Vol.71, No.1, 2022, pp.1025-1034, doi:10.32604/cmc.2022.012635
OPEN ACCESS
ARTICLE
Heat Transfer of Casson Fluid over a Vertical Plate with Arbitrary Shear Stress and Exponential Heating
• Dolat Khan1, Gohar Ali1, Arshad Khan2, Ilyas Khan3,*
1 Department of Mathematics, City University of Science and Information Technology, Peshawar, 25000, Pakistan
2 Institute of Computer Sciences and Information Technology, The University of Agriculture, Peshawar, Pakistan
3 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, 72915, Vietnam
* Corresponding Author: Ilyas Khan. Email:
Received 30 June 2020; Accepted 30 August 2020; Issue published 03 November 2021
Abstract
The basic objective of this work is to study the heat transfer of Casson fluid of non-Newtonian nature. The fluid is considered over a vertical plate such that the plate exhibits arbitrary wall shear stress at the boundary. Heat transfers due to exponential plate heating and natural convection are due to buoyancy force. Magnetohydrodynamic (MHD) analysis in the occurrence of a uniform magnetic field is also considered. The medium over the plate is porous and hence Darcy’s law is applied. The governing equations are established for the velocity and temperature fields by the usual Boussinesq approximation. The problem is first written in dimensionless form using some useful non-dimensional quantities and then solved. The exact analysis is performed and hence solutions via integral transform are established. The analysis of various pertinent parameters on temperature distribution and velocity field are reported graphically. It is found that pours medium permeability parameter retards the fluid motion whereas, velocity decreases with increasing magnetic parameter. Velocity and temperature decrease with increasing Prandtl number whereas the Grashof number enhances the fluid motion. Further, it is concluded from this study that the results obtained here are more general and in a limiting sense several other solutions can be recovered. The Newtonian fluid results can be easily established by taking the Casson parameter infinitely large i.e., when .
Keywords
Heat transfer; casson fluid; shear stress; natural convection