Developing Nonthermal-Equilibrium Convection in Porous Media With Negligible Fluid Conduction

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Nihad Dukhan
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Solid Phase ◽  
Separation Of Variables ◽  
Plug Flow ◽  
Constant Heat Flux ◽  
Axial Distance ◽  
Equilibrium Equations ◽  
Solid Phase Conductivity

In certain contemporary technologies, porous media with high solid-phase conductivity are impregnated with low-conductivity fluids, e.g., metal and graphite foam cooled by air. For such cases, an approximate analytical model for the developing heat transfer inside a two-dimensional rectangular porous medium subjected to constant heat flux is presented. The model neglects conduction in the fluid and assumes plug flow. The resulting nonthermal-equilibrium equations are solved for the solid and fluid temperatures by separation of variables. The temperatures decay exponentially as the distance from the heated base increases. The effects of the Biot and Peclet numbers are presented. Fully developed heat-transfer conditions are achieved at an axial distance equal to five times the height of the porous medium, with a constant Nusselt number equal to 3.

An Engineering Estimate for Plug-Flow Convection in Porous Media Discarding Fluid Conduction

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Nihad Dukhan
Keyword(s):  
Porous Media ◽  
Solid Phase ◽  
Plug Flow ◽  
Convection Heat Transfer ◽  
Constant Heat Flux ◽  
Heated Wall ◽  
Local Thermal Equilibrium ◽  
Equilibrium Equations ◽  
Non Local ◽  
Flow Through

Metal and graphite foam are relatively new types of porous materials characterized by having high-solid phase conductivities. In many cooling applications of these materials, including high-power electronics, low-conductivity fluids flow through them, e.g., air. A simple approximate engineering solution for the convection heat transfer inside a two-dimensional rectangular porous media subjected to constant heat flux on one side is presented. The conduction in the fluid is set to zero, and for simplicity, a plug flow is considered. As a result, the non-local-thermal equilibrium equations are significantly simplified and solved. The solid and fluid temperatures decay in what looks like an exponential fashion as the distance from the heated wall increases. The results are in good agreement with one more complex analytical solution in the literature, in the region far from the heated wall only.

Approximate Analysis for Darcy-Flow Convection in Porous Media With Zero Fluid Conduction

2009 ◽  
Author(s):  
Nihad Dukhan
Keyword(s):  
Porous Media ◽  
Solid Phase ◽  
Convection Heat Transfer ◽  
Fluid Phase ◽  
Constant Heat Flux ◽  
Local Thermal Equilibrium ◽  
Electronic Systems ◽  
Air Cooling ◽  
Equilibrium Equations ◽  
Heat Rejection

The heat rejection device is a key component in virtually all electronic systems. New core materials for compact and efficient heat exchangers or heat rejection devices are contemporary porous media including metal and graphite foam. In such materials the solid phase has a relatively high conductivity, especially when the fluid phase has a low conductivity. This condition is realized in air-cooling thermal management systems. Simple models are needed for scientists and engineers who work with these materials. Approximate engineering analysis for the convection heat transfer inside a two-dimensional rectangular porous media subjected to constant heat flux on one side is presented. The analysis sets the conduction in the fluid’s governing equation to zero, and for simplicity assumes Darcian flow. The Darcian flow assumption is valid far enough from the solid boundaries, ant it prevails for most of the cross section. The non-local-thermal equilibrium equations are significantly simplified and solved. The solid and fluid temperatures decay in what looks like an exponential fashion as the distance from the heated base increases. The results are in good qualitative agreement with more complex analytical and numerical results in the literature. The proposed model may prove to be time-savings for design purposes.

