Brinkman-Forchheimer Extended Darcy Model Research Articles

Analysis of the heat transfer and airflow in solar chimney drying system with porous absorber

In this paper, the chimney is assembled with porous absorber for the indirect-mode solar dryer. Local thermal non-equilibrium (LTNE) exists in the porous absorber, so the double energy equations and Brinkman–Forchheimer extended Darcy model are employed to analyze the heat transfer and flow in the solar porous absorber, and the k-ε turbulent model coupled with the above equations are also used to investigate the influences of the porous absorber inclination and the height of drying system on the heat transfer in the solar dryer. The specific heat capacities (ρc) and thermal conductivity ks have remarkable effects on the average temperature of solar porous absorber in the drying system. The mean temperature of the higher (ρc) Aluminous solar absorber is lower and the top temperature of porous absorber delays due to lower thermal conductivity ks. The inclined angle of porous absorber influences the airflow and temperature field in the solar dryer greatly. With the height of solar dryer changing from 1.41 m to 1.81 m, the higher airflow velocity and the lower temperature at chimney exit can be achieved. The simulations agree with the published experimental data. All these results should be taken into account for the promotion and application of the solar chimney dryer with porous absorber.

Rotation effects on non-Darcy convection in an enclosure filled with porous medium

Natural convection heat transfer in a rotating, differentially heated enclosure is studied numerically in this paper taking into consideration the Forchheimer–Brinkman-extended Darcy model. The enclosure is filled with a fluid-saturated porous medium and executes a steady counterclockwise angular velocity about its longitudinal axis. The staggered grid arrangement together with the Marker and Cell (MAC) method was employed to solve the governing equations. The governing parameters considered are the porosity, 0.4≤ϵ≤0.99, the Darcy number, 0.005≤Da≤0.01 and the Taylor number, 8.9×104≤Ta≤3.8×105, and the centrifugal force is assumed weaker than the Coriolis force. It is found that higher porosities have weaker flow circulation when the Coriolis effect is smaller than the buoyancy effect. The global quantity of the heat transfer rate increases by increasing the porosity and the Darcy number and decreases by increasing the Taylor number.

Numerical Analysis of Natural Convection in Porous Media Subjected to Electromagnetic Energy Using Local Thermal Nonequilibrium (LTNE) Models

The present work numerically investigates the natural convection of fluid in saturated porous media under an electromagnetic field. The porous medium consists of water and spherical solid particles. The Brinkman–Forchheimer extended Darcy model for the momentum equation is employed, and two energy equations are solved with local thermal nonequilibrium (LTNE) models. The study aims at a comprehensive analysis of the influence of material properties, microwave power levels, and operating frequencies on the transport processes in porous media. The results show that all effects have significant consequences on the flow field and heat transfer in porous media. These findings can explain the phenomena taking place inside saturated porous media in electromagnetic wave drying processes using LTNE and local thermal equilibrium (LTE) models.

Natural Convection in a Porous Cavity with Sinusoidal Heating on Both Sidewalls

A numerical study has been performed on buoyancy-induced convection in a square porous cavity. The vertical sidewalls of the cavity are maintained with sinusoidal temperature distribution. The finite volume method is used to numerically solve the nondimensional governing equations. The Brinkman Forchheimer extended Darcy model is used in the present study. The results are analyzed over a range of the amplitude ratio, phase deviation, porosity, and Grashof and Darcy numbers. It is found that the heat transfer rate is increased when increasing the amplitude ratio, porosity, and Darcy number. The nonuniform heating on both sidewalls provides higher heat transfer rate than the nonuniform heating of one wall.

Transient behavior of fluid flow and heat transfer in vertical channels partially filled with porous medium: Effects of inertial term and viscous dissipation

In this article, transient hydrodynamic and heat-transfer behavior of Newtonian fluid flow in vertical parallel-plate channels partially filled with a porous medium has been investigated numerically. In this regard, the influences of macroscopic local inertial term and the viscous heating due to the viscous dissipation were taken into account in the momentum equations of porous region and the thermal energy equations, respectively. Moreover, Forchheimer–Brinkman extended Darcy model was used to model fluid flow in the porous region. In addition, an analytical solution was obtained in the case of negligible Brinkman and Forchheimer number values at the steady-state conditions. The predicted results were compared with those predicted by a two-parameter perturbation technique developed by the present authors at the steady-state conditions and good agreement was obtained. The predicted results clearly indicate that neglecting the inertial effect in high permeability porous media or high velocity flows can alter substantially the flow and heat transfer characteristics.

