An effect of magnetohydrodynamic and radiation on axisymmetric flow of non-Newtonian fluid past a porous shrinking/stretching surface

The magnetohydrodynamic axisymmetric flow of Casson fluid over a nonlinear permeable shrinking or stretched surface is discussed in this article. Indeed, the heat transfer characteristics of an axisymmetric fluid across a non-linearly shrinking or stretching surface provided by a Casson fluid are examined analytically. Thermal radiation term is incorporated into the equation for the temperature field. Through sufficient transformations, the aforementioned non-linear PDEs are turned into ODEs. The transformed equations are then solved analytically. And an incomplete gamma function is used to depict the temperature solution analytically. The temperature equation is transformed to an incomplete gamma functions using the Rosseland approximation for the radiation and solved analytically. To estimate mass transpiration analytically, the momentum equation is investigated. To acquire the analytical results, this mass transpiration is carried out in the analysis of heat transfer under the Navier slip condition. Graphical analysis can be used to assess important physical aspects like the magnetic field, Casson parameter, mass transpiration, radiation, and Prandtl number. Dual solutions for the velocity, temperature and skin friction were obtained. In fact, for higher Prandtl number, the temperature inside the boundary layer reduces. The resulting dual solution projects that local skin friction coefficient a escalates in the first branch solution and decelerates in the second branch solution with the increase in the magnetic parameter. additionally, efficiency is increased for higher values of thermal radiation.