The effect of the thermal conductivity on the propagation of small perturbations in viscous compressible fluid

Summary

The effect of thermal conductivity on the propagation of small perturbations in a viscous compressible fluid is investigated by adopting slow motion. The equations of motion are deduced with the constitutive equation between the stress and deformation rate tensors obtained by C. Ferrari in [1] and the equation of energy applying the constitutive equation between the heat flux density and the gradient of temperature obtained by C. Cattaneo in [2]. The initial value problem (Cauchy’s problem) is represented by a system of five partial differential equations of first order which is totally hyperbolic. In each point of the flow field passes five characteristic lines, two corresponding to progressing waves in the direction of the flow, two corresponding to waves propagating in opposite direction, and one corresponding to a discontinuity line fixed to the fluid. The equations defining the variation law of any physical quantity along characteristics are deduced: the problem can be solved either numerically or iteratively. The propagation of the discontinuities of the initial data along these characteristics is then studied.