Dissipative heating under conditions of shear flow of liquid in a flat channel of finite length in view of temperature dependence of viscosity

A steady-state process of heat transfer is considered under conditions of Couette-type shear flow in a flat channel of finite length. The problem is solved in view of dissipation of mechanical energy and of temperature dependence of viscosity under symmetric boundary conditions of the third kind on the channel walls. A number of simplifying assumptions are made, and approximate solutions are obtained within two formulations of the initial problem. In the first case, the constant velocity of the moving channel wall is assigned. This problem is conventional and leads to quite predictable results. In the second case, it is assumed that it is the resultant force applied to the moving channel wall which is assigned. The wall velocity in the steady-state mode is not known in advance. It is found that, in this case, the dependence of kinematic and thermal characteristics of the process on Froude number exhibits a hysteretic pattern.