Implicit Continuum Mechanics Approach to Heat Conduction in Granular Materials

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• 作者：Mehrdad Massoudi ; Morteza M. Mehrabadi
• 刊名：Industrial & Engineering Chemistry Research
• 出版年：2010
• 出版时间：June 2, 2010
• 年：2010
• 卷：49
• 期：11
• 页码：5215-5221
• 全文大小：140K
• 年卷期：v.49,no.11(June 2, 2010)
• ISSN：1520-5045

文摘

In this paper, we derive a properly frame-invariant implicit constitutive relationship for the heat flux vector for a granular medium (or a density-gradient-type fluid). The heat flux vector is commonly modeled by Fourier’s law of heat conduction, and for complex materials such as nonlinear fluids, porous media, or granular materials, the coefficient of thermal conductivity is generalized by assuming that it would depend on a host of material and kinematic parameters such as temperature, shear rate, porosity, concentration, etc. In this paper, we extend the approach of Massoudi [Massoudi, M. Math. Methods Appl. Sci. 2006, 29, 1585; Massoudi, M. Math. Methods Appl. Sci. 2006, 29, 1599], who provided explicit constitutive relations for the heat flux vector for flowing granular materials; in order to do so, we use the implicit scheme suggested by Fox [Fox, N. Int. J. Eng. Sci. 1969, 7, 437], who obtained implicit relations in thermoelasticity.