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.

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.

scholarly journals Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review

Energies ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 8114
Author(s):  
Gazy F. Al-Sumaily ◽  
Amged Al Ezzi ◽  
Hayder A. Dhahad ◽  
Mark C. Thompson ◽  
Talal Yusaf
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Porous Media ◽  
Thermal Equilibrium ◽  
Solid Phase ◽  
Convection Heat Transfer ◽  
Thermal Response ◽  
Darcy Number ◽  
Industrial Applications ◽  
Local Thermal Equilibrium

Local thermal equilibrium (LTE) is a frequently-employed hypothesis when analysing convection heat transfer in porous media. However, investigation of the non-equilibrium phenomenon exhibits that such hypothesis is typically not true for many circumstances such as rapid cooling or heating, and in industrial applications involving immediate transient thermal response, leading to a lack of local thermal equilibrium (LTE). Therefore, for the sake of appropriately conduct the technological process, it has become necessary to examine the validity of the LTE assumption before deciding which energy model should be used. Indeed, the legitimacy of the LTE hypothesis has been widely investigated in different applications and different modes of heat transfer, and many criteria have been developed. This paper summarises the studies that investigated this hypothesis in forced, free, and mixed convection, and presents the appropriate circumstances that can make the LTE hypothesis to be valid. For example, in forced convection, the literature shows that this hypothesis is valid for lower Darcy number, lower Reynolds number, lower Prandtl number, and/or lower solid phase thermal conductivity; however, it becomes invalid for higher effective fluid thermal conductivity and/or lower interstitial heat transfer coefficient.

Nanofluid Treatment in Existence of Magnetic Field Using Non-Darcy Model for Porous Media

2018 ◽  
pp. 456-555
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Finite Element Method ◽  
Porous Media ◽  
Control Volume ◽  
Convection Heat Transfer ◽  
Darcy Number ◽  
Convection Heat ◽  
Darcy Model ◽  
Flow And Heat Transfer

In this chapter, the non-Darcy model is employed for porous media filled with nanofluid. Both natural and forced convection heat transfer can be analyzed with this model. The governing equations in forms of vorticity stream function are derived and then they are solved via control volume-based finite element method (CVFEM). The effect of Darcy number on nanofluid flow and heat transfer is examined.

Numerical Simulation of Convection Heat Transfer in a Plate Channel with Sintered Copper Porous Ribs

2012 ◽  
Vol 605-607 ◽  
pp. 1350-1355
Author(s):  
Xin Wei Lu ◽  
De Zhi Yang ◽  
Wen Jiong Cao ◽  
Zhao Yao Zhou
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Porous Media ◽  
Convection Heat Transfer ◽  
Copper Plate ◽  
Local Thermal Equilibrium ◽  
Convection Heat ◽  
Sintered Copper ◽  
Plate Channel

Convection heat transfer in a plate channel periodically fitted with sintered copper porous ribs attached to a copper plate was numerically studied. The local thermal equilibrium model was adopted in the energy equation to evaluate the temperature of fluid and solid. The effect of porosity, Reynolds number and heat flux applied to the copper plate on the heat transfer characteristic of the porous media was investigated respectively. The numerical results show that the heat transfer can be enhanced by increasing Reynolds number, decreasing the porosity and the heat transfer enhancement of the porous media took effect significantly when subjected to high heat flux. Detailed development of the porous media temperature field and the Nusselt number of the wall as a function of Reynolds number for different porosity and heat flux were also presented.

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.

Sign in / Sign up

Export Citation Format

Share Document