Simulation of mixed convection in a vertical channel containing discrete porous-covering heat blocks

A numerical investigation is made of fully developed laminar mixed convection in a vertical channel with multiple porous-covered heated blocks on one channel wall. The Brinkman–Forchheimer-Extended Darcy model with the Boussinesq approximation is used to characterize the flowfield inside the porous region. Solution of the coupled governing equations for the fluid/porous/solid composite system is obtained by utilizing control volume method through the use of a stream function-vorticity approach. The dependence of streamlines, isotherms, and local and overall mean Nusselt numbers on the governing parameters, such as the Darcy number, Reynolds number, Grashof number, effective conductivity ratio, and geometric parameter, is documented in detail. The results show that the strength and extent of recirculating flow induced by porous-covering block make significant changes in the cooling of block heater, especially on block back faces.

Numerical Model of Microwave Driven Convection in Multilayer Porous Packed Bed Using a Rectangular Waveguide

The present work studies numerically the heating of multilayer porous packed bed which is subjected to the microwave radiation with a rectangular waveguide. The multilayer porous packed bed consists of the layers of fine and coarse beds. The simulations of electromagnetic field are described by solving Maxwell’s equations with the finite difference time domain (FDTD) method. The flow fields and the temperature profiles are determined by the solutions of the Brinkman–Forchheimer extended Darcy model, energy, and Maxwell’s equations. The study aims to understand of the influences of layered configuration, layered thickness, and operating frequency on the transport processes in a multilayer porous packed bed. The results show that all parameters have significant effect on the distributions of electromagnetic field inside a waveguide, temperature profiles, and velocity fields within the multilayer porous packed bed.

The structural flow in pipe containing porous medium saturated with power-law fluid

In this article, the method of volume averaging of flow in porous media and averaging theorem was employed to the Navier-Stokes equations. The total drag force per unit volume was considered as the bulk damping resistance due to the porous structure (i.e., the Darcy resistance) and the resistance due to the inertia force (i.e., the Forchheimer resistance), then the Brinkman-Forchheimer extended Darcy model was obtained from average momentum equation. The structural flow in a pipe containing porous medium saturated with power law fluid was applied in the present study. A new theoretical analysis of fully developed non-Darcy flow in a pipe containing a fibrous medium saturated with power law fluid was conducted. Using the integration method, the boundary layer solutions were obtained for flow core velocity and its radius. These theoretical solutions were used to analyze the effects of the Darcy number and inertia parameter on the axial velocity profile in the porous medium pipe.

Analysis of nanofluid heat transfer in parallel-plate vertical channels partially filled with porous medium

In this article, mixed-convective heat transfer of nanofluids in a vertical channel partially filled with highly porous medium was studied. In the porous region, the Brinkman–Forchheimer extended Darcy model was used to describe the fluid flow pattern. Different viscous dissipation models were also applied to account for viscous heating. At the porous medium–fluid interface, interfacial coupling conditions for the fluid velocity and temperature were used to derive the analytical solution using a two-parameter perturbation method. The model used for the nanofluids incorporates the effects of Brownian motion and thermophoresis. With constant wall temperature, velocity and temperature profiles and expressions for the Nusselt number values were obtained for fully-developed fluid flow. In addition, a numerical analysis was conducted using finite-difference method to compare the obtained results. Finally, a parametric study was conducted to investigate the influences of various parameters on the fluid flow pattern and heat-transfer performance. The predicted results clearly indicate that the presence of nanoparticles in the base fluid enhances the heat-transfer process significantly.

Transient Buoyancy-driven Convection of Water Saturated Porous Cavity Near its Density Maximum

The transient buoyancy-driven convection in a water saturated porous cavity is studied numerically. The left vertical wall is considered into three different partially heating locations. The Brinkman-Forchheimer extended Darcy model is used to investigate the average heat transfer rate. The governing equations are solved using the finite volume method. The results obtained for various values of parameters are presented graphically in the form of streamlines, isotherms, and velocity at the mid-plane of the cavity. In addition, numerical results for the average Nusselt number are presented for various parametric conditions. It is found that the heat transfer rate is enhanced when the heating location is at the bottom of the cavity for increasing value of temperature.

