Archive
Special Issues Volume 5, Issue 1, June 2019, Page: 15-25
A Class of Exact Solutions for a Variable Viscosity Flow with Body Force for Moderate Peclet Number ViaVon-Mises Coordinates
Mushtaq Ahmed, Department of Mathematics, University of Karachi, Karachi, Pakistan
Received: Mar. 13, 2019;       Accepted: May 7, 2019;       Published: Jun. 4, 2019
Abstract
The objective of this article is to communicate a class of new exact solutions of the plane equation of momentum with body force, energy and continuity for moderate Peclet number in von-Mises coordinates. Viscosity of fluid is variable but its density and thermal conductivity are constant. The class characterizes the streamlines pattern through an equation relating two continuously differentiable functions and a function of stream function ψ. Applying the successive transformation technique, the basic equations are prepared for exact solutions. It finds exact solutions for class of flows for which the function of stream function varies linearly and exponentially. The linear case shows viscosity and temperature for moderate Peclet number for two variety of velocity profile. The first velocity profile fixes both the functions of characteristic equation whereas the second keeps one of them arbitrary. The exponential case finds that the temperature distribution, due to heat generation, remains constant for all Peclet numbers except at 4 where it follows a specific formula. There are streamlines, velocity components, viscosity and temperature distribution in presence of body force for a large number of the finite Peclet number.
Keywords
Successive Transformation Technique, Variable Viscosity Fluids, Navier-Stokes Equations with Body Force, Martin’s Coordinates, Von-MisesCoordinates
Mushtaq Ahmed, A Class of Exact Solutions for a Variable Viscosity Flow with Body Force for Moderate Peclet Number ViaVon-Mises Coordinates, Fluid Mechanics. Vol. 5, No. 1, 2019, pp. 15-25. doi: 10.11648/j.fm.20190501.13
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