Institute of Mechanics

Abstract: It was found that Maxwell-Cattaneo law for the relaxation processes in heat conduction leads to paradoxical results if the material body is moving, and it was shown that the use of a convective derivative removes the paradox (see [1]). In the resting frame, the equations are the same as in a frame that moves with constant velocity. The formulation of [1] led to a typical coupled system, from which a single equation for the temperature could not be obtained. A material-invariant (frame indifferent) version of the Maxwell-Cattaneo law has been recently proposed in [2] where the relaxation rate of the heat flux is given by Oldroyd's upper-convected derivative. We discuss here the features of the new formulation, e.g., the possibility of elimination of the heat flux and obtaining a single equation for the temperature field. This feature is to be expected from a truly frame indifferent description. The problem of heat convection in a vertical slot subject two both horizontal and vertical pressure gradient is considered as a featuring example where the contribution of Oldroyd terms can be identified explicitly.