On Two-Dimensional Variable Viscosity Fluid Motion with Body Forcefor Intermediate Peclet Number Via von-Mises Coordinates

摘要

This article uses von-Mises coordinates to present a class of new exact solutions of the system of partial differential equations for the plane steady motion of incompressible fluid of variable viscosity in presence of body forcefor moderate Peclet number. This communication applies successive transformation technique and characterizes streamlines through an equation relating a differentiable function f(x) and a function of stream function. Considering the function of stream function satisfies a specific relation, the exact solutions for moderate Peclet number with body force are determined for given one component of the body force when f(x) takes a specific value and when it is not. In both the cases, it shows an infinite set of streamlines, the velocity components, viscosity function, generalized energy function and temperature distribution for intermediate Peclet number in presence of body force. When f(x) takes a specific value, a relation between viscosity and temperature function is observed.