Local thermal equilibrium for transient heat conduction: theory and comparison with numerical experiments

1995 ◽  
Vol 38 (15) ◽  
pp. 2779-2796 ◽  
Author(s):  
Michel Quintard ◽  
Stephen Whitaker
Keyword(s):  
Heat Conduction ◽  
Thermal Equilibrium ◽  
Numerical Experiments ◽  
Transient Heat Conduction ◽  
Local Thermal Equilibrium ◽  
Conduction Theory

Nanofluid Suspensions as Derivative of Interface Heat Transfer Modeling in Porous Media

2009 ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Porous Media ◽  
Heat Conduction ◽  
Thermal Equilibrium ◽  
Local Thermal Equilibrium ◽  
Interface Heat Transfer ◽  
Wire Method ◽  
Special Case ◽  
Heat Conduction Process

Spectacular heat transfer enhancement has been measured in nanofluid suspensions. Attempts in explaining these experimental results did not yield yet a definite answer. Modeling the heat conduction process in nanofluid suspensions is being shown to be a special case of heat conduction in porous media subject to Lack of Local thermal equilibrium (LaLotheq). The topic of heat conduction in porous media subject to Lack of Local thermal equilibrium (LaLotheq) is reviewed, introducing one of the most accurate methods of measuring the thermal conductivity, the transient hot wire method, and discusses its possible application to dual-phase systems. Maxwell’s concept of effective thermal conductivity is then introduced and theoretical results applicable for nanofluid suspensions are compared with published experimental data.

A Paradox of Heat Conduction in Porous Media Subject to Lack of Local Thermal Equilibrium

2006 ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Constant Temperature ◽  
Thermal Equilibrium ◽  
Local Thermal Equilibrium ◽  
Apparent Paradox

Based on the traditional formulation of heat transfer in porous media it is demonstrated that Local Thermal Equilibrium (Lotheq) applies generally for any boundary conditions that are a combination of constant temperature and insulation. The resulting consequences raising an apparent paradox are being analyzed and discussed.

Absence of Oscillations and Resonance in Porous Media Dual-Phase-Lagging Fourier Heat Conduction

2005 ◽  
Vol 127 (3) ◽  
pp. 307-314 ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Porous Media ◽  
Heat Conduction ◽  
Thermal Equilibrium ◽  
Local Thermal Equilibrium ◽  
Dual Phase ◽  
Thermal Waves ◽  
Conduction Model ◽  
Physical Conditions ◽  
Fourier Heat Conduction ◽  
Thermal Oscillations

The approximate equivalence between the dual-phase-lagging heat conduction model and the Fourier heat conduction in porous media subject to lack of local thermal equilibrium suggested the possibility of thermal oscillations and resonance. The present investigation demonstrates that the physical conditions necessary for such thermal waves and, possibly resonance, to materialize are not attainable in a porous slab subject to constant temperature conditions applied on the boundaries.

Transient Heat Conduction in Functionally Graded Hollow Cylinders and Spheres

2012 ◽  
Author(s):  
A. H. Akbarzadeh ◽  
Z. T. Chen
Keyword(s):  
Heat Conduction ◽  
Transient Heat Conduction ◽  
Functionally Graded ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Dual Phase ◽  
Conduction Theory ◽  
Hollow Cylinders ◽  
Fourier Heat Conduction ◽  
Cylinders And Spheres

In the present work, transient heat conduction in functionally graded (FG) hollow cylinders and spheres is investigated based on the non-Fourier heat conduction theories. Since the heat transmission has been observed to propagate at a finite speed for applications with very low temperature, short-pulse thermal-heating, and micro temporal and spatial scales, dual phase lag (DPL) and hyperbolic heat conduction theories are considered in current study instead of the conventional Fourier heat conduction theory. Except the phase lags which are assumed to be constant, all the other material properties of the hollow cylinders and spheres are taken to change continuously along the radial direction according to a power-law formulation with different non-homogeneity indices. The heat conduction equations are written based on the dual phase lag theory which includes the hyperbolic heat conduction theory as well. These equations are applied for axisymmetric hollow cylinders of infinite lengths and spherically symmetric hollow spheres. Using the Laplace transform and Bessel functions, the analytical solutions for temperature and heat flux are obtained in the Laplace domain. The solutions are then converted into the time domain by employing the fast Laplace inversion technique. The exact expression is obtained for the speed of thermal wave in FG cylinders and spheres based on the DPL and hyperbolic heat conduction theories. Finally, the current results are verified with those reported in the literature based on the hyperbolic heat conduction theory.

TRANSIENT HEAT CONDUCTION IN ANISOTROPIC SOLIDS

1974 ◽  
Author(s):  
Kozo Katayama ◽  
Akio Saito ◽  
Nariyoshi Kobayashi
Keyword(s):  
Heat Conduction ◽  
Transient Heat Conduction
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