Convective Heat Transfer of Al2O3 Nanofluids in Porous Media

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Navid O. Ghaziani ◽  
Fatemeh Hassanipour
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Porous Medium ◽  
Porous Media ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Particle Concentration ◽  
Metal Foam ◽  
Volume Fraction ◽  
Constant Heat Flux

In this study, the performance of a heat sink embedded with a porous medium and nanofluids as coolants is analyzed experimentally. The nanofluid is a mixture of de-ionized water and nanoscale Al2O3 particles with three different volumetric concentrations: ζ = 0.41%, 0.58%, and 0.83%. The experimental test section is a rectangular minichannel filled with metal foam, which is electrically heated to provide a constant heat flux. The porous medium is assumed to be homogeneous and the flow regime is laminar. The result of heat transfer enhancement by slurry of Al2O3 nanofluid in porous media is studied under various flow velocities, heat flux, porous media structure, and particle concentration of nanofluid. The effect of particles volume fraction on heat transfer coefficient is also studied. This experimental study discovers and/or confirms the following hypotheses: (1) nanoparticle slurry in conjunction with metal foam has a significant effect on heat transfer rate; (2) there is an optimum permeability for the foam resulting in maximal heat transfer rate; (3) for a fixed particle concentration, smaller particles are more effective in enhancing heat transfer; and (4) increasing particle concentration results in some gains, but this trend weakens after a threshold.

Buoyancy-Driven Flow in Saturated Porous Media

2005 ◽  
Author(s):  
Hitoshi Sakamoto ◽  
Francis A. Kulacki
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Saturated Porous Medium ◽  
Constant Heat Flux ◽  
Transfer Coefficients ◽  
Particulate Solid ◽  
Bulk Medium ◽  
Steady State Heat Transfer ◽  
Buoyancy Driven Convection

Buoyancy-driven convection on a vertical, constant heat flux surface that bounds a fluid-saturated porous medium is experimentally studied with a primary focus on developing steady-state heat transfer correlations for porous media comprising different particulate solid with water being the interstitial fluid. Results show that heat transfer coefficients can be adequately determined via a Darcy-based model, and our results confirm a correlation proposed by Bejan [1]. It is speculated that the reason that the Darcy model works well in the present case is that the porous medium has a lower effective Prandtl number near the wall than in the bulk medium. The factors that contribute to this effects include the thinning of the boundary layer near the wall and an increase of effective thermal conductivity.

Approximate Analysis for Darcy-Flow Convection in Cylindrical Porous Media With Zero Fluid Conduction

2011 ◽  
Author(s):  
Nihad Dukhan
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Solid Phase ◽  
Convection Heat Transfer ◽  
Darcy Number ◽  
Darcy Flow ◽  
Heated Wall ◽  
Local Thermal Equilibrium ◽  
Convection Heat ◽  
Equilibrium Equations

Contemporary porous media that are used in cooling designs include metal and graphite foam. These materials are excellent heat transfer cores due to their large surface area density and the relatively high conductivity of the solid phase. Engineering models for convection heat transfer in such media are needed for thermal system design. When the cooling fluid has a low conductivity, e.g., air, its conduction can be set to zero. Engineering analysis for the fully-developed convection heat transfer inside a confined cylindrical isotropic porous media subjected to constant heat flux is presented. The analysis considers the Darcy flow model and high Pe´clet number. The non-local-thermal equilibrium equations are significantly simplified and solved. The solid and fluid temperatures decay in what looks like an exponential fashion as the distance from the heated wall increases. The effects of the Biot number and the Darcy number are investigated. The results are in qualitative agreement with more complex analytical and numerical results in the literature. The solution is of utility for initial heat transfer designs, and for more complex numerical modeling of the heat transfer phenomenon in porous media.

scholarly journals Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

Fluids ◽  
2021 ◽  
Vol 6 (8) ◽  
pp. 266
Author(s):  
Péter German ◽  
Mauricio E. Tano ◽  
Carlo Fiorina ◽  
Jean C. Ragusa
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Steady State ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Data Driven ◽  
Reduced Order ◽  
Medium Formulation ◽  
Flow Resistances

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

Natural Convection Inside a Bidisperse Porous Medium Enclosure

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Arunn Narasimhan ◽  
B. V. K. Reddy
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Volume Fraction ◽  
Solid Phase ◽  
Darcy Number ◽  
The Core ◽  
Side Walls ◽  
Porous Blocks ◽  
Rayleigh Numbers

