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Heat transfer in granular materials: effects of nonlinear heat conduction and viscous dissipation
Author(s) -
Yang Hyunjin,
Aubry Nadine,
Massoudi Mehrdad
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2740
Subject(s) - heat flux , heat transfer , mechanics , mathematics , thermal conduction , adiabatic process , temperature gradient , nonlinear system , mathematical analysis , boundary value problem , dissipation , thermodynamics , physics , quantum mechanics
In this paper, we study the heat transfer in a one‐dimensional fully developed flow of granular materials down a heated inclined plane. For the heat flux vector, we use a recently derived constitutive equation that reflects the dependence of the heat flux vector on the temperature gradient, the density gradient, and the velocity gradient in an appropriate frame invariant formulation. We use two different boundary conditions at the inclined surface: a constant temperature boundary condition and an adiabatic condition. A parametric study is performed to examine the effects of the material dimensionless parameters. The derived governing equations are coupled nonlinear second‐order ordinary differential equations, which are solved numerically, and the results are shown for the temperature, volume fraction, and velocity profiles. Copyright © 2013 John Wiley & Sons, Ltd.