Total str
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.
e-mail: [email protected]
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.
