Brinkman-Forchheimer Extended Darcy Model Research Articles

충돌 공기제트에서 국한 유로 내 발포 알루미늄 방열기의 열전달 수치해석

A numerical study has been carried out to investigate the flow and heat transfer from an aluminum foam heat sink in a confined channel. A uniform heat flux is given at the bottom of the aluminum foam heat sink, which is horizontally placed on the heated surface. The channel walls are assumed to be adiabatic. Cold air is supplied from the top opening of the channel and exhausted to the channel outlet. Comprehensive numerical solutions are acquired to the governing Wavier-Stokes and energy equations, using the Brinkman-Forchheimer extended Darcy model and the local thermal non-equilibrium model f3r the region of porous media. Details of flow and thermal fields are examined over wide ranges of the principal parameters; i.e., the Reynolds number Re, the height of heat sink h/H, porosity and pore diameter ratio .

EFFECT OF ANISOTROPY IN PERMEABILITY AND EFFECTIVE THERMAL CONDUCTIVITY ON THERMAL PERFORMANCE OF AN ALUMINUM FOAM HEAT SINK

A numerical study has been carried out to investigate the thermal characteristics of an aluminum foam heat sink. An aluminum foam heat sink horizontally placed in a channel is modeled as a hydraulically and thermally anisotropic porous medium. A uniform heat flux is given from the bottom of the heat sink. Cold air is supplied from the top opening of the channel and exhausts to the channel outlet. Comprehensive numerical solutions are acquired to the governing Navier-Stokes and energy equations, using the Brinkman-Forchheimer extended Darcy model for the region of heat sink. It is assumed that the solid is in the local thermal equilibrium with the fluid. Details of flow and thermal fields are examined over wide ranges of the principal parameters: the Darcy number Da, the anisotropic permeability ratio K*(=K 2/K 1), and the anisotropic effective thermal conductivity ratio k*(=k 2/k 1). The results indicate that the anisotropy in permeability and effective thermal conductivity yields a significant change in the heat transfer rate. The same numerical approach that involves the anisotropic porous medium model is also applied to the thermal analysis of a conventional pin-fin heat sink.

Forced Convection Heat Transfer with Evaporation in a Heat Generating Porous Medium

A numerical investigation of internal forced convective flow with boiling through a duct filled with a heat generating porous medium is carried out. At a first stage, inertial as well as variable porosity effects are considered using a homogeneous, two-phase flow model and the Brinkman—Forchheimer extended Darcy model. The capillary effects and liquid-vapor slip are considered next using the multiphase mixture model (MMM). Nonlocal thermal equilibrium between the flowing fluid and the solid matrix is accounted for in each case using two energy equations. The results presented in this work provide detailed information on the influences of wall channeling and capillary effects on velocity and temperature fields in both subcooled and boiling regions. The vapor production process Is studied for various values of the heat generation rate. To end, comparisons are made between the two approaches used in this study.

Natural convection due to heat and mass transfer in a composite system

A numerical study is performed to analyse heat and mass transfer phenomena due to natural convection in a composite cavity containing a fluid layer overlying a porous layer saturated with the same fluid. The flow in the porous region is modelled using Brinkman–Forchheimer-extended Darcy model that includes both the effect of macroscopic shear (Brinkman effect) and flow inertia (Forchheimer effect). The vertical walls of the two-dimensional enclosure are isothermal whilst the horizontal walls are adiabatic. The two regions are coupled by equating the velocity and stress components at the interface. The resulting coupled equations in non-dimensional form are solved by an alternating direction implicit method by transforming them into parabolic form by the addition of false transient terms. The numerical results show that the amount of fluid penetration into the porous layer depends strongly upon the Darcy, thermal and solutal Rayleigh numbers. Average Nusselt number decreases while average Sherwood number increases with an increase of the Lewis number. The transfer of heat and mass on the heated wall near the interface depends strongly on the Darcy number.

Forced Convection of a Power-Law Fluid in a Porous Channel—Integral Solutions

The integral method based on the boundary layer analysis is used to conduct a theoretical study of the primary hydrodynamic and heat transfer mechanisms for forced convection of a power-law fluid in a porous channel for both cases of uniform heat flux (UHF) and uniform wall temperature (UWT) boundary conditions. The flow in the porous medium is modeled using the modified Brinkman—Forchheimer-extended Darcy model for power-law fluids. The results indicate that for a high-permeability porous medium, the thickness of the momentum boundary layer depends on the Darcy number, inertia parameter, and power law index, but for a low-permeability porous medium it depends only on the Darcy number. Consequently in the non-Darcy regime, the effects of power law index on hydrodynamic and heat transfer behaviors in the porous channel are significant, whereas in the Darcy regime, the effects of Darcy number are predominant. Also the hydrodynamic behavior of shear thickening fluids (n > 1.0) is more sensitive to the Darcy number whereas the behavior of shear thinning fluids (n < 1.0) is more sensitive to the inertia parameter in the non-Darcy regime. Based on the fully developed Nusselt number solutions, the valid region for the applicability of the present integral method is illustrated graphically. The valid region of the integral solutions covers the Darcy regime for any value of the power law index within the range considered, while in the non-Darcy regime, the valid region for a shear thinning fluid becomes smaller than that for a shear thickening fluid as the inertia parameter decreases.

