Journal of Prime Research in Mathematics

# Some exact solutions for the flow of a Newtonian fluid with heat transfer via prescribed vorticity

M. Jamil
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.
N. A. Khan
Department of Mathematics, University of Karachi, Karachi, Pakistan.
A. Mahmood
Department of Mathematics, COMSATS Institute if IT, Lahore, Pakistan.
G. Murtaza
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.
Q. Din
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.

$$^{1}$$Corresponding Author: jqrza26@yahoo.com

### Abstract

Two-dimensional , steady, laminar equations of motion of an incompressible fluid with variable viscosity and heat transfer equations are considered. The problem investigated is the flow for which the vorticity distribution is proportional to the stream function perturbed by a sinusoidal stream. Employing transformation variable, the governing Navier-Stokes Equations are transformed into the ordinary differential equations and exact solutions are obtained. Finally, the influence of different parameters of interest on the velocity, temperature and pressure profiles are plotted and discussed.

#### Keywords:

Exact solutions, Navier-Stokes equations, steady plane flows, incompressible fluid, variable viscosity, heat transfer, prescribed vorticity.