Open Access

ARTICLE

GENERAL HEAT CONDUCTION EQUATIONS BASED ON THE THERMOMASS THEORY

Moran Wang^a, Bin-Yang Cao^b, Zeng-Yuan Guo^b,*

a Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
b Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China

* Corresponding Authors: E-mail: (ZG); (MW)

Frontiers in Heat and Mass Transfer 2010, 1(1), 1-8. https://doi.org/10.5098/hmt.v1.1.3004

Abstract

The thermomass theory regards heat owning mass-energy duality, exhibiting energy-like features in conversion and mass-like features in transfer processes. The equivalent mass of thermal energy is determined by the mass-energy equivalence of Einstein, which therefore leads to the inertia of heat in transfer. In this work, we build up a thermomass gas model based on this theory to describe the fluid-flow-like heat conduction process in a medium. The equation of state and the governing equations for transport for the thermomass gas have been derived based on methodologies of the classical mechanics since the drift speed of thermomass gas is generally far lower than the speed of light. We therefore present the general heat conduction law to describe the relationship between the heat flux and the temperature fields. The general law provides us a new viewpoint to understand the previous laws for heat conduction, such as the Fourier’s law and the CV (Cattaneo-Vernotte) model. The general law will degenerate to the Fourier’s law when all the thermal inertial effects are negligible or to the CV model for the unsteady heat conduction when the spacedependent inertial effects are negligible. The non-Fourier conductions, both the ultrafast heating/cooling and the ultrahigh-rate steady-state ones, have been studied using the general heat conduction law with the thermal inertial effects fully considered, and compared with the previous theoretical models and experimental data.

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Keywords

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