Forced convection cooling enhancement by use of porous materials

Abstract Results are presented for laminar forced convection cooling of heat generating blocks mounted on a wall in a parallel plate channel. The effect on heat transfer of insertion of a porous matrix between the blocks is considered. The flow in the porous medium is modeled using the Brinkman–Forchheimer extended Darcy model. The mass, momentum and energy equations are solved numerically by a control-volume-based procedure. The local Nusselt number at the walls of the blocks, the mean Nusselt numbers and the maximum temperature in the blocks are examined for a wide range of Darcy number and thermal conductivity ratio. The computations are first conducted for a single block, then for evenly mounted blocks. The results show that the insertion of a porous material between the blocks may enhance the heat transfer rate on the vertical sides of the blocks. Although the porous matrix reduces the heat transfer coefficient on the horizontal face, significant increases in the mean Nusselt number (up to 50%) are predicted and the maximum temperatures within the heated blocks are reduced in comparison with the pure fluid case.

Enhancement of natural convection heat transfer from an array of discrete heat sources

Single-phase, natural convection heat transfer data have been obtained for an array of highly-finned, discrete heat sources mounted to one wall of a cavity filled with a dielectric liquid (FC-77). Dense, parallel plate fin arrays were considered for both vertical and horizontal cavity orientations, and the finned surfaces were found to enhance heat transfer by as much as a factor of 24. Thermal resistances approaching 2 cm 2°C W −1 were realized, while maintaining the temperature difference between the fin base and an opposing cold plate below 70°C. In a parallel numerical study, flow and heat transfer conditions were calculated by treating the fin array as a porous medium characterized by the Brinkman-Forchheimerextended Darcy model. The model provided a reasonable approximation which captured the experimental trends and predicted the data to within 30%.

Numerical Study of Forced Convection in a Partially Porous Channel With Discrete Heat Sources

A numerical study was performed to analyze steady laminar forced convection in a channel partially filled with a fluid-saturated porous medium and containing discrete heat sources on the bottom wall. Hydrodynamic and heat transfer results are reported for the configuration in which the porous layers are located above the heat sources while the rest of the channel is nonporous. The flow in the porous medium was modeled using the Brinkman-Forchheimer extended Darcy model. Parametric studies were conducted to evaluate the effects of variable heat source spacing and heat source width on heat transfer enhancement and pressure drop in the channel. The results indicate that when the heat source spacing was increased within the range considered, there was a negligible change in heat transfer enhancement while the pressure drop decreased significantly. When the heat source width was decreased, there was a moderate increase in heat transfer enhancement and a significant decrease in pressure drop.

Forced Convection in a Porous Channel With Localized Heat Sources

A numerical study is performed to analyze steady laminar forced convection in a channel filled with a fluid-saturated porous medium and containing discrete heat sources on the bottom wall. Hydrodynamic and heat transfer results are reported for two configurations: (1) a fully porous channel, and (2) a partially porous channel, which contains porous layers above the heat sources and is nonporous elsewhere. The flow in the porous medium is modeled using the Brinkman-Forchheimer extended Darcy model. Heat transfer rates and pressure drop are evaluated for wide ranges of Darcy and Reynolds numbers. Detailed results of the evolution of the hydrodynamic and thermal boundary layers are also provided. The results indicate that as the Darcy number decreases, a significant increase in heat transfer is obtained, especially at the leading edge of each heat source. For fixed Reynolds number, the length-averaged Nusselt number reaches an asymptotic value in the Darcian regime. In the partially porous channel, it is found that when the width of the heat source and the spacing between the porous layers are of the same magnitude as the channel height, the heat transfer enhancement is almost the same as in the fully porous channel while the pressure drop is significantly lower. These results suggest that the partially porous channel configuration is a potentially attractive heat transfer augmentation technique for electronic equipment cooling, an end that motivated this study.

Natural convection from a vertical surface covered with hair

Heat transfer through a vertical skin surface covered with perpendicular hair strands of uniform density is investigated numerically. The heat transfer rate is the result of (1) direct heat transfer to the air that makes contact with the skin and (2) the heat conducted by each strand away from the skin. The hair strand and its surrounding air are not in local thermal equilibrium. Hair strands have the desirable effect of slowing the air that sweeps the vertical surface and the undesirable effect of acting as fins, thereby augmenting the overall heat transfer rate. Two distinct air flow models are considered: the Darcy model and the Forchheimer-Brinkman extended Darcy model. The overall heat transfer charts reported in this paper show that heat transfer rate can greatly exceed the estimate based on the traditional homogeneous porous medium model. By means of numerical examples, the Darcy model is shown to be adequate for modeling air flow through mammal hair.