Analysis of the process of heat transfer for free steady-state flow of liquid in a flat channel in view of the dissipation of mechanical energy and of the temperature dependence of viscosity

The steady-state process of heat transfer is analyzed with due regard for the dissipation of mechanical energy and for the temperature dependence of viscosity of liquid under boundary conditions of the first kind. A free steady-state flow is treated for the case when a preassigned constant tangential stress is applied to one of the channel walls. An analysis is performed of the range of permissible values of the Name–Griffiths number, in which a steady-state solution to the heat-transfer equation exists. The distributions of the velocity and temperature of liquid in the channel are obtained for this range, and the effect of the main parameters of the system on these distributions is investigated. The basic regularities of the "behavior" of the maximum point of temperature are described.