Local Thermal Non-equilibrium Condition Research Articles

Transient behaviour of heat transfer with complete evaporation process in Porous Channel with localised heating using non-Darcian flow and LTNE model

This study numerically presents the transient behaviour of complete evaporation process inside porous channel. Based on the modified enthalpy formulation under non-Darcy flow and Local Thermal Non-Equilibrium (LTNE) conditions, solutions have been obtained utilizing the finite volume method for various relevant parameters. The results have been validated with the experiments and they show good agreement between them. The results demonstrate that LTNE model should be employed while modelling the transient complete evaporation process in porous media. The non-Darcy effects have considerable influences on the locations of the initiation and termination of the phase change processes as compared to Darcy flow model. Therefore, the behaviours of the two-phase and the superheated vapour zones, when the steady-state solutions is reached, are substantially changed for non-Darcy flow as compared to Darcy model due this assumption provides an additional mechanism for heat transfer that represented by the heat exchange between the solid and fluid phases. It has been observed that the two-phase zone is considerably extended in the axial direction and this zone has not been occupied a large size towards transverse direction due to the axial velocity is noticeably higher than the transverse velocity, caused by reducing the diffusive energy through the two-phase region. The results indicate that non-Darcian effects leads to considerably extend the size of superheated region towards the outlet of the channel, which is not the case for Darcy model. The non-Darican effects become more pronounced for high Reynolds number and heat flux. The influences of varying in Reynolds number, heat flux, porosity, and solid thermal conductivity are substantial near the heated surface, whereas Darcy number has a minor impact on the solution of complete evaporation process. It can be emphasised from the present predictions that the non-Darcy flow along with LTNE condition is indispensable model for the complete evaporation process, especially under high mass flowrate as well heat flux.

A thermal nonequilibrium model to natural convection inside non‐Darcy porous layer surrounded by horizontal heated plates with periodic boundary temperatures

AbstractThis article displays a numerical investigation on natural convection within non‐Darcy porous layer surrounded by two horizontal surfaces having sinusoidal temperature profiles with difference in phase and wave number. The Darcy–Brinkman–Forchheimer model and local thermal nonequilibrium condition have been employed. Simulations have been performed for wide ranges of inertia coefficient (10–4 ≤ Fs/Pr* ≤ 10–2), thermal conductivity ratio (0.1 ≤ K r ≤ 100), phase difference (0 ≤ β ≤ π), modified Rayleigh number (200 ≤ Ra* ≤ 1000), wavelength (3 ≤ k ≤ 12), and nondimensional heat transfer coefficient (0.1 ≤ H ≤ 100). Results demonstrate that Nusselt number highly relies on Fs/Pr*, K r, β, Ra*, and k as compared to H. A considerable enhancement in fluid, solid, and overall Nusselt numbers has been observed with diminishing Fs/Pr* and β and increasing k, K r, and H. The raising in β has a significant impact on Nu for smaller k and this effect is almost ignored when k > 12. The increase in Ra*, K r, β, and H and decrease in Fs/Pr* and k acts to reduce the severity of nonequilibrium zone and increase the size of thermal equilibrium zone. The influence of H on nonequilibrium area is more evident than K r.

Semi-analytical study of impingement cooling of metal foam heat sinks of CPUs with air and hydrogen jets under LTNE condition

In this paper, a mathematical model for heat transfer in a heat sink covered by an open-cell metal foam under impinging jet flow is presented. Hydrogen and air were considered as the cooling fluids. The Darcy–Brinkman–Forchheimer relationship for the momentum equation was employed, while the two-equation energy model under the local thermal non-equilibrium (LTNE) condition for the energy equation was used. The mathematical model of similarity solution was first validated with analytical and experimental data from literature, and numerical data from Ansys-Fluent®. Then, the differences between numerical predictions under the local thermal equilibrium (LTE) and LTNE on flow and temperature distributions were presented and analyzed. It was shown that when the effective thermal conductivity of solid is very low, the difference of temperature of solid and gas cannot be neglected and LTNE should be considered. In other words, when effective thermal conductivity ratio, β, declines, the deviation between the LTNE and LTE models increases considerably. Finally, the effects of critical dimensionless parameters on the flow and heat transfer characteristics were investigated. The results indicate that cooling performance of the metal foam can be improved by increasing the Reynolds and Darcy numbers while decreasing the aspect ratio of the heat sink. Besides, the properties of metal foam and gas were studied. Hydrogen, as a cooling gas, has better thermal performance than air.