Effect of aspect ratio on convection in a porous enclosure with partially active thermal walls

The aim of the present numerical investigation is to understand the effect of aspect ratio and partially thermally active zones on convective flow and heat transfer in a rectangular porous enclosure. Five different heating and cooling zones are considered along the vertical walls while the remaining portions of the sidewalls and top and bottom of the enclosure are adiabatic. The Brinkman–Forchheimer extended Darcy model is used in the study. The governing equations are solved by the finite volume method with the SIMPLE algorithm. The computations are carried out for a wide range of parameters and the results are presented graphically. The results reveal that the location of heating and cooling zones has a significant influence on the flow pattern and the corresponding heat transfer in the enclosure. The rate of heat transfer approaches to a constant value for very low values of the Darcy number. The heat transfer rate is decreased on increasing the aspect ratio.

Buoyancy induced convection in a porous cavity with partially thermally active sidewalls

This study reports a numerical investigation of the convective flow and heat transfer in a square porous cavity with partially active thermal walls. Five different heating and cooling zones are considered along the vertical walls while the remaining portions of the side walls as well as the top and bottom of the cavity are adiabatic. The Brinkman Forchheimer extended Darcy model is used in the present study and the resulting governing equations are solved by finite volume method with SIMPLE algorithm. The computations are carried out for a wide range of parameters and the results are presented graphically. The results reveal that the location of heating and cooling zones has a significant influence on the flow pattern and the corresponding heat transfer in the enclosure. The location of partial heating has different effect on velocity and heat transfer, and the heat transfer rate approaches to a constant value for very low values of the Darcy number.

Unsteady hydromagnetic convective flow in a vertical channel using Darcy–Brinkman–Forchheimer extended model with heat generation/absorption: Analysis with asymmetric heating/cooling of the channel walls

In the present paper transient as well as non-Darcian effects on laminar natural convection flow in a vertical channel embedded in a porous medium in the presence of uniform magnetic field applied normal to the flow region is studied. Forchheimer–Brinkman extended Darcy model is assumed to simulate momentum transfer within the porous medium. Approximate solutions are obtained using multi-parameter perturbation technique. Variations in the velocity field with Darcy number, Grashof number, kinematic viscosity ratio and variations in the temperature distribution are obtained and depicted graphically. Expression for the skin-friction and the rate of heat transfer at the channel walls are also derived and the numerical values for various physical parameters are presented in tabular form.

Mixed Convection in a Vertical Channel Containing Porous and Viscous Fluid Regions With Viscous Dissipation and Inertial Effects: A Perturbation Solution

In this paper, combined forced and natural convection in a vertical channel containing both porous and viscous regions taking into account the influences of inertial force and viscous dissipation has been studied. In this regard, fully developed fluid flow in the porous region was modeled using the Brinkman–Forchheimer extended Darcy model. To solve governing equations of both the porous and viscous regions including thermal energy and momentum equations, a two-parameter perturbation method was applied. The velocity and temperature distributions of both the regions were obtained in terms of various parameters such as inertial force, Grashof, Reynolds, and Brinkman numbers, as well as various types of viscous dissipation models. In addition, numerical solution was conducted using finite difference method to compare the results. The predicted results clearly indicate that the type of viscous dissipation model has significant effect on the temperature and velocity distributions. The acquired knowledge in this study can be used by designers to control channel flow as suitable for a certain application.

Non-Newtonian fluid flow in plane channels: Heat transfer enhancement using porous blocks

A numerical investigation is performed for heat transfer enhancement in a parallel-plate channel. Porous blocks are inserted to partially fill the channel, which is crossed by a power-law fluid. The modified Brinkman–Forchheimer extended Darcy model for power-law fluids is used in the porous layer while the Navier–Stokes equation are employed in the clear region of the channel. Results are reported for two cases: (1) a channel with a single porous block and (2) a channel with two porous blocks mounted alternatively at the bottom and top walls of the channel. The combined effects of both the porous blocks and the non-Newtonian fluid properties on the hydrodynamic and thermal characteristics of the flow are analyzed. To this end, computations are performed to highlight the effect of parameters such as the Darcy number, the Reynolds number, and the power-law index. For the case of the single porous block, the heat transfer is enhanced and maximized at low permeability. In the second configuration as well, heat transfer improvement can also be obtained, even if the thermal conductivity ratio is equal to 1. This enhancement is maximized for particular values of the Darcy number that depend on the flow pattern and the power-law index. Concerning the rheological aspect, it is found that pseudo plastic fluids exhibit the highest Nusselt number and the lowest pressure loss. The presence of the porous inserts causes a significant increase in pressure drop, which is found to be more important with dilatant fluids.

