laws for generalized shallow water wave equation
  27. Alternative methods for solving nonlinear two-point boundary value problems
  28. Global model simulation of OH production in pulsed-DC atmospheric pressure helium-air plasma jets
  29. Experimental investigation on optical vortex tweezers for microbubble trapping
  30. Joint measurements of optical parameters by irradiance scintillation and angle-of-arrival fluctuations
  31. M-polynomials and topological indices of hex-derived networks
  32. Generalized convergence analysis of the fractional order systems
  33. Porous flow characteristics of solution-gas drive in tight oil reservoirs
  34. Complementary wave solutions for the long-short wave resonance model via the extended trial equation method and the generalized Kudryashov method
  35. A Note on Koide’s Doubly Special Parametrization of Quark Masses
  36. On right-angled spherical Artin monoid of type Dn
  37. Gas flow regimes judgement in nanoporous media by digital core analysis
  38. 4 + n-dimensional water and waves on four and eleven-dimensional manifolds
  39. Stabilization and Analytic Approximate Solutions of an Optimal Control Problem
  40. On the equations of electrodynamics in a flat or curved spacetime and a possible interaction energy
  41. New prediction method for transient productivity of fractured five-spot patterns in low permeability reservoirs at high water cut stages
  42. The collinear equilibrium points in the restricted three body problem with triaxial primaries
  43. Detection of the damage threshold of fused silica components and morphologies of repaired damage sites based on the beam deflection method
  44. On the bivariate spectral quasi-linearization method for solving the two-dimensional Bratu problem
  45. Ion acoustic quasi-soliton in an electron-positron-ion plasma with superthermal electrons and positrons
  46. Analysis of projectile motion in view of conformable derivative
  47. Computing multiple ABC index and multiple GA index of some grid graphs
  48. Terahertz pulse imaging: A novel denoising method by combing the ant colony algorithm with the compressive sensing
  49. Characteristics of microscopic pore-throat structure of tight oil reservoirs in Sichuan Basin measured by rate-controlled mercury injection
  50. An activity window model for social interaction structure on Twitter
  51. Transient thermal regime trough the constitutive matrix applied to asynchronous electrical machine using the cell method
  52. On the zagreb polynomials of benzenoid systems
  53. Integrability analysis of the partial differential equation describing the classical bond-pricing model of mathematical finance
  54. The Greek parameters of a continuous arithmetic Asian option pricing model via Laplace Adomian decomposition method
  55. Quantifying the global solar radiation received in Pietermaritzburg, KwaZulu-Natal to motivate the consumption of solar technologies
  56. Sturm-Liouville difference equations having Bessel and hydrogen atom potential type
  57. Study on the response characteristics of oil wells after deep profile control in low permeability fractured reservoirs
  58. Depiction and analysis of a modified theta shaped double negative metamaterial for satellite application
  59. An attempt to geometrize electromagnetism
  60. Structure of traveling wave solutions for some nonlinear models via modified mathematical method
  61. Thermo-convective instability in a rotating ferromagnetic fluid layer with temperature modulation
  62. Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations
  63. Effect of magnetic field and heat source on Upper-convected-maxwell fluid in a porous channel
  64. Physical cues of biomaterials guide stem cell fate of differentiation: The effect of elasticity of cell culture biomaterials
  65. Shooting method analysis in wire coating withdrawing from a bath of Oldroyd 8-constant fluid with temperature dependent viscosity
  66. Rank correlation between centrality metrics in complex networks: an empirical study
  67. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering
  68. Modeling of electric and heat processes in spot resistance welding of cross-wire steel bars
  69. Dynamic characteristics of triaxial active control magnetic bearing with asymmetric structure
  70. Design optimization of an axial-field eddy-current magnetic coupling based on magneto-thermal analytical model
  71. Thermal constitutive matrix applied to asynchronous electrical machine using the cell method
  72. Temperature distribution around thin electroconductive layers created on composite textile substrates
  73. Model of the multipolar engine with decreased cogging torque by asymmetrical distribution of the magnets
  74. Analysis of spatial thermal field in a magnetic bearing
  75. Use of the mathematical model of the ignition system to analyze the spark discharge, including the destruction of spark plug electrodes
  76. Assessment of short/long term electric field strength measurements for a pilot district
  77. Simulation study and experimental results for detection and classification of the transient capacitor inrush current using discrete wavelet transform and artificial intelligence
  78. Magnetic transmission gear finite element simulation with iron pole hysteresis
  79. Pulsed excitation terahertz tomography – multiparametric approach
  80. Low and high frequency model of three phase transformer by frequency response analysis measurement
  81. Multivariable polynomial fitting of controlled single-phase nonlinear load of input current total harmonic distortion
  82. Optimal design of a for middle-low-speed maglev trains
  83. Eddy current modeling in linear and nonlinear multifilamentary composite materials
  84. The visual attention saliency map for movie retrospection
  85. AC/DC current ratio in a current superimposition variable flux reluctance machine
  86. Influence of material uncertainties on the RLC parameters of wound inductors modeled using the finite element method
  87. Cogging force reduction in linear tubular flux switching permanent-magnet machines
  88. Modeling hysteresis curves of La(FeCoSi)13 compound near the transition point with the GRUCAD model
  89. Electro-magneto-hydrodynamic lubrication
  90. 3-D Electromagnetic field analysis of wireless power transfer system using K computer
  91. Simplified simulation technique of rotating, induction heated, calender rolls for study of temperature field control
  92. Design, fabrication and testing of electroadhesive interdigital electrodes
  93. A method to reduce partial discharges in motor windings fed by PWM inverter
  94. Reluctance network lumped mechanical & thermal models for the modeling and predesign of concentrated flux synchronous machine
  95. Special Issue Applications of Nonlinear Dynamics
  96. Study on dynamic characteristics of silo-stock-foundation interaction system under seismic load
  97. Microblog topic evolution computing based on LDA algorithm
  98. Modeling the creep damage effect on the creep crack growth behavior of rotor steel
  99. Neighborhood condition for all fractional (g, f, n′, m)-critical deleted graphs
  100. Chinese open information extraction based on DBMCSS in the field of national information resources
  101. 10.1515/phys-2018-0079
  102. CPW-fed circularly-polarized antenna array with high front-to-back ratio and low-profile
  103. Intelligent Monitoring Network Construction based on the utilization of the Internet of things (IoT) in the Metallurgical Coking Process
  104. Temperature detection technology of power equipment based on Fiber Bragg Grating
  105. Research on a rotational speed control strategy of the mandrel in a rotary steering system
  106. Dynamic load balancing algorithm for large data flow in distributed complex networks
  107. Super-structured photonic crystal fiber Bragg grating biosensor image model based on sparse matrix
  108. Fractal-based techniques for physiological time series: An updated approach
  109. Analysis of the Imaging Characteristics of the KB and KBA X-ray Microscopes at Non-coaxial Grazing Incidence
  110. Application of modified culture Kalman filter in bearing fault diagnosis
  111. Exact solutions and conservation laws for the modified equal width-Burgers equation
  112. On topological properties of block shift and hierarchical hypercube networks
  113. Elastic properties and plane acoustic velocity of cubic Sr2CaMoO6 and Sr2CaWO6 from first-principles calculations
  114. A note on the transmission feasibility problem in networks
  115. Ontology learning algorithm using weak functions
  116. Diagnosis of the power frequency vacuum arc shape based on 2D-PIV
  117. Parametric simulation analysis and reliability of escalator truss
  118. A new algorithm for real economy benefit evaluation based on big data analysis
  119. Synergy analysis of agricultural economic cycle fluctuation based on ant colony algorithm
  120. Multi-level encryption algorithm for user-related information across social networks
  121. Multi-target tracking algorithm in intelligent transportation based on wireless sensor network
  122. Fast recognition method of moving video images based on BP neural networks
  123. Compressed sensing image restoration algorithm based on improved SURF operator
  124. Design of load optimal control algorithm for smart grid based on demand response in different scenarios
  125. Face recognition method based on GA-BP neural network algorithm
  126. Optimal path selection algorithm for mobile beacons in sensor network under non-dense distribution
  127. Localization and recognition algorithm for fuzzy anomaly data in big data networks
  128. Urban road traffic flow control under incidental congestion as a function of accident duration
  129. Optimization design of reconfiguration algorithm for high voltage power distribution network based on ant colony algorithm
  130. Feasibility simulation of aseismic structure design for long-span bridges
  131. Construction of renewable energy supply chain model based on LCA
  132. The tribological properties study of carbon fabric/ epoxy composites reinforced by nano-TiO2 and MWNTs
  133. A text-Image feature mapping algorithm based on transfer learning
  134. Fast recognition algorithm for static traffic sign information
  135. Topical Issue: Clean Energy: Materials, Processes and Energy Generation
  136. An investigation of the melting process of RT-35 filled circular thermal energy storage system
  137. Numerical analysis on the dynamic response of a plate-and-frame membrane humidifier for PEMFC vehicles under various operating conditions
  138. Energy converting layers for thin-film flexible photovoltaic structures
  139. Effect of convection heat transfer on thermal energy storage unit
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