Unsteady Casson Fluid Flow Subject to Natural Convection and Quadratic Free Convection along with Applied Transverse Magnetic Field

In the present study, Casson fluid flow past an instantly stretched sheet is studied. The initial fluid flow is of Crane type. At , the fluid is subject to sudden stretching as well as Quadratic free convection along with the application of a sudden transverse Magnetic field. This sets in unsteadiness in the fluid flow. As time progresses, , the fluid flow becomes steady.  The fluid flow settles down to steadiness at different time intervals for different values of parameters. The parameters include Quadratic free convective parameter, Grashof number, transverse magnetic field parameter, and Casson fluid parameter. