Extended Darcy Model Research Articles

Performance optimization of triple tube heat exchanger using aluminum metal foam: A comprehensive numerical investigation

Metal foam is a porous medium with high porosity, convoluted flow pathways, strength-to-weight ratio, and thermal conductivity employed in heat exchanges and other engineering applications because of its properties. Therefore, a novel circular tube filled with aluminum metallic foam is proposed to improve hydraulic thermal performance and reduce pumping power losses and metal foam volume. The current work considers the Brinkman-Forchheimer Extended Darcy model for forced convection flow and the local thermal equilibrium (LTE) model for heat transfer under a constant thermal boundary condition. The governing equations are solved using the finite volume method (FVM). The variable parameters are the pore per inch (PPI) of 10–50, the porosity εrange of 0.79–0.95, and the Reynolds number range of 2500–7000. The results show that the performance index (PI) has its maximum value of 6.8 at 10PPI and ε =0.95 in the heat exchanger; this enhancement at 10PPI is 13% and 34.48% more as compared to the PI value at ε =0.85 and ε =0.79 and at a fixed inner annulus Re of 7000. The average Nusselt number (Nu) increased by 81.63%, 104.3%, and 120% compared to the foamless tube at 10, 20, and 30PPI andε =0.95, respectively, in an intermediate tube. Heat transfer coefficients (HTC) considerably increase compared to foamless tubes nearly 3.2 times, 3.8 times, and 4.2 times at 10, 20, and 30PPI, respectively, at 2500 Re and 144%, 175% and 200% more at 7000 Re. The maximum reduction ratio in normalized friction factor ratio (fP/fNoP) at 10PPI is approximately 50% compared to (fP/fNoP) at 30PPI and 25% at 20PPI; it occurs at 7000 Re. The normalized area goodness factor ratio has the maximum value at 10PPI and ε =0.95, which is 5.8, and for 20 and 30PPI, it is 3.5 and 2.3, respectively. This shows that aluminum metal foam in triple tube heat exchanger's intermediate tube at 10PPI and porosity of 0.95 can be the optimized results for performance enhancement.

Enhanced heat transfer in sandwich heat transfer unit with metal foam: A numerical investigation

In this study, a novel configuration of a sandwich heat transfer unit (SHTU) is proposed, characterized by the partial filling of metal foam on both sides of the fin. The thermal–hydraulic characteristics of the SHTU are investigated numerically using the local non-equilibrium method and Forchheimer-Brinkman extended Darcy model, and compared with those of traditional flat plate-fin heat transfer unit (PHTU). The effect of geometrical parameters, mass distribution of fin and metal foam, and morphological parameters of metal foam on the characteristic of SHTU was explored. Compared to PHTU the Nusselt number of SHTU increases by 13.1% and 27.6%, while the friction factor increases by 6.2% and 33.1% at Reynolds numbers of 100 and 900, respectively. At a Reynolds number of 500, as the filling ratio increases from 0 to 0.95, the Nusselt number, friction factor, and comprehensive thermal performance enhancement increase by factors of 10, 20, and 3, respectively. When the foam fraction increases from 0.30 to 0.90, the thermal performance enhancement improves by 4–5 times within the investigated range. The impact of porosity (ε) and pore density (ω) on the performance of SHTU is not monotonic. The optimal ω was observed to be in the range of 15–20 PPI, while the optimal ε was found between 0.90–0.92.

Investigation of Magneto-convection in Viscoelastic Fluid Saturated Anisotropic Porous Layer Under Local Thermal Non-equilibrium Condition

The problem of magneto-convection in viscoelastic fluid saturated anisotropic porous layer under local thermal non-equilibrium (LTNE) effect is investigated. Extended Darcy model with time derivative term for viscoelastic fluid of the Oldroyd type with an externally imposed vertical magnetic field is used to model the momentum equation. The entire investigation has been split into two parts: (i) linear stability analysis (ii) weakly non-linear stability analysis. We perform normal mode technique to examine linear stability analysis while truncated representation of Fourier series method is used for weakly non-linear stability analysis. The onset of convection is set in through oscillatory rather than stationary mode due to competition between the processes of thermal, magnetic effect and viscoelasticity. A comparative study between anisotropic and isotropic porous medium is made as a function of Q (Chandrasekhar number), 𝛤 (non dimensional inter phase heat transfer coefficient), 𝜆1 (Relaxation time) and λ2 (Retardation time). Apart from this, Q, 𝛤 and λ2 stabilize the system in oscillatory case while 𝜆1 destabilize the system. Furthermore 𝜉 (mechanical anisotropic parameter), 𝜂s (thermal anisotropic parameter for solid phase), destabilizes the system and 𝜂f (thermal anisotropic parameter for fluid phase) stabilizes the system. The effect of Q, 𝜆1, λ2, 𝛤, 𝜉, 𝜂f and 𝜂s on heat transfer is also examined.

A parallel computational study of power-law non-Newtonian nanofluid in a C-shaped enclosure by multiple-relaxation-time lattice Boltzmann simulation

ABSTRACT This study aims to numerically examine the heat transfer and entropy generation of non-Newtonian power-law nanofluids in a C-shaped cavity filled with porous media considering the Brinkman-Forchheimer extended Darcy model (BFEDM). The graphics processing unit (GPU) based multiple-relaxation-time lattice Boltzmann method (MRT-LBM) was used through computing unified device architecture (CUDA) C/C++ platform. It is a known fact that the fluid viscosity varies with the shear rate and nanoparticle sizes and the thermal conductivity also varies with the fluid temperature. However, the extension of such phenomena needs to be further investigated to understand any specific threshold in heat transfer application. To leverage such characteristics, it is permissible to add certain input parameters. As a result, the power-law indices ( n ), the Darcy number ( Da ), the volume fraction of nanoparticles ( ϕ ), the Rayleigh number ( Ra ), and the fixed porosity ( ε = 0.4 ) were the five key parameters considered to analyze the numerical results. The GPU-based numerical code was validated with the available benchmark results, and good agreements were obtained. The results showed that the average rate of heat transfer in terms of the average Nusselt number ( Nu ‾ ) increased due to an increase in Ra due to the enhanced buoyancy force and a reduction in the .

Analysis of heat transfer in a parallelogram-shaped cavity with porous medium under non-uniform temperature

This study investigates fluid flow and natural convection heat transfer in a parallelogram-shaped cavity with a porous medium under non-uniform temperature condition. The bottom wall is heated with a non-uniform temperature, the side walls are cooled, and the upper wall is adiabatic. The governing equations, along with corresponding boundary conditions, are formulated in dimensionless stream function and vorticity using the extended Darcy model for the porous medium. The equations are solved by employing the finite difference method. The study presents outcomes for isotherms, streamlines, and Nusselt numbers across range of parameters, including the Rayleigh number (104≤Ra≤108), Darcy number (10−1≤Da≤10−6), Prandtl numbers (Pr=0.71,1,7.1), fluid porosity (ϵ=0.8), and inclination angles (30∘≤ϕ≤90∘), about flow and heat transfer characteristics. The results indicate that an increase in Ra, Pr, and ϕ, along with a decrease in Da, leads to an enhancement in the strength of vortexes. It is observed that for constant Ra⁎=RaDa, Rate of heat transfer increases with an increase in Ra and a decrease in Da. The maximum value observed is 10.15. Also rate of Heat transfer increases with the increase in angle and maximum rate of heat transfer is observed at ϕ=90∘.

IMPACT OF POROUS AND MAGNETIC DISSIPATION ON DISSIPATIVE FLUID FLOW AND HEAT TRANSFER IN THE PRESENCE OF DARCY-BRINKMAN POROUS MEDIUM

In this article, the boundary layer flow of an electrically-conducting fluid through a porous medium attached with a radiative permeable stretching sheet is analyzed. Following the Brinkman theory, an extended Darcy model (Darcy-Brinkman model) is utilized for the model momentum equation. Heat transfer analysis is also performed in the presence of viscous and Joule dissipation. Moreover, in the modeling of the energy equation, the effects of internal heating resulting from the mechanical effort required to squeeze out the fluid through the porous medium are also included in porous dissipation. Suitable dimensionless variables are introduced to convert the governing boundary layer equations into a dimensionless form, which are then converted into self-similar, nonlinear ordinary differential equations by utilizing similarity transformations. The exact solution of the nonlinear self-similar momentum equation is obtained in the form of the exponential function. In contrast, the solution of the energy equation is computed through the Laplace transform technique in the form of Kummer confluent hypergeometric functions. Effects of involved physical parameters on the momentum boundary layer (MBL), thermal boundary layer (TBL), wall shear stress, and local Nusselt number are explored through graphs and tables. Moreover, the slope linear regression (SLR) technique is used to calculate the rate of decrease/increase in shear stress and the rate of heat transfer at the boundary. The velocity and momentum boundary layer decreases for large values of porosity parameter and increases by increasing the viscosity ratio. The shear stress increases by increasing the porosity parameter, Hartman number, and suction parameter, while the opposite effect is examined with increasing values of viscosity ratio parameter. Heat transfer rate also enhances by increasing the Brinkman viscosity ratio parameter and wall suction velocity.

Free Convection Heat Transfer in Composite Enclosures with Porous and Nanofluid Layers

This work conducts a numerical investigation of convection heat transfer within two composite enclosures. These enclosures consist of porous and nanofluidic layers, where the porous layers are saturated with the same nanofluid. The first enclosure has two porous layers of different sizes and permeabilities, while the second is separated by a single porous layer. As the porous layer thickness approaches zero, both enclosures transition to clear nanofluid enclosures. The study uses the Navier–Stokes equations to govern fluid flow in the nanofluid domain and the Brinkman–Forchheimer extended Darcy model to describe flow within the saturated porous layer. Numerical solutions are obtained using an iterative finite difference method. Key parameters studied include the porous thickness ( 0.0 ≤ S ≤ 1.0 ), the nanoparticle volume fraction ( 0.0 ≤ ϕ ≤ 0.05 ), the thermal conductivity ratio ( 0.5 ≤ R k ≤ 10 ), and the Darcy number ( 10 − 5 ≤ D a ≤ 10 − 2 ). Key findings include the observation that the highest heat transfer is achieved at the highest concentration, regardless of the porous layer configuration, permeability value, or thermal conductivity ratio. Specifically, an augmentation in values of N u ― I up to 22% is obtained as concentration is adjusted from 1% to 5%. Similarly, an augmentation in values of N u ― II up to 25% is obtained as concentration is adjusted from 1% to 5%.

Optimization of entropy generation and thermal mechanism of MHD hybrid nanoliquid flow in a sinusoidally heated porous cylindrical chamber

The present computational investigation explores the fluid and thermal characteristics along with entropy generation due to buoyancy-driven magnetohydrodynamic (MHD) convective flow of aqueous hybrid nanoliquid filled in a nonuniformly heated porous cylindrical chamber. The fluid motion in the enclosure is modeled by Brinkman — extended Darcy model. The modeled equations are resolved by finite difference approach. The computations are conducted for Rayleigh number (103–105), Hartmann number (0–50), Darcy number (10−5–10−1), different nanoparticle shapes and nanoparticle volume fraction (Ag/MgO: 0–0.05) to understand the characteristic of flow, thermal and irreversibility distribution. With vast numerical simulations, the outcomes reveal that though the buoyancy force is greater, the fluidity cannot be enhanced unless the permeability and magnetic field strength are optimally maintained. As Ra,Ha and Da is varied respectively from 103 to 105, 50 to 0 and 10−5 to 10−1, the fluidity has been enhanced by 99.39%,83.26% and 99.79%. Among all considered parametric combinations, it has been noticed that the choice of Ha=0,Ra=105,Da=10−1 with proper ratio of nanoparticles enhance the system efficiency. However, minimal entropy generation can be achieved with greater Hartmann and lower Darcy numbers. Furthermore, it has been found that blade shaped nanoparticles lead to increase the performance of thermal system.

Analyzing the pressure drop in spacer stacks for electrodialytic processes considering the effect of mechanical compression: Experimental vs. free and porous flow model prediction

There is a growing interest in using electromembrane processes in sustainable applications. However, it involves designing efficient cells with low pressure drops, which is particularly important in processes requiring high energy efficiency. In order to analyze the fluid dynamics in spacer-filled channels, manifolds and stacks used primarily in acid base flow batteries a free and porous flow model was developed. The predictive model composed by Navier-Stokes equations and Brinkman Forchheimer extended Darcy model closely follows the experimental pressure drop in a single spacer-filled channel. According to the model results, the entrance and exit zones of the spacer produce the highest pressure drop per axial longitude, highlighting the strong effect of the design of spacer in these zones. In the case of stacks the mechanical compression among spacers as revealed by measurement with compression film suggests some spacer deformation on entrance and exit zones that intensified the inlet and outlet effects.

Computational analysis of nonsimilar electromagnetohydrodynamic radiative nanofluid flow across Darcy–Forchheimer–Brinkman porous media

This study develops nonsimilar analysis for the electrically conducting nanofluid flow over a vertically placed stretching surface adjacent to porous medium with transverse magnetic field assumption. The features of thermal radiations, viscous dissipation, and heat source factors are also incorporated to scrutinize the thermal prospective. The Brinkman–Forchheimer who extended Darcy model is considered for the porous medium and a Rosseland approximation is employed for thermal radiations. Titanium oxide and silica are considered nanoparticles, while kerosine oil and silicon ceramic serving as the base fluids in porous medium, respectively. Tiwari–Dass approach is used to derive the governing system. Appropriate transformations are deployed to render the governing partial differential equations into a dimensionless system. To address the transformed system, the local nonsimilarity technique in conjunction with the bvp4c (fourth-order method boundary value problem) is used. Variations in velocity and thermal distributions of nanofluids have been investigated in relation to developing dimensionless parameters such as nanoparticle concentration, Darcy porosity parameter, Darcy number, electric parameter, Hartmann number, radiation parameter, Richardson number, heat source/sink parameter, and Eckert number. Numerical findings are found to interpret the role of the emerging parameters on physical quantities. The obtained findings reveals that the surge in the estimations of Richardson number enhances the nanofluid velocity while it diminishes the temperature profile. The concentration of nanoparticles improves the thermal profile of both nanofluids under consideration, whereas the enhancement in Darcy porosity parameter reduces velocity and improves temperature distributions. Results found to be in excellent agreement with published results on a special case of the considered problem.

Three-dimensional transient CFD modeling of multiple finned aluminum foam heat sinks in a horizontal channel

Finned metal foam heat sinks are well-known because of their excellent performance in cooling of powered electronics. In this study, three-dimensional transient numerical simulations of finned aluminum foam heat sinks in a forced convection of air were carried out using commercial COMSOL. The geometry under consideration consists of an array of finned aluminum foam heat sinks mounted on heater blocks and placed on a plate in a horizontal channel. Heat sink aluminum foam regions were considered as porous media with a local non-equilibrium thermal model to evaluate thermal characteristics, while the Forchheimer-Brinkman extended Darcy model is considered for the flow analysis. Our main concern in the present study is to evaluate the transient thermal–hydraulic behavior and the cooling performance under constant flux heat sources while varying the Reynolds number and variable morphological parameters of the aluminum foam, i.e., porosity (ε) varied from 0.85 to 0.95. The thermal performance ratio and the average Nusselt number of the finned aluminum foam heat sinks are 23.14% and 30%, respectively, larger than the finned aluminum heat sinks. As the Reynolds number increases, the thermal characteristics are enhanced, and the pressure drop is increased. An increase in porosity causes a reduction in heat transfer rate and an elevation of pressure drop.

Mathematical modeling of unsteady convective flow analysis of water and nano-encapsulated phase change particles in composite enclosure subject to rotation

Free convection heat transfer in water and hybrid particles in an enclosure is studied. A layer of porous material with various thickness and permeability is attached to the enclosure. Both fluid and porous layers rotate with a specific speed. Hybrid particles are formed by a polyurethane (PU) and an N-nonadecane (ND). PU acts as shell and ND goes through a phase change and it capables of preserving and releasing a considerable amount of latent heat. The enclosure movement can be controlled through a rotation speed. The Brinkman-Forchheimer extended Darcy model is used for governing the flow within a fully saturated porous layer. The governing equations for the convective flow and phase change heat transfer, including specific heat capacity and permeability, were introduced and solved by FEM. The impact of the porous thickness, permeability, fusion temperature and rotation speed on the heat capacity ratio, streamline and isotherms structures were investigated. The results showed that a high Darcy number and thin porous thickness were a good candidate for the improvement of average heat transfer rate since reinforcing the melting process and heat transmitting.

Heat Transfer and Performance Enhancement of Porous Split Elliptical Fins

To augment the heat transfer phenomenon, the infusion of various fin geometry over the heated plate is being investigated by various researchers. Solid fins of the porous medium can enhance the convective heat transfer, providing a higher surface area-to-volume ratio for heat transfer. In this work, the fluid flow pattern and thermodynamic analysis of porous-based split elliptical fins mounted staggered over a heated base plate is numerically studied with the Reynolds numbers in the range of 783 to 1839, which is dependent on the fin dimension. The variable parameters were dimensionless transverse offset ( TO ∗ = transverse offset / diameter ), which varied from 0 to 0.5; dimensionless longitudinal offset ( L O ∗ = longitudinal offset / diameter ), which varied from 0 to 0.25; porosity (ɸ), which varies from 0.8 to 0.92; pores per inch (PPI), which was 10; permeability ( P n ); and inertial parameter ( F ). To count the viscous and inertial effect inside the porous zone, the Forchheimer–Brinkman extended Darcy model was adopted. The associated parameters, the Nusselt number (Nu), frictional coefficient ( C f ), and performance evaluation criteria (PEC), are thoroughly analyzed over the TO ∗ and LO ∗ combination. The results of the investigation revealed that the highest value of Nu and PEC was obtained by TO ∗ = 0.5 and L O ∗ = 0 at ɸ = 0.92 , which were approximately 54% and 79% higher than the solid circular fin at Re = 1839 . Additionally, a response function based on Nu was obtained using the response surface method, and cuckoo optimization was assessed to identify the optimal Nu. The optimal Nu is established at TO ∗ = 0.4141 and L O ∗ = 0 ( ɸ = 0.92 and Re = 1839 ) and was validated with the present investigation with an accuracy of 1.20%.

Impact of titling angle and density extremum on transient convection in a porous chamber with sinusoidal heating

The aim of the present study is to investigate numerically the 2D unsteady transient convection of cold water near its highest density value in an inclined square porous enclosed space. The horizontal walls are kept in adiabatic condition. The temperature of left sidewall varies in sinusoidal manner whereas the opposing right sidewall is sustained with constant lower temperature. The range of angle of inclination is considered from 0° to 90°. The finite volume method (FVM) was applied to portray all mathematical equations. The special outcome of inclination angle, Darcy number, maximum density parameter and porosity are obtained in the present study with the use of Brinkmann–Forchheimer extended Darcy model. The change in the angle of inclination is noteworthy in the structure and direction of the flow of the fluid. The bicellular structure of the fluid is identified because of the density inversion effect. Increasing Darcy number and porosity values enhance the average rate of energy transport across the chamber. The lowest heat transfer is noticed for due to supreme density effect. Here the energy transfer from one cell to another cell is by conduction mode due to the existence of dual cell structure.

Exact analytical solution of forced convection through a porous‐saturated duct

AbstractIn the current paper, the effect of a magnetic field on the fully developed forced convective flow and heat transfer is studied. An exact solution is extracted when the flow in the porous medium is governed by the Brinkman–Forchheimer Extended Darcy model. First, the problem formulation is explained to obtain a new system of mathematical formulation. Then, by utilizing the properties which are imposed into the problem, the exact closed‐form analytical solution of the problem is explored. Finally, the main results are illustrated to show the impact of the porous media‐shaped parameter, magnetic parameter, Forchheimer number, and viscosity ratio. It should be mentioned that the asymptotic results achieved in this study were compared with the exact results and it is found that they are in good agreement.

DOUBLE DIFFUSIVE FREE CONVECTION IN A PACKED BED SQUARE ENCLOSURE BY USING LOCAL THERMAL NON-EQUILIBRIUM (LTNE) MODEL

In the present study, free convection heat and mass transfer of fluid in a square packed bed enclosure is numerically investigated. For the considered geometrical shape, the left vertical wall of enclosure was assumed to be kept at high temperature and concentration while the opposite wall was kept at low temperature and concentration with insulating both the top and bottom walls of enclosure. The Brinkman– Forchheimer extended Darcy model was used to solve the momentum equations, while the energy equations for fluid and solid phases were solved by using the local thermal non-equilibrium (LTNE) model.Computations are performed for a range of the Darcy number from 10-5 to 10-1, the porosity from 0.5 to 0.9, and buoyancy ratio from -15 to 15. The results showed that both the buoyancy ratio and the packed bed characteristics have significant effect on each one of the flow field, heat transfer and mass transfer.

Integrated intelligent neuro computing technique for mixed convective flow and heat transfer in heterogeneous permeability media

This article examines the flow and heat transfer characteristics of variable permeability such as linear, exponential and quadratic permeability functions with Brinkmann–Forchheimer extended Darcy model by utilizing the intelligent computing paradigm via artificial Levenberg–Marquardt back propagated neural networks (ALM – BPNNs). The vertical porous channel walls are considered as electrically conducting and non-conducting. The variable permeability and induced magnetic field effects are significant on flow and heat transfer. To solve the obtained governing equations, finite element method is adopted. It is observed that for the three cases of permeability functions, increase in Hartmann number drops the velocity profile and is accompanied with an increase in the fluid thermal state level. The significance of the Brinkmann number on the fluid temperature in all the cases of permeability indicates a rise in temperature due to increased heat generation. But, the reverse effect is observed when the mixed convection parameter rises, and the boundary layer thickness reduces due to which temperature drops for distinct cases of permeability under consideration. The heat transfer characteristics are analyzed through an artificial neural network and multiple linear regression models. The present work finds its applications in studying packed bed heat exchangers and fixed-bed catalytic reactors.

