Nonisothermal viscoplastic fluid flow through porous media (Q809832)

The Alishaev model [\textit{M. G. Alishaev}, \textit{G. G. Vokhitov}, \textit{M. M. Gekhtman} and \textit{I. F. Glumov}, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No.3, 166 ff. (1966)] is extended to the case of nonisothermal flow. Neglecting conductive heat transfer, it is shown that for the model in question in the plane of the complex potential not only are the problems linear but the decoupling of the thermal and hydrodynamic problems is also allowed. The latter is reduced to a mixed problem for an analytic function. This makes it possible to use the well-known methods and results of the theory of limiting equilibrium pillars for isothermal flow. It is also established that the solutions of the unsteady problems tend asymptotically to the solutions of the corresponding steady-state problems and can be obtained from the latter by simpler conversion.