Local Thermal Nonequilibrium Natural Convection in a Cavity with Heat-Generating Porous Layer

Natural convection in a partially porous cavity with a heat generating source in the solid phase is studied numerically under a local thermal nonequilibrium condition. The right and left walls of the cavity are maintained at hot and cold temperatures, respectively. The horizontal walls are thermally insulated. The finite volume method and the semi-implicit method for pressure-linked equations (SIMPLER) algorithm are used to solve the conservation equations. The effects of relevant parameters, such as internal and external Rayleigh numbers , , interphase heat transfer coefficient , modified thermal conductivity ratio , and dimensionless porous layer thickness are discussed. The results revealed that at high values of the interphase heat transfer coefficient, the impact of an internal Rayleigh number on the dynamic and thermal fields decreases with an increase in the modified thermal conductivity ratio.

Numerical Investigation of Thermally Developing Non-Darcy Forced Convection in a Porous Circular Duct with Asymmetric Entrance Temperature Under LTNE Condition

This paper numerically investigates the heat transfer performance of thermally developing non-Darcy forced convection in a fluid-saturated porous medium tube under asymmetric entrance temperature boundary conditions. The Brinkman flow model and the local thermal non-equilibrium (LTNE) model are employed to establish the mathematical model of the studied problem to predict the forced convective heat transfer. Then, the mathematical model is numerically solved using COMSOL Multiphysics. Consequently, the fluid velocity field, the solid temperature field, the fluid temperature field and the Nusselt number are obtained. Moreover, the dependences of the Nusselt number on some key parameters are analyzed in detail. The results show that the distribution characteristics of the Nusselt number are strongly dependent on the form of the entrance temperature function. Meanwhile, it is found that the Nusselt number increases first and then tends to approach an asymptotic value with the increase in the Darcy number and the Biot number. The Nusselt number monotonously increases with increasing the Peclet number. On the contrary, the Nusselt number decreases first and then tends to be an asymptotic value owing to the increase in the thermal conductivity ratio and the viscosity ratio. This study is of benefit to provide in-depth insights into the non-Darcy forced convective heat transfer in porous tubes with asymmetric inlet temperature under LTNE condition.

Convergence - Divergence of the Finite Volume Method for the Fluid and Heat Flow in Heterogeneous Porous Rocks

Fluid velocity has an important impact in the Finite Volume numerical method (FVM) used to model fluid and energy flows in heterogeneous porous media. This formulation is based on the energy flow conservation equations under local thermal non-equilibrium conditions (LTNE). The heat transfer from the solid matrix to the moving non-isothermal fluid inside the pores is simulated for several velocities and global different heat transfer coefficients. During the numerical simulation of coupled heat/mass flow in a heterogeneous porous system it is necessary to average highly variable physical parameters at the boundaries between different domains represented geometrically in the computational mesh of the FVM. This can be effectively achieved using appropriate average techniques at the contact interfaces of each domain. The averaging process should correctly represent the behaviour of the fluid velocity crossing different areas of the reservoir. Many numerical divergence problems arise from the fluid velocity value and the interfacial interactions at the boundaries of different continua. The averages have a decisive influence on the numeric results of the simulation. A very stable, convergent averaging scheme for the FVM is presented herein and compared to new analytical diffusion-convection models. Especial attention is paid to the dynamic process of cold water (50°C) injected into a geothermal reservoir at higher temperature (350°C). The fluid temperature profile is calculated when the fluid migrates at constant speed through a permeable corridor from a fluid injection point to an extraction zone. The physical reason for the divergence of a numerical model, and the exploration of the range of validity of the LTNE hypothesis during the injection of cold water into a hot reservoir are both explained.

Advanced thermal lattice Boltzmann method for the simulation of latent heat thermal energy in a porous storage unit

The current research expounds numerical investigation of key parameters effects, namely porosity ( ε= 0.4, 0.6, 0.7 and 0.8), Reynolds number (Re = 100, 200, 400 and 600) and Eckert number (Ec= 0, 1, 5 and 10) on the forced convective laminar flow and heat transfer through a horizontal porous channel filled with a metal foam structure impregnated with paraffin as a phase change material (PCM). The Darcy-Brinkman-Forchheimer model under the local thermal non-equilibrium (LTNE) condition is deemed at the representative elementary volume (REV) scale. The fully coupled equations of Navier-Stokes, Poisson’s equation, energy equations, and continuity equation were handled numerically via a thermal single relaxation time lattice Boltzmann method (TSRT-LBM). To facilitate implementation, all LB equations are based on the same speed discretization scheme (D2Q9). Three-population distribution functions were applied to simulate the fluid flow, and temperatures of the fluid and solid phases. Previously, the numerical model was validated by available cases. Then, a comprehensive investigation has been performed to investigate the influence of the aforementioned dimensionless numbers. All LBM results are found to be highly consistent with other numerical works. The outcomes reported that at lower porosities, the energy and exergy efficiencies increased with increasing Re and Ec. However, for large porosity values, the efficiencies were optimum for a critical Re ~ 400. To sum up, it can be stated that the implemented thermal lattice Boltzmann method has been demonstrated as a suitable approach study the thermal sensible energy storage.

Thermal storage analysis of a foam-filled PCM heat exchanger subjected to fluctuating flow conditions

A dynamic heat transfer model is developed to investigate the transient thermal storage characteristics of a heat exchanger with foam-filled phase change material (PCM) under the fluctuating flow conditions. The thermal energy storage (TES) configuration of double pipe is considered, while using the highly porous metal foam to intensify the heat transfer in both the PCM and heat transfer fluid (HTF) regions. The paraffin RT50 is used as the PCM and water is selected as the HTF. The energy transport between the inner and outer pipes is thoroughly taken into account. The Darcy-Forchheimer equation is adopted to model the fluid flow through metal foam, and the enthalpy-porosity method is employed to simulate the phase change process within the PCM/foam composite under the local thermal non-equilibrium (LTNE) condition. The performance of heat exchanger during the charging process is firstly predicted under steady HTF flow, and then the effects of fluctuating inlet temperature and velocity are examined respectively. In the case of steady flow, compared with the pure PCM case, inserting metal foam in both the PCM and HTF regions shortens the melting time by 93.6% and augments the heat storage rate by 9 times. Fluctuation in the inlet temperature leads to a visibly oscillating variation in the PCM temperature and heat storage, which are 15 K, 65 kJ at a fluctuation amplitude of 30 K and 17 K, 105 kJ at a periodicity of 400 s. However, fluctuation in the velocity has no considerable influence. The heat exchanger with lower porosity foam presents more sensitive to the fluctuating inlet temperature.

Numerical investigation of porosity effect on a PCM's thermal performance in a porous rectangular channel via thermal lattice Boltzmann method

This paper performs a numerical assessment of the porosity effect on heat transfer under forced convection in an open-ended horizontal channel filled with a porous structure and a phase change material (PCM). To take into account forced convection between the solid matrix and the PCM, the dimensionless Darcy-Brinkman-Forchheimer equations and the local thermal non-equilibrium condition are considered. Simulations are achieved via the single relaxation time thermal lattice Boltzmann method using three distribution functions to handle the fluid velocity, and fluid and solid temperatures while translating the computational domain boundary conditions in terms of microscopic distribution functions. The numerical outcomes obtained were used to investigate the porosity effect (0.5 ≤ ε ≤ 0.9) on dynamic and thermal fields, entropy generation rate (Ns), and Bejan number (Be) of the considered system under influence of the Reynolds number (Re) during the charging and discharging processes. Based on the findings presented, it can be deduced that, among the various characteristics of metal foam such as conductivity and porosity, the decrease of the latter and the increase in Re speeds up the melting under the unsteady, forced and laminar convection. In addition, the overall irreversibility distribution in the proposed system is dominated by the heat transfer irreversibility.

Natural convection heat transfer from a bank of orthogonal heated plates embedded in a porous medium using LTNE model: A comparison between in-line and staggered arrangements

This study numerically presents the characteristics of natural convection induced by a bank of orthogonal heated plates instilled inside porous cavity using the assumption of local thermal non-equilibrium (LTNE) and non-Darcian conditions. In-line and staggered arrangements of heated sections have been investigated for the purpose of comparison. Attention has been given on how the arrangement of heated sections affects the performance of heat transfer for various related parameters. Numerical solutions demonstrated that the average Nusselt number (Nu) is robustly depends on thermal conductivity ratio (Kr), inertia parameter (Fs/Pr*) and modified Rayleigh number (Ra*) in comparison with scaled heat transfer coefficient (H). The results show that the solid Nusselt number (Nus) is lower than fluid Nusselt number (Nuf) for same value of Fs/Pr* owing to Fs/Pr* is directly affected on the fluid phase. Although Kr has a considerable effect on all Nu in comparison with H, H has a substantial impact on the strength of LTNE zone as compared to Kr, particularly for smaller Kr and H. The medium inside the enclosure nearly reaches the equilibrium condition for larger values of H and Kr. Most importantly, the results indicated that the performance of in-line arrangement is better than that obtained with staggered ones. Therefore, in-line arrangement can be recommended to be employed in manufacturing flat heat exchangers for applications involving porous media under natural convection case.

Natural convection of mathrm {Al}_{2}mathrm {O}_{3}-water nanofluid in a non-Darcian wavy porous cavity under the local thermal non-equilibrium condition

This study investigates thermal natural convective heat transfer in a nanofluid filled-non-Darcian porous and wavy-walled domain under the local thermal non-equilibrium condition. The considered cavity has corrugated and cold vertical walls and insulated horizontal walls except the heated part positioned at the bottom wall. The transport equations in their non-dimensional model are numerically solved based on the Galerkin finite-element discretization technique. The dimensionless governing parameters of the present work are the nanoparticle in volume concentration, the Darcy number, number of undulations, modified heat conductivity ratio, dimensionless heated part length, and location. Comparisons with other published theoretical and experimental results show good agreement with the present outcomes. The findings indicate that the heater length, its position, and the waves number on the side vertical walls as well as the nanoparticles concentration can be the control parameters for free convective motion and heat transport within the wavy cavity.

Entropy generation of mixed convection of SWCNT–water nanofluid filled an annulus with a rotating cylinder and porous lining under LTNE

PurposeThe purpose of this study is to numerically analyze the mixed convection and entropy generation in an annulus with a rotating heated inner cylinder for single-wall carbon nanotube (SWCNT)–water nanofluid flow using local thermal nonequilibrium (LTNE) model. An examination of the system behavior is presented considering the heat-generating solid phase inside the porous layer partly filled at the inner surface of the outer cylinder.Design/methodology/approachThe discretized governing equations for nanofluid and porous layer by means of the finite volume method are solved by using the SIMPLE algorithm.FindingsIt is found that the buoyancy force and rotational effect have an important impact on the change of the strength of streamlines and isotherms for nanofluid flow. The minimum average Nusselt number on the inner cylinder is obtained at Ra$_E$ = 10$^4$, and the minimum total entropy generation is found at Re = 400 for given parameters. The entropy generation minimization is determined in case of different nanoparticle volume fractions. It is observed that at the same external Rayleigh numbers, the LTNE condition obtained with internal heat generation is very different from that without heat generation.Originality/valueTo the best of the authors’ knowledge, there is no previous paper presenting mixed convection and entropy generation of SWCNT–water nanofluid in a porous annulus under LTNE condition. The addition of nanoparticles to based fluid leads to a decrease in the value of minimum total entropy generation. Thus, using nanofluid has a significant role in the thermal design and optimization of heat transfer applications.

Effects of temperature-dependent viscosity on natural convection in a porous cavity with a circular cylinder under local thermal non-equilibrium condition

In the present work, the influences of exponentially temperature-dependent viscosity on free convection in a porous cavity with a circular cylinder under local thermal non-equilibrium (LTNE) condition are investigated numerically via lattice Boltzmann (LB) method. To incorporate the LTNE effects, the temperature evolution equations are constructed by adding some unified source terms, which also preserve the parallel computation feature of the standard LB method. The effects of several physical parameters, including viscosity variation index (n), Rayleigh number (Ra), Darcy number (Da), ratio of fluid-to-solid thermal conductivity (λ) and inter-phase heat transfer coefficient (H) on flow and heat transfer characteristics are numerically studied. The numerical results show that as the LTNE parameters increase (i.e., H and λ), the solid heat transfer rate increases dramatically, while few changes are found for the heat transfer rate of fluid. Additionally, we find that for most given parameters, both the heat transfer rate of fluid and solid are generally decreased with the increase of n, while for relatively small values of H and λ, the heat transfer coefficient of solid phase depends little on the value of n. Further, the impacts of the porosity (ε) as well as the aspect ratio (Γ) are also considered.

Numerical analysis of time-fractional non-Fourier heat conduction in porous media based on Caputo fractional derivative under short heating pulses

In this research, the heat transport in porous media (sand particles and interstitial gas) under short heating pulses is examined, taking into account the non-Fourier effects. The time-fractional heat conduction equation based on the Caputo definition is proposed to examine the thermal response of porous media in short-time scales. The results of the time-fractional model are compared to experimental data, which proves the accuracy of this model as well as its capability to describe the fast transient thermal process, the local thermal nonequilibrium condition, and the energy exchange between the solid and gaseous phases. Additionally, the influence of variation in the different parameters, including the order of fractionality and heating pulse widths are investigated, and it has been proved that the gas-solid interactions in the fast transient process play a vital role in heat transfer mechanism of porous media, especially in the near-field locations to the heater with short pulse width.

Pulsating flow in a channel filled with a porous medium under local thermal non-equilibrium condition: an exact solution

The present work investigates analytically the problem of forced convection heat transfer of a pulsating flow, in a channel filled with a porous medium under local thermal non-equilibrium condition. Internal heat generation is considered in the porous medium, and the channel walls are subjected to constant heat flux boundary condition. Exact solutions are obtained for velocity, Nusselt number and temperature distributions of the fluid and solid phases in the porous medium. The influence of pertinent parameters, including Biot number, Darcy number, fluid-to-solid effective thermal conductivity ratio and Prandtl number are discussed. The applied pressure gradient is considered in a sinusoidal waveform. The effect of dimensionless frequency and coefficient of the pressure amplitude on the system’s velocity and temperature fields are discussed. The general shape of the unsteady velocity for different times is found to be very similar to the steady data. Results show that the amplitudes of the unsteady temperatures for the fluid and solid phases decrease with the increase in Biot number or thermal conductivity ratio. For large Biot numbers, dimensionless temperatures of the solid and fluid phases are similar and are close to their steady counterparts. Results for the Nusselt number indicate that increasing Biot number or thermal conductivity ratio decreases the amplitude of Nusselt number. Increase in the internal heat generation in the solid phase does not have a significant influence on the ratio of amplitude-to-mean value of the Nusselt number, while internal heat generation in the fluid phase enhances this ratio.

A Multiple-Relaxation-Time Lattice Boltzmann Model for Natural Convection in a Hydrodynamically and Thermally Anisotropic Porous Medium under Local Thermal Non-Equilibrium Conditions

To investigate the natural convective process in a hydrodynamically and thermally anisotropic porous medium at the representative elementary volume (REV) scale, the present work presented a multiple-relaxation-time lattice Boltzmann method (MRT-LBM) based on the assumption of local thermal non-equilibrium conditions (LTNE). Three sets of distribution function were used to solve the coupled momentum and heat transfer equations. One set was used to compute the flow field based on the generalized non-Darcy model; the other two sets were used to solve the temperature fields of fluid and solid under the LTNE. To describe the anisotropy of flow field of the porous media, a permeability tensor and a Forchheimer coefficient tensor were introduced into the model. Additionally, a heat conductivity tensor and a special relaxation matrix with some off-diagonal elements were selected for the thermal anisotropy. Furthermore, by selecting an appropriate equilibrium moments and discrete source terms accounting for the local thermal non-equilibrium effect, as well as choosing an off-diagonal relaxation matrix with some specific elements, the presented model can recover the exact governing equations for natural convection under LTNE with anisotropic permeability and thermal conductivity with no deviation terms through the Chapman-Enskog procedure. Finally, the proposed model was adopted to simulate several benchmark problems. Good agreements with results in the available literatures can be achieved, which indicate the wide practicability and the good accuracy of the present model.

Entropy generation in hydromagnetic nanofluids flow inside a tilted square enclosure under local thermal nonequilibrium condition

Abstract This paper investigates the entropy generations due to the multiple factors such as base fluid, nanoparticles, viscosity, and the inclined magnetic field for the convective flow of nanofluids inside a titled square enclosure considering local thermal nonequilibrium (LTNE) condition. One of the walls of the enclosure is kept heated changing its position such as (a) bottom, (b) near, (c) top, and (d) vertical while the corresponding opposite wall is kept cold. The other two walls are reserved insulated. The dimensionless constituting equations of the physical model are simulated numerically using FEM (finite element method). The numerically simulated data are matched with the data available in the open literature and noticed excellent agreement among them. The results indicate that nanoparticle loading and the Nield number strongly control the LTNE conditions among the regular fluid and nanoparticles. The Rayleigh and Hartmann numbers intensely control the system irreversibility while the magnetic field leaning angle acts slightly on it. We identified that fluid friction mainly contributes to the total entropy generation. The system produced maximum entropy for a bottom heated wall whereas the minimum entropy for the top heated wall. The entropy generated due to heat transfer dominates the frictional entropy only for the top heated wall.