Performance analysis of porous-based taper-shaped fin for enhanced heat transfer rate using cuckoo search algorithm

This paper deals with the thermal and fluid flow behavior of porous and non-porous fins. Initially, a solid heat sink with circular fins is analyzed and validated. Further work is done making circular tapered porous fin of the same volume and height as of uniform circular fin. The geometrical parameters are porosity (Ø = 0.1–0.92), pore diameter ( dp), fiber diameter ( df), radius ratio ( R*), and pores per inch (PPI = 10). Four different cases viz., case I ( R* = 1.2), case II ( R* = 1.5), case III ( R* = 2), and case IV ( R* = 4) of taper porous fins are considered in a computational domain with Reynolds number ( Re) ranging 400–1900 (based upon channel inlet parameter) and air as working fluid. The Forchheimer–Brinkman extended Darcy model is considered to characterize the flow in porous media. The value of Nusselt number ( Nu), friction factor ( f), and thermal performance factor (TPF) is evaluated. Results reveal that, for case I at Ø = 0.92 and PPI = 10, the value of Nu and TPF is approximately 63% and 159% higher than solid circular fin at Re = 1876.11. For case IV, the reduction in pressure drop is approximately 21.15% compared to solid circular fin at Re = 1876.11. For optimum Nu, a cuckoo search optimization is evaluated using the response surface method. Upon examination, the optimum Nu is obtained at the combination of R* = 1.2, Ø = 0.92, and Re = 1876.11, which got validated against the numerical work with 0.15% accuracy.

Effects of viscous and darcy dissipation on fully developed natural convection flow in a composite channel partially filled with porous material: Homotopy perturbation method (HPM)

AbstractA steady natural convection flow in a composite channel partially filled with porous material is investigated analytically in this paper. In this respect, the effects of heat generation due to viscous dissipation and darcy dissipation were considered in the energy equations of the porous region and that of clear fluid region. In addition, the Brinkmann extended Darcy model was applied to model the flow in the porous region. The coupled system of nonlinear ordinary differential equations that governed the flow is solved by the homotopy perturbation method. The analytical solution results for velocity, temperature, and Nusselt number are provided and analyzed. The investigation reveals that increase in the thickness of the porous region hampers the hydrodynamics while it promotes the thermodynamics within the composite channel.

Validation of the local thermal equilibrium assumption for free convection boundary layer flow over a horizontal cylinder embedded in an infinite saturated porous medium

This study numerically investigated the validity of the local thermal equilibrium model for free convection over a horizontal cylinder embedded in an infinitely packed bed of spherical particles saturated with Newtonian fluid. The local thermal non-equilibrium and Forchhemimer-Brinkman extended Darcy model were used by considering the boundary-layer theory assumptions and were solved with the implicit Keller box finite difference scheme. The governing parameters considered are the porosity, thermal conductivity ratio, Rayleigh number, Prandtl number, the ratio of cylinder diameter to spherical particle diameter and Biot number. The results showed the two parameters of conductivity ratio and Biot number can significantly affect the other parameters. For low Biot number and conduction coefficient ratio, the local thermal non-equilibrium assumption was inapplicable in almost all cases. Significantly, for high values of the conductivity ratio and Biot number, the assumption that the fluid and solid matrix are isothermal, could be used in almost all cases studied. Furthermore, increasing the amount of Rayleigh number, Porosity and Prandtl increased the temperature difference between the solid and fluid phases. In addition, increasing the ratio of cylinder diameter to particle diameter reduced the temperature difference between the two phases. The average temperature difference between fluid and solid can have the most changes as follows: It can experience 200% growth when the Prandtl number changes from 2 to 7. Also, it can reduce by 33% by increasing the Bio number from 0.01 to 10. In addition, the temperature difference of two phases can be increased by 7 and 0.5 times by increasing the porosity from 0.25 to 0.85 and increasing the ratio of cylinder diameter to particle diameter from 20 to 100, respectively.