The numerical assessment of volume averaging method in heat transfer modeling of tissue-like porous media

2015 ◽  
Vol 63 ◽  
pp. 41-48 ◽  
Author(s):  
Saeid Hassanpour ◽  
Ahmad Saboonchi
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Averaging Method ◽  
Volume Averaging ◽  
Heat Transfer Modeling ◽  
Numerical Assessment

VAT Based Optimization of Heat Transfer in a Flat Channel Filled With a Porous Media

2003 ◽  
Author(s):  
Ivan Catton ◽  
Kunzhong Hu
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Dissipation ◽  
Energy Transport ◽  
Heterogeneous Media ◽  
Statistical Design ◽  
Frictional Resistance ◽  
Volume Averaging ◽  
Statistical Design Of Experiments ◽  
Optimization Parameters

Developments of volume averaging theory (VAT) used to describe transport phenomena in heterogeneous media are applied to optimization of heat dissipation from a heterogeneous media. The media is a porous media representation of a pin fin heat sink (a heterogeneous layer) and the optimization process is accomplished with rigor using the idea of scaled energy transport. The problem is addressed in four steps: 1) determine the parameters needed for optimization from the two temperature VAT equations, 2) use statistical design of experiments (simulating the problem) for the many optimization parameters, 3) perform numerical simulation of the cases that are suggested through the statistical analysis of the optimization parameters, and 4) statistically analyze the numerical results to obtain an optimization response surface. The two applications are enhancement of heat transfer dissipation from a heterogeneous media while minimizing the frictional resistance and minimization of the thermal resistance (a problem of importance to all designers of heat exchangers).

Statistics of Mathematical Two-Scale Closure of Momentum, Heat and Charge Transport Problems With Stochastic Orientation of Porous Medium Capillaries

2001 ◽  
Author(s):  
V. S. Travkin ◽  
K. Hu ◽  
I. Catton
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Volume Averaging ◽  
Governing Equations ◽  
Rigorous Approach ◽  
Flow And Heat Transfer ◽  
Model Flow ◽  
History Of ◽  
Transport Problems

Abstract The history of stochastic capillary porous media transport problem treatments almost corresponds to the history of porous media transport developments. Volume Averaging Theory (VAT), shown to be an effective and rigorous approach for study of transport (laminar and turbulent) phenomena, is used to model flow and heat transfer in capillary porous media. VAT based modeling of pore level transport in stochastic capillaries results in two sets of scale governing equations. This work shows how the two scale equations could be solved and how the results could be presented using statistical analysis. We demonstrate that stochastic orientation and diameter of the pores are incorporated in the upper scale simulation procedures. We are treating this problem with conditions of Bi for each pore is in a range when Bi ≳ 0.1 which allows even greater distinction in assessing an each additional differential, integral, or integral-differential term in the VAT equations.

scholarly journals Obtaining Closure for Fin-and-Tube Heat Exchanger Modeling Based on Volume Averaging Theory (VAT)

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Feng Zhou ◽  
Nicholas E. Hansen ◽  
David J. Geb ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Exchanger ◽  
Friction Factor ◽  
Heat Exchangers ◽  
Volume Averaging ◽  
Averaging Theory ◽  
Length Scale ◽  
Tube Heat Exchanger ◽  
Volume Averaging Theory

Modeling a fin-and-tube heat exchanger as porous media based on volume averaging theory (VAT), specific geometry can be accounted for in such a way that the details of the original structure can be replaced by their averaged counterparts, and the VAT based governing equations can be solved for a wide range of heat exchanger designs. To complete the VAT based model, proper closure is needed, which is related to a local friction factor and a heat transfer coefficient of a representative elementary volume. The present paper describes an effort to model a fin-and-tube heat exchanger based on VAT and obtain closure for the model. Experiment data and correlations for the air side characteristics of fin-and-tube heat exchangers from the published literature were collected and rescaled using the “porous media” length scale suggested by VAT. The results were surprisingly good, collapsing all the data onto a single curve for friction factor and Nusselt number, respectively. It was shown that using the porous media length scale is very beneficial in collapsing complex data yielding simple heat transfer and friction factor correlations and that by proper scaling, closure is a function of the porous media, which further generalizes macroscale porous media equations. The current work is a step closer to our final goal, which is to develop a universal fast running computational tool for multiple-parameter optimization of heat exchangers.

