Total stress tensors and heat fluxes of single flow through a porous viscoelastic medium
Tshepo O Tong and Matthew T Kambule
Department of Mathematical Sciences, North-West University, Mafikeng, South Africa.
Abstract: Using the second law of thermodynamics, we examine the macroscopic equations for mass, momentum, energy and entropy for a biphasic system whose interface has thermodynamic properties. This system is made up of a mesoscopic particle and a fluid, including mass exchange and different phase temperatures. By exploiting the entropy inequality in terms of Coleman and Noll's method we obtain nonequilibrium and equilibrium results. We show how the solid phase stress tensor depends on the solid phase pressure, the Terzaghi stress, the hydration stress and the stress contributed by the interface properties, which is similar to the Terzaghi stress. We determine the heat fluxes. We further linearize the non-equilibrium parts of their constitutive forms in terms of heat conduction, fluid viscosity and viscoelasticity about the equilibrium. Finally we obtain expressions of the total stress and the total heat flux for a particle.
[Tshepo O Tong and Matthew T Kambule. Total stress tensors and heat fluxes of single flow through a porous viscoelastic medium. Life Sci J 2012;9(1):1-12] (ISSN:1097-8135). http://www.lifesciencesite.com. 1
Keywords: Cauchy stress tensors; heat fluxes; Hybrid mixture Theory method; viscoelaticity.