Couette Flow of an Incompressible Heat Conducting Fluid with Temperature Dependent Viscosity

Abstract

The problem of determining a steady Couette flow in an infinite parallel-wall channel occupied by a viscous, heat-conducting, incompressible fluid, with temperature-dependent viscosity, is considered; the channel width is not assumed to be fixed, a priori, but is determined as part of the solution to the boundary-value problem associated with the equations governing the velocity and temperature fields subject to the specification of a given mass flow in the channel.  The upper wall of the channel is fixed while the bottom wall moves to the right with a given positive speed and the viscosity is taken to be a linear, monotonically decreasing function of temperature.  Exact solutions for the temperature distribution and velocity field associated with the flow are computed and numerical results are presented as a number of physical parameters are varied from their base values.