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 .
Highlights
Non-Newtonian fluids have various important industrial applications in many fields [1,2], due to which the researchers are paying attention to study the non-Newtonian fluids in their investigations
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
Summary
Non-Newtonian fluids have various important industrial applications in many fields [1,2], due to which the researchers are paying attention to study the non-Newtonian fluids in their investigations. In literature many non-Newtonian fluids was investigated, one of them is Casson fluid. In 1959 the Casson have presented this fluid model. Oka [3] was the first researcher who used the Casson fluid model in tube problem. Casson fluids examples are blood, honey, soup, stuffs, jelly, artificial fibers, slurries, etc. Casson fluids have various industrial, engineering and medical applications [4]. The investigation of Casson fluid with magnetohydrodynamic (MHD)
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