Thermodynamically Constrained Averaging Theory Approach for Heat Transport in Single-Fluid-Phase Porous Medium Systems

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
William G. Gray ◽  
Cass T. Miller
Keyword(s):  
Porous Medium ◽  
Fluid Phase ◽  
Entropy Inequality ◽  
Averaging Theory ◽  
Local Thermal Equilibrium ◽  
Theory Approach ◽  
Equilibrium Conditions ◽  
Medium System ◽  
Closure Relations ◽  
Microscale Simulations

The recently developed thermodynamically constrained averaging theory is briefly summarized as a tool for the building of rigorous macroscale models of transport phenomena in complex systems. The specific case of thermal transport in a single-fluid-phase porous medium system is considered. Key results from the application of this theory are used to develop a simplified entropy inequality, which is in turn used to guide the development of closure relations. The decomposition of exchange terms is considered, and closed models for internal energy are derived for the case of nonequilibrium and local thermal equilibrium conditions. Since all variables are expressed in terms of precisely defined averages of microscale quantities, the resultant models can be compared with highly resolved microscale simulations to determine the range of validity of the upscaled models.

Local Thermal Non-equilibrium Analysis of Boundary Layer Flow of Carreau Fluid Over a Wedge in a Porous Medium

2021 ◽  
Author(s):  
Ramesh Kudenatti ◽  
Sandhya L
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Layer Flow ◽  
Fluid Phase ◽  
Equilibrium Analysis ◽  
Local Thermal Equilibrium ◽  
Carreau Fluid ◽  
Layer Flow ◽  
Non Equilibrium

Abstract This work examines the steady two-dimensional mixed convection boundary layer flow of non-Newtonian Carreau fluid embedded in a porous medium. The impermeable wedge is at rest over which the momentum and thermal boundary layers form due to motion of Carreau fluid with a large Reynolds number. We consider local thermal non-equilibrium for which the temperature of the solid porous medium is different from that of fluid phase, and hence, a single heat-transport equation is replaced by a two-temperature model. The governed equations for flow and heat transfer are converted into a system of ordinary differential equations using a similarity approach. It is observed that local thermal non-equilibrium effects are dominant for small interphase heat transfer rate and porosity scaled conductivity parameters. It is shown that the temperature at any location of the solid porous medium is always higher than that of fluid phase. When these parameters are increased gradually the local thermal equilibrium phase is recovered at which the temperatures of the fluid and solid are identical at each pore. Similar trend is noticed for both shear-thinning and shear-thickening fluids. The results further show that heat exchange between the fluid and solid porous medium is similar to both assisted and opposed flows and Carreau fluid. The velocity and temperature fields for the various increasing fluid index, Grashof number and permeability show that the thickness of the momentum and thermal boundary layer is thinner.

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.

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