Effect of heat source on forced convection in a partially-filled porous channel under LTNE condition

An analysis of forced convection is presented within a channel partially filled by porous medium inserted in the core, with the inclusion of internal heat source in fluid and solid phases. By employing Brinkman extended Darcy model and local thermal non-equilibrium (LTNE) model in porous region, exact solutions are obtained including fluid velocity, solid and fluid temperatures and Nusselt number, and pertinent parameters' effects on heat transfer enhancement are performed. In addition, the solutions are also compared to that by applying the local thermal equilibrium (LTE) assumption and the LTE validity is discussed. The results find that for a partially-filled porous channel, existed heat source terms can intensify the occurrence of the singularity in Nusselt number, especially with the variation of porous filling ratio more than one singularity points can be observed under both LTE and LTNE conditions. In addition, even if the singularity exists the Nusselt number can reach to LTE condition at a high Biot number (Bi) or at a very high solid to fluid thermal conductivity ratio (K), and at a small K the LTE also holds with the fluid heat source only. Overall, partially-filled porous systems with internal heat source have more rich thermal characteristics.

An Analysis of Thermal Radiation in Porous Media Under Local Thermal Non-equilibrium

The present work investigates the thermal radiation transport inside porous media under local thermal non-equilibrium conditions. Two different geometrical situations, a two-dimensional channel and a cylindrical geometry, are considered in the analysis. Porous media application is generally associated with high-temperature combustion, and radiative heat transfer is dominant. In this paper, by considering a stream of high-temperature flow in geometries filled with porous medium, the effect of thermal radiation on the solid- and fluid-phase temperature fields is calculated and analyzed. Two radiative heat transfer techniques, the discrete ordinate method (DOM) and the finite volume method (FVM), are tested, and the results are compared with a non-radiative model and with a model-based Rosseland approximation. A sensitivity study for the variation in absorption and scattering coefficients and the effect on the solid- and fluid-phase temperature fields is also undertaken. The effect of the extinction coefficient on the Nusselt number is also examined. The temperatures obtained through the Rosseland model show differences up to + 34% and − 26% compared to temperatures calculated with the DOM or FVM radiation calculation methods. The temperature fields obtained through DOM and FVM are very similar, and some significant differences can only be seen in the cases where a very low number of angular directions are used.

Heat transfer and entropy generation analysis in a three-dimensional impinging jet porous heat sink under local thermal non-equilibrium condition

A precise heat transfer simulation of a three-dimensional impinging jet porous heat sink is presented and is analyzed from thermodynamics vantage point under local thermal non-equilibrium condition. To increase the computational efficiency of the analysis, pore-scale modeling based on lattice Boltzmann method (LBM) is used inside the porous media (at a meso-scale), whilst finite volume method (FVM) is employed around it (at a macro-scale). The effects of the Reynolds number, porous layer thickness, solid/fluid thermal conductivity ratio, and porosity on the critical heat transfer and entropy generation parameters are investigated. Additionally, the relations between viscous entropy generation and pressure drop and thermal entropy generation with thermodynamic non-equilibrium are presented. The results indicated that among all parameters, the effects of the porous layer thickness on the fluid permeability are more substantial than other investigated parameters. Also, it is found that increasing the Reynolds number or porous layer thickness increases the total pressure drop, average viscous entropy generation number, and Nusselt number. For each porous layer thickness and Reynolds number, the minimum thermal conductivity ratio (that porous layer had no significant effect on heat transfer) is obtained 200. Moreover, it is determined that increasing the porous layer thickness or reducing the solid/fluid thermal conductivity ratio reduces the thermal entropy generation number, leading to a move toward the local thermal equilibrium condition. Additionally, in contrast to the fluid-phase thermal entropy generation number, the total entropy generation number in most porous layer cases was greater than the entropy generated by the surface without porous media.