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We present a model describing unsteady flows of a heat conducting mixture composed from L constituents in two and three dimensional bounded domain. We assume that the flow of the mixture is described only by the barycentric velocity, and that the fluid is non-Newtonian. In addition, we assume that the diffusion flux depends also on the temperature gradient, describing the Soret effect, and that the heat flux depends also on the chemical potentials gradient, describing the Dufour effect. We briefly show under which assumptions on the constitutive equations the model obeys the first and the second laws of thermodynamics and for a large class of physically well-motivated constitutive relations we establish the existence of a weak solution. For simplicity we restrict ourselves only onto the linear models, i.e., the diffusion and the heat flux depend linearly on the temperature and chemical potentials gradients. [ABSTRACT FROM AUTHOR]

The radial planar wedge pattern flow with friction and normalized non‐uniform viscosity function will be discussed here. Solving this problem will be done using the flow theory equations for Newtonian and Non‐Newtonian cases with non‐uniform viscosity assumption. General differential equation that connects between the normalized velocity profile and the normalized viscosity has been derived analytically from the flow equations. It was found that for specific wedge semi angle, the radial assumption is no longer valid for the flow velocity. Moreover, it was found that for inlet/outlet conditions the normalized mean hydrostatic pressure for Newtonian fluid is dependent on the geometry, the normalized velocity and the viscosity functions. In addition, it was found that inertia phenomenon can be neglected for small wedge semi angle. A comparison between the axial and the hydrostatic pressure distributions for inlet/outlet conditions was performed for Newtonian and non‐Newtonian flows. Finally, it was found that the axial pressure distribution profile was converged to the hydrostatic profile for critical wedge semi angle. [ABSTRACT FROM AUTHOR]