Abstract
Bulk kinematic properties of mixtures such as velocity are known to be the density weighed averages of the constituent velocities. No such paradigm exists for the heat flux of mixtures when the constituents have different temperatures. Using standard principles such as frame indifference, we address this topic by developing linear constitutive equations for the constituent heat fluxes, the interaction force between constituents, and the stresses for a mixture of two fluids. Although these equations contain 18 phenomenological coefficients, we are able to use the Clausius-Duhem inequality to obtain inequalities involving the principal and cross flux coefficients. The theory is applied to some special cases and shown to reduce to standard results when the constituents have the same temperature.
Highlights
Of general concern here are the heat fluxes of multicomponent materials where the temperatures of the components are not equal
As well as many examples from both the environment and industry of multicomponent materials with distinct constituent temperatures, there is a paucity of research on the thermodynamic implications of characterizing the bulk properties of the heat fluxes of such materials
Perhaps this is due to the myth that such materials quickly come to thermal equilibrium
Summary
Of general concern here are the heat fluxes of multicomponent materials where the temperatures of the components are not equal. Stokes fluids by Ahmadi [3] Despite this theoretical framework, as well as many examples from both the environment and industry of multicomponent materials with distinct constituent temperatures, there is a paucity of research on the thermodynamic implications of characterizing the bulk properties of the heat fluxes of such materials. We intend for this study to provide some theoretical guidance for experimenters attempting to establish the phenomenological parameters for mixtures To achieve this we utilize the second law requirement that the rate of entropy production of the mixture as a whole is non-negative to establish inequality constraints on the phenomenological coefficients. In this regard some investigators have imposed Onsager’s reciprocal relations to reduce the number of cross flux coefficients.
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