Bidisperse porous medium (BDPM) consists of a macroporous medium whose solid phase is replaced with a microporous medium. This study investigates using numerical simulations, steady natural convection inside a square BDPM enclosure made from uniformly spaced, disconnected square porous blocks that form the microporous medium. The side walls are subjected to differential heating, while the top and bottom ones are kept adiabatic. The bidispersion effect is generated by varying the number of blocks (N2), macropore volume fraction (ϕE), and internal Darcy number (DaI) for several enclosure Rayleigh numbers (Ra). Their effect on the BDPM heat transfer (Nu) is investigated. When Ra is fixed, the Nu increases with an increase in both DaI and DaE. At low Ra values, Nu is strongly affected by both DaI and ϕE. When N2 is fixed, at high Ra values, the porous blocks in the core region have negligible effect on the Nu. A correlation is proposed to evaluate the heat transfer from the BDPM enclosure, Nu, as a function of Raϕ, DaE, DaI, and N2. It predicts the numerical results of Nu within ±15% and ±9% in two successive ranges of modified Rayleigh number, RaϕDaE.

scholarly journals Analytical Analysis of Heat Transfer and Entropy Generation in a Tube Filled with Double-Layer Porous Media

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1214 ◽  
Author(s):  
Kun Yang ◽  
Wei Huang ◽  
Xin Li ◽  
Jiabing Wang
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Nusselt Number ◽  
Double Layer ◽  
Entropy Generation ◽  
Single Layer ◽  
Entropy Generation Rate ◽  
Total Entropy ◽  
Interfacial Radius

The heat transfer and entropy generation in a tube filled with double-layer porous media are analytically investigated. The wall of the tube is subjected to a constant heat flux. The Darcy-Brinkman model is utilized to describe the fluid flow, and the local thermal non-equilibrium model is employed to establish the energy equations. The solutions of the temperature and velocity distributions are analytically derived and validated in limiting case. The analytical solutions of the local and total entropy generation, as well as the Nusselt number, are further derived to analyze the performance of heat transfer and irreversibility of the tube. The influences of the Darcy number, the Biot number, the dimensionless interfacial radius, and the thermal conductivity ratio, on flow and heat transfer are discussed. The results indicate, for the first time, that the Nusselt number for the tube filled with double-layer porous media can be larger than that for the tube filled with single layer porous medium, while the total entropy generation rate for the tube filled with double-layer porous media can be less than that for the tube filled with single layer porous medium. And the dimensionless interfacial radius corresponding to the maximum value of the Nusselt number is different from that corresponding to the minimum value of the total entropy generation rate.

Experimental Investigation on Convective Heat Transfer Enhancement of Laminar Slot Jet Impingement in the Presence of Porous Medium

2016 ◽  
Author(s):  
Sampath Kumar Chinige ◽  
Arvind Pattamatta
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Porous Medium ◽  
Porous Media ◽  
Nusselt Number ◽  
Heat Sink ◽  
Average Nusselt Number ◽  
Jet Impingement ◽  
Transfer Enhancement ◽  
Porous Obstacle

An experimental study using Liquid crystal thermography technique is conducted to study the convective heat transfer enhancement in jet impingement cooling in the presence of porous media. Aluminium porous sample of 10 PPI with permeability 2.48e−7 and porosity 0.95 is used in the present study. Results are presented for two different Reynolds number 400 and 700 with four different configurations of jet impingement (1) without porous foams (2) over porous heat sink (3) with porous obstacle case (4) through porous passage. Jet impingement with porous heat sink showed a deterioration in average Nusselt number by 10.5% and 18.1% for Reynolds number of 400 and 700 respectively when compared with jet impingement without porous heat sink configuration. The results show that for Reynolds number 400, jet impingement through porous passage augments average Nusselt number by 30.73% whereas obstacle configuration enhances the heat transfer by 25.6% over jet impingement without porous medium. Similarly for Reynolds number 700, the porous passage configuration shows average Nusselt number enhancement by 71.09% and porous obstacle by 33.4 % over jet impingement in the absence of porous media respectively.

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