Modeling of Forced Convection in an Electronic Device Heat Sink as Porous Media Flow

2002 ◽  
Author(s):  
Andrej Horvat ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Sink ◽  
Electronic Device ◽  
Computer Code ◽  
Local Heat ◽  
Volume Averaging ◽  
Temperature Fields ◽  
Porous Media Flow ◽  
Transfer Coefficients

An algorithm for simulation of conjugate heat transfer used to find the most suitable geometry for an electronic chip heat sink is described. Applying Volume Averaging Theory (VAT) to a system of transport equations, a heat exchanger structure was modeled as a homogeneous porous media. The interaction between the fluid and the structure, the VAT equation closure requirement, was accomplished with drag and heat transfer coefficients, which were taken from the available literature and inserted into a computer code. The example calculations were performed for an aluminum heat sink exposed to force convection airflow. The geometry of the simulation domain and boundary conditions followed the geometry of the experimental test section. The comparison of the whole-section drag coefficient and Nusselt number as functions of Reynolds number shows a good agreement with the experimental data. The calculated temperature fields reveal the local heat flow distribution and enable further improvements of the heat sink geometry.

Heat Transfer Modeling of a High-Temperature Porous-Medium Filled Solar Thermochemical Reactor for Hydrogen and Synthesis Gas Production

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Ruming Pan ◽  
Bachirou Guene Lougou ◽  
Yong Shuai ◽  
Guohua Zhang ◽  
Hao Zhang
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
High Temperature ◽  
Temperature Distribution ◽  
Synthesis Gas ◽  
Gas Production ◽  
Operating Conditions ◽  
Heat Transfer Modeling ◽  
Solar Thermochemical

In this paper, heat transfer modeling of a high-temperature porous-medium filled solar thermochemical reactor for hydrogen and synthesis gas production is investigated. The numerical simulation is performed using a three-dimensional (3D) numerical model and surface-to-surface radiation model coupled to Rosseland approximation for radiation heat transfer. The effects of operating conditions and the porous structural parameters on the reactor thermal performance were investigated significantly. It was found that large axial temperature gradient and high-temperature distribution throughout the reactor were strongly dependent on the operating conditions. The inlet gas temperature has remarkable effects on the temperature distribution. The thermal performance of porous-medium filled solar thermochemical reactor could be improved by preheating the inlet gas up to 393.15 K. Moreover, a correlation was established between the protective gas inlet velocity and the porosity of porous media. The temperature difference decreased with the increase in the porosity of the inner cavity of the reactor. In contrast to the front and back parts of the inner cavity of the reactor, higher temperature distribution could be obtained in the porous region by increasing the average cell diameters of porous media.

Exact Closure Procedures of Hierarchical VAT Capillary Thermo-Convective Problem for Turbulent and Laminar Regimes

2001 ◽  
Author(s):  
V. S. Travkin ◽  
K. Hu ◽  
I. Catton
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Turbulent Transport ◽  
Volume Averaging ◽  
Turbulent Regime ◽  
Rigorous Approach ◽  
Flow And Heat Transfer ◽  
Pore Level ◽  
Scale Properties ◽  
The Many

Abstract Volume Averaging Theory (VAT), an effective and rigorous approach for study of transport (laminar and turbulent) phenomena, is used to model flow and heat transfer in porous media. The modeling is based on a simple pore level network. The primary difficulties in applying VAT to straight capillary networks, the many unknown integral and differential terms that are needed for closure, are overcome. VAT based modeling of pore level transport in straight capillaries results in two sets of scale governing equations. One scale is the upper scale VAT equations which describe ensemble properties for flow and heat transfer in porous media. The other scale is the lower scale laminar and turbulent transport equations that represent flow and heat transport in each straight pore capillary. It is how the unknown VAT terms in the upper scale equations can be estimated using the relationships between upper scale properties and lower scale properties. Exact closures and mathematical procedures are developed for the turbulent regime, extending the previous laminar regime work. Numerical results for turbulent and laminar transport in straight capillary porous media are shown in this paper.

Sign in / Sign up

Export Citation Format

Share Document