Brinkman–Forchheimer modeling for porous media thermoacoustic system

In this paper, analytical studies have been conducted on the flow and thermal fields of unsteady compressible viscous oscillating flow through channels filled with porous media representing stacks in thermoacoustic systems. The flow in the porous material is described by the Brinkman–Forchheimer–extended Darcy model. Analytical expressions for oscillating velocity, temperature, and energy flux density are obtained after linearizing and solving the governing differential equations with long wave, short stack, and small amplitude oscillation approximations. Experimental work is also conducted to verify the temperature difference obtained across the porous stack ends. To produce the experimental results, a thermoacoustic heat pump is designed and constructed where reticulated vitreous carbon (RVC) is used as the stack material. A very good agreement is obtained between the modeling and the experimental results. The expression of temperature difference across the stack ends obtained in the present study is also compared with the existing thermoacoustic literature. The proposed expression surpasses the existing expression available in the literature. The system of equations developed in the present study is a helpful tool for thermal engineers and physicist to design porous stacks for thermoacoustic devices.

Control of Flow and Heat Transfer in a Porous Enclosure due to an Adiabatic Thin fin on the Hot Wall

Natural convection flow in a differentially heated square enclosure filled with porous matrix with a solid adiabatic thin fin attached at the hot left wall is studied numerically. The Brinkman–Forchheimer-extended Darcy model is used to solve the momentum equations, in the porous medium. The numerical investigation is done through streamlines, isotherms, and heat transfer rates. A parametric study is carried out using the following parameters: Darcy number (Da) from 10−4 to 10−2, dimensionless thin fin lengths (Lp) 0.3, 0.5, and 0.7, dimensionless positions (Sp) 0.25, 0.5, and 0.75 with Prandtl numbers (Pr) 0.7 and 100 for Ra = 106. For Da = 10−3 and Pr = 0.7, it is observed that there is a counter clock-wise secondary flow formation around the tip of the fin for Sp = 0.5 for all lengths of Lp. Moreover when Da = 10−2 the secondary circulation behavior has been observed for Sp = 0.25 and 0.75 and there is another circulation between the top wall and the fin that is separated from the primary circulation. However, these secondary circulations features are not observed for Pr = 100. It is also found that the average Nusselt number decreases as the length of the fin increases for all locations. However, the rate of decrease of average Nusselt number becomes slower as the location of fin moves from the bottom wall to the top wall. The overall heat transfer rate can be controlled with a suitable selection of the fin location and length.

Non-Darcy effects on conjugate double-diffusive natural convection in a variable porous layer sandwiched by finite thickness walls

Steady conjugate double-diffusive natural convective heat and mass transfer in a two-dimensional variable porosity layer sandwiched between two walls has been studied numerically. The Forchheimer–Brinkman–extended Darcy model has been used to solve the governing equations in the saturated porous region. The flow is driven by a combined buoyancy effect due to both temperature and concentration variations. An exponential variation of the porosity near the hot wall is considered. The vertical walls are impermeable and subjected to a horizontal gradient of both temperature and concentration while the horizontal walls are adiabatic. A finite volume approach has been used to solve the dimensionless governing equations and the pressure velocity coupling is treated with the SIMPLE algorithm. The model has been validated with available experimental, analytical/computational studies.

Approximate Analytical Solutions for the Nonlinear Brinkman-Forchheimer-Extended Darcy Flow Model

New approximate analytical solutions for steady flow in parallel-plates channels filled with porous materials governed by non-linear Brinkman-Forchheimer extended Darcy model for three different physical situations are presented. These results are compared with those obtained from an implicit finite-difference solution of the corresponding time dependent flow problem. It is seen that the time dependent flow solutions yield the almost same steady state values as obtained by using the new approximate analytical solutions

Transient and non-Darcian effects on natural convection flow in a vertical channel partially filled with porous medium: Analysis with Forchheimer–Brinkman extended Darcy model

The present study addresses the transient as well as non-Darcian effects on laminar natural convection flow in a vertical channel partially filled with porous medium. Forchheimer–Brinkman extended Darcy model is assumed to simulate momentum transfer within the porous medium. Two regions are coupled by equating the velocity and shear stress in the case of momentum equation while matching of the temperature and heat flux is taken for thermal energy equation. Approximate solutions are obtained using perturbation technique. Variations in velocity field with Darcy number, Grashof number, kinematic viscosity ratio, distance of interface and variations in temperature distribution with thermal conductivity ratio, distance of interface are obtained and depicted graphically. The skin-friction and rate of heat transfer at the channel walls are also derived and the numerical values for various physical parameters are tabulated.