The two dimensional Couette flow of a non-homogeneous viscous fluid is studied. The plane boundaries of the channel are maintained at different temperatures. The upper plane moves with a uniform horizontal velocity and the lower plane is at rest. The fluid is subjected to suction and injection at the boundaries. Thesteady equations are solved by introducing similarity variables which are expanded in series of powers of a small stratification parameter. The non-linear theory predicts that the temperature depends on the distancex from the throat section, an observation which is not predicted by the linear theory. The non-linear effects on velocity and temperature are studied. The rate of heat transfer is discussed.

A viscous incompressible fluid between two plane boundaries is stratified by maintaining the planes at different temperatures. The upper plane moves with a uniform velocity. The suction/injection mechanism with constant injection velocity at the upper plane and suction velocity varying sinusoidally along the lower plane with a wave numberk is introduced at the boundaries. The steady linearised equations are solved using similarity variables for the velocity components. The wave numberk is shown to be effective in controlling the boundary layer thickness.