Open AccessA class of exact solutions of equations for plane steady motion of incompressible fluids of variable viscosity in presence of body force
Author(s) -
Mushtaq Ahmed,
Waseem S. Khan,
S M. Shad Ahsen
Publication year - 2018
Publication title -
international journal of applied mathematical research
Language(s) - English
Resource type - Journals
ISSN - 2227-4324
DOI - 10.14419/ijamr.v7i3.12326
Subject(s) - mathematics , viscosity , compressibility , motion (physics) , class (philosophy) , plane (geometry) , variable (mathematics) , mathematical analysis , classical mechanics , mechanics , geometry , physics , thermodynamics , artificial intelligence , computer science
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.