Abstract
In this paper, the rate of heat transfer of the steady MHD stagnation point flow of Casson fluid on the shrinking/stretching surface has been investigated with the effect of thermal radiation and viscous dissipation. The governing partial differential equations are first transformed into the ordinary (similarity) differential equations. The obtained system of equations is converted from boundary value problems (BVPs) to initial value problems (IVPs) with the help of the shooting method which then solved by the RK method with help of maple software. Furthermore, the three-stage Labatto III-A method is applied to perform stability analysis with the help of a bvp4c solver in MATLAB. Current outcomes contradict numerically with published results and found inastounding agreements. The results reveal that there exist dual solutions in both shrinking and stretching surfaces. Furthermore, the temperature increases when thermal radiation, Eckert number, and magnetic number are increased. Signs of the smallest eigenvalue reveal that only the first solution is stable and can be realizable physically.
Highlights
In this paper, the rate of heat transfer of the steady MHD stagnation point flow of Casson fluid on the shrinking/stretching surface has been investigated with the effect of thermal radiation and viscous dissipation
Double solutions were found by Hamid et al.[15] within the sight of thermal radiation
Stability analysis was performed by utilizing of BVP4C in the MATLAB programming
Summary
There has been studied as steady incompressible 2-D stagnation point flow of Casson electrically leading fluid on an exponentially shrinking and stretching surfaces with the impact of thick viscous dissipations and thermal radiation. There has been supposed that rheological equation of the state for the isotropic and the incompressible progression of the Casson fluid which are reported as (allude10): τij. A system of cartesian coordinate is taken into account, where the x-axis is supposed alongside the shrinking/Stretching surface and the y-axis is normal to it. The uniform magnetic field is applied to the normal of the fluid flow B=B0ex/2l where B0 is the constant magnetic strength (Fig. 1). The field of induced magnetic is disregarded as a result of the small estimation of the magnetic Reynolds number.
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