Local Thermal Equilibrium in Forced Convection Through Porous Media

2010 ◽  
Author(s):  
A. Nouri-Borujerdi
Keyword(s):  
Porous Medium ◽  
Pressure Gradient ◽  
Forced Convection ◽  
Thermal Equilibrium ◽  
Fluid Transport ◽  
Convection Heat Transfer ◽  
Darcy Number ◽  
Equation Model ◽  
Temperature Fields ◽  
Local Thermal Equilibrium

Forced convection heat transfer through a channel filled with a porous medium is investigated using perturbation method. Two-energy equation model is utilized to represent the assumption of local thermal non-equilibrium which exists between the solid and fluid phases. The Brinkman-Forchheimer extension of the Darcy model is used to represent the fluid transport within the porous medium. Analytical solution is obtained for both fluid and solid temperature fields incorporating the effects of various pertinent parameters such as the Darcy number, the Biot number, the thermal conductivity and the pressure gradient. It is found that the Darcy number and the pressure gradient have significant effects on the local thermal equilibrium assumption.

Numerical Study on the Performance of a Tube With Inserted Porous Media of Various Thermal Conductivities

2016 ◽  
Author(s):  
Tariq Amin Khan ◽  
Wei Li
Keyword(s):  
Thermal Conductivity ◽  
Porous Medium ◽  
Porous Media ◽  
Velocity Profile ◽  
Fluid Transport ◽  
Energy Transport ◽  
Numerical Study ◽  
Darcy Number ◽  
Local Thermal Equilibrium ◽  
Working Fluid

Numerical study is performed on the effect of thermal conductivity of porous media (k) on the Nusselt number (Nu) and performance evaluation criteria (PEC) of a tube. Two-dimensional axisymmetric forced laminar and fully developed flow is assumed. Porous medium partially inserted in the core of a tube is investigated under varied Darcy number (Da), i.e., 10−6 ≤ Da ≤ 10−2. The range of Re number used is 100 to 2000 and the conductivity of porous medium is 1.4 to 202.4 W/(m.K) with air as the working fluid. The momentum equations are used to describe the fluid flow in the clear region. The Darcy-Forchheimer-Brinkman model is adopted for the fluid transport in the porous region. The mathematical model for energy transport is based on the one equation model which assumes a local thermal equilibrium between the fluid and the solid phases. Results are different from the conventional thoughts that porous media of higher thermal conductivity can enhance the performance (PEC) of a tube. Due to partial porous media insertion, the upstream parabolic velocity profile is destroyed and the flow is redistributed to create a new fully develop velocity profile downstream. The length of this flow redistribution to a new developed laminar flow depends on the Da number and the hydrodynamic developing length increases with increasing Da number. Moreover, the temperature profile is also readjusted within the tube. The Nu and PEC numbers have a nonlinear trend with varying k. At very low Da number and at a lower k, the Nu number decreases with increasing Re number while at higher k, the Nu number first increases to reach its peak value and then decreases. At higher Re number, the results are independent of k. However, at a higher Da number, the Nu and PEC numbers significantly increases at low Re number while slightly increases at higher Re number. Hence, the change in Nu and PEC numbers neither increases monotonically with k, nor with Re number. Investigation of PEC number shows that at very low Da number (Da = 10−6), inserting porous media of a low k is effective at low Re number (Re ≤ 500) while at high Re number, using porous material is not effective for the overall performance of a tube. However, at a relatively higher Da number (Da = 10−2), high k can be effective at higher Re number. Moreover, it is found that the results are not very sensitive to the inertia term at lower Da number.

scholarly journals Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition – An exact solution

2014 ◽  
Vol 228 (15) ◽  
pp. 2778-2789 ◽  
Author(s):  
Nader Karimi ◽  
Yasser Mahmoudi ◽  
Kiumars Mazaheri
Keyword(s):  
Porous Material ◽  
Fluid Transport ◽  
Darcy Number ◽  
Equation Model ◽  
Temperature Fields ◽  
Thermal Conductivity Ratio ◽  
Fluid Temperature ◽  
Thermal Boundary Conditions ◽  
Constant Wall Heat Flux ◽  
Non Equilibrium

This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers.

scholarly journals Local thermal non-equilibrium effects arising from the injection of a hot fluid into a porous medium

2007 ◽  
Vol 594 ◽  
pp. 379-398 ◽  
Author(s):  
D. ANDREW S. REES ◽  
ANDREW P. BASSOM ◽  
PRADEEP G. SIDDHESHWAR
Keyword(s):  
Porous Medium ◽  
Parabolic Equations ◽  
Thermal Equilibrium ◽  
Fluid Phase ◽  
Single Equation ◽  
Porous Matrix ◽  
Temperature Fields ◽  
Local Thermal Equilibrium ◽  
Thermal Front ◽  
Non Equilibrium

We examine the effect of local thermal non-equilibrium on the infiltration of a hot fluid into a cold porous medium. The temperature fields of the solid porous matrix and the saturating fluid are governed by separate, but coupled, parabolic equations, forming a system governed by three dimensionless parameters. A scale analysis and numerical simulations are performed to determine the different manners in which the temperature fields evolve in time. These are supplemented by a large-time analysis showing that local thermal equilibrium between the phases is eventually attained. It is found that the thickness of the advancing thermal front is a function of the governing parameters rather than being independent of them. This has the implication that local thermal equilibrium is not equivalent to a single equation formulation of the energy equation as might have been expected. When the velocity of the infiltrating fluid is sufficiently large, the equations reduce to a hyperbolic system and a thermal shock wave is formed within the fluid phase. The strength of the shock decays exponentially with time, but the approach to local thermal equilibrium is slower and is achieved algebraically in time.

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.

Forced convection heat transfer from a plate stack embedded in a homogeneous porous medium

2021 ◽  
Author(s):  
Khadija Tul Kubra Lehre ◽  
R. McKibbin ◽  
Sana Ullah Ullah Lehre ◽  
Muhammad Khalid ◽  
Winston L. Sweatman
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Forced Convection ◽  
Convection Heat Transfer ◽  
Convection Heat ◽  
Forced Convection Heat Transfer ◽  
Homogeneous Porous Medium

Numerical simulations of MHD forced convection flow of micropolar fluid inside a right-angled triangular cavity saturated with porous medium: Effects of vertical moving wall

2019 ◽  
Vol 97 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Mubbashar Nazeer ◽  
N. Ali ◽  
Tariq Javed
Keyword(s):  
Porous Medium ◽  
Prandtl Number ◽  
Forced Convection ◽  
Micropolar Fluid ◽  
Richardson Number ◽  
Hartmann Number ◽  
Darcy Number ◽  
Convection Flow ◽  
Penalty Parameter ◽  
Forced Convection Flow

The present article explores the effects of moving lid on the forced convection flow of micropolar fluid inside a right-angle triangular cavity saturated with porous medium. The base and hypotenuse or inclined sides of the cavity are maintained at constant temperatures, while the vertical side of the enclosure is adiabatic and moving with constant velocity in upward or downward direction. The flow equations are simulated by using the robust finite element numerical technique. The pressure term from the momentum equations is eliminated by using the penalty parameter. For a consistent solution, the value of the penalty parameter is selected as 107. The simulations are performed for the cases based on the direction of moving lid. The numerical outcomes are shown in terms of streamlines, temperature contours, and local and average Nusselt numbers for sundry parameters, such as micropolar parameter, Reynolds number, Richardson number, Darcy number, Hartmann number, and Prandtl number. It is observed that the shape of the inner circulating cell is elliptic when the lid is moving in the upward direction and fluid is clear (Newtonian fluid). It is also found that average Nusselt number in both cases increases with increasing Prandtl number, Richardson number, micropolar parameter, and Darcy number, whereas it decreases with increasing Hartmann number. Further, it achieves a maximum when the lid is moving in the downward direction, regardless of the choice of involved parameters. The numerical code is also validated with previous published results. The investigation of the current study is beneficial in porous heat exchangers, construction of triangular-shaped solar collectors, rigid crystal, polymeric fluid transport, etc.

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