Implicit continuum mechanics approach to heat conduction in granular materials
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.
- Research Organization:
- National Energy Technology Lab. (NETL), Pittsburgh, PA, and Morgantown, WV (United States). In-house Research; National Energy Technology Laboratory (NETL), Pittsburgh, PA, Morgantown, WV (United States)
- Sponsoring Organization:
- USDOE Office of Fossil Energy (FE)
- OSTI ID:
- 1012349
- Report Number(s):
- NETL-TPR-3080; TRN: US201109%%791
- Journal Information:
- Ind. Eng. Chem. Res., Vol. 49, Issue 11; ISSN 0888--5885
- Publisher:
- American Chemical Society
- Country of Publication:
- United States
- Language:
- English
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