A class of exact solutions of equations for plane steady motion of incompressible fluids of variable viscosity in presence of body force

This paper determines a class of exact solutions for plane steady motion of incompressible fluids of variable viscosity with body force term in the Navier-Stokes equations. The class consists of stream function characterized by equation , in polar coordinates , where , and are continuously differentiable functions, derivative of is non-zero but double derivative of is zero. We find exact solutions, for a suitable component of body force, considering two cases based on velocity profile. The first case fixes both the functions , and provides viscosity as function of temperature. Where as the second case fixes the function , leaves arbitrary and provides viscosity and temperature for the arbitrary function . In both the cases, we can create infinite set of expressions for streamlines, viscosity function, generalized energy function and temperature distribution in the presence of body force.