Volume 45, Issue 4

The effect of the temperature gradient on the Soret coefficient in n-pentane/n-decane (n-C 5 /n-C 10 ) mixtures was investigated using non-equilibrium molecular dynamics (NEMD) with the heat exchange (eHEX) algorithm. n-Pentane/n-decane mixtures with three different compositions (0.25, 0.5, and 0.75 mole fractions, respectively) and the TraPPE-UA force field were used in computing the Soret coefficient (ST{S_{T}}) at 300 K and 1 atm. Added/removed heat quantities (Δ Q ) of 0.002, 0.004, 0.006, 0.008, and 0.01 kcal/mol were employed in eHEX processes in order to study the effect of different thermal gradients on the Soret coefficient. Moreover, a phenomenological description was applied to discuss the mechanism of this effect. Present results show that the Soret coefficient values firstly fluctuate violently and then become increasingly stable with increasing Δ Q (especially in the mixture with a mole fraction of 0.75), which means that Δ Q has a smaller effect on the Soret coefficient when the temperature gradient is higher than a certain thermal gradient. Thus, a high temperature gradient is recommended for calculating the Soret coefficient under the conditions that a linear response and constant phase are ensured in the system. In addition, the simulated Soret coefficient obtained at the highest Δ Q within three different compositions is in great agreement with experimental data.

The performance of the microchannel heat sink (MCHS) in electronic applications needs to be optimized corresponding to the number of channels ( N ). In this study optimization of the number of channels corresponding to the diameter of the microchannel (DN{D_{N}}) using an entropy generation minimization approach is achieved for the MCHS used in electronic applications. The numerical study is performed for constant total heat flow rate (q˙tot)({\dot{q}_{tot}}) and total mass flow rate (m˙tot)({\dot{m}_{tot}}). The results indicate that the dominance of frictional entropy generation (Sgen,Fr{S_{gen,Fr}}) increases with the reduction in diameter. However, the entropy generation due to heat transfer (Sgen,HT{S_{gen,HT}}) decreases with the reduction in diameter. Therefore, the optimum diameter (D∗{D^{\ast }}) is calculated corresponding to the minimum total entropy generation (Sgen,total{S_{gen,total}}) for the optimum number of channels (N∗{N^{\ast }}). Furthermore, the entropy generation number (NS{N_{S}}) and Bejan number (BeBe) are also calculated.

Transport coefficients (like diffusion and thermodiffusion) are the key parameters to be studied in non-equilibrium thermodynamics. For practical applications, it is important to predict them based on the thermodynamic parameters of a mixture under study: pressure, temperature, composition, and thermodynamic functions, like enthalpies or chemical potentials. The current study develops a thermodynamic framework for such prediction. The theory is based on a system of physically interpretable postulates; in this respect, it is better grounded theoretically than the previously suggested models for diffusion and thermodiffusion coefficients. In fact, it translates onto the thermodynamic language of the previously developed model for the transport properties based on the statistical fluctuation theory. Many statements of the previously developed model are simplified and amplified, and the derivation is made transparent and ready for further applications. The n(n+1)/2n(n+1)/2 independent Onsager coefficients are reduced to 2n+12n+1 determining parameters: the emission functions and the penetration lengths. The transport coefficients are expressed in terms of these parameters. These expressions are much simplified based on the Onsager symmetry property for the phenomenological coefficients. The model is verified by comparison with the known expressions for the diffusion coefficients that were previously considered in the literature.

A mathematical model for mixed convection flow of a nanofluid along a vertical wavy surface has been studied. Numerical results reveal the effects of the volume fraction of nanoparticles, the axial distribution, the Richardson number, and the amplitude/wavelength ratio on the heat transfer of Al 2 O 3 -water nanofluid. By increasing the volume fraction of nanoparticles, the local Nusselt number and the thermal boundary layer increases significantly. In case of Ri=1.0\mathrm{Ri}=1.0, the inclusion of 2 % and 5 % nanoparticles in the pure fluid augments the local Nusselt number, measured at the axial position 6.0, by 6.6 % and 16.3 % for a flat plate and by 5.9 % and 14.5 %, and 5.4 % and 13.3 % for the wavy surfaces with an amplitude/wavelength ratio of 0.1 and 0.2, respectively. However, when the Richardson number is increased, the local Nusselt number is found to increase but the thermal boundary layer decreases. For small values of the amplitude/wavelength ratio, the two harmonics pattern of the energy field cannot be detected by the local Nusselt number curve, however the isotherms clearly demonstrate this characteristic. The pressure leads to the first harmonic, and the buoyancy, diffusion, and inertia forces produce the second harmonic.

A model of the S -entropy production in a system with a membrane which separates non-electrolyte aqueous solutions was presented. The differences between fluxes in non-homogeneous and homogeneous conditions for volume and solute fluxes, respectively, are non-linear functions of the glucose osmotic pressure difference (OPD) in ranges dependent on the initial ethanol OPD. A decrease of ethanol OPD causes a shift of this range into the lower values of glucose OPD; this shift is also observed for negative values of glucose and ethanol OPDs. The coefficient of concentration polarization of the membrane as a function of glucose OPD has a sigmoidal shape. For suitably great negative values of glucose OPD this coefficient is very small, while for suitably high positive glucose OPD this coefficient is equal to 0.5. An increase of ethanol OPD at the initial moment causes a shift of this curve towards the direction of positive values of glucose OPD. In turn the S -entropy production in non-homogeneous conditions has low values for negative values of glucose OPD (convective range) while for suitably high positive glucose OPD it has greater values (diffusive and convective range). A change of ethanol OPD at the initial moment causes a shift of this curve along the horizontal axis.

Two types of additional variables were included in the set of state variables and were used for a thermodynamic description of diffusion in an ordinary thermodynamic system. Vacancies are included in the mass balance. Internal surfaces are massless but are characterized by some energy, which is included in the energy balance of the thermodynamic system. Fluxes of components, vacancies, and surfaces were expressed via two groups of thermodynamic constitutive equations of with cross effects. The first group follows from the Gibbs equation. These are state equations in a differential form. The second group relates generalized thermodynamic fluxes to generalized thermodynamic forces. It was shown for a binary system that only three of six transfer coefficients are independent even if the mass transfer mechanism caused by the stress gradient is taken into account.

This study deals with the entropy generation in magnetized blood flow through a channel. The blood is modeled as a non-Newtonian fluid that circulates by a uniform peristaltic wave with slip at the boundaries. An inertia free flow is considered using an approximation of the long-wavelength peristaltic wave. The governing equations of the flow are formulated and numerically solved using computational software to identify the characteristics of this non-uniform and time-dependent flow system. In addition, several closed-form solutions of the problem are explicitly presented.

Phonons are the main contributors to thermal energy transfer in thin films. The size dependence of the thermal transport characteristics alters the film properties such as thermal conductivity. Hence, in the present study, three-dimensional, transient phonon transport in dielectric material is studied through the Equation of Phonon Radiative Transport (EPRT) to assess the size dependence of thermal conductivity. The numerical scheme is introduced solving the EPRT in three dimensions and the governing algorithm is described in detail. A parametric study is carried out examining the effect of the Kn\mathrm{Kn} number on the thermal energy transport characteristics in three-dimensional thermally excited film. The formulation and estimation of the effective thermal conductivity tensor is presented and discussed, thereby extending, to some extent, the one-dimensional results obtained earlier. We demonstrate that thermal conductivity changes in all directions, depending on the size effect. In addition, the directions of the temperature gradient and heat flux vectors differ as the Kn\mathrm{Kn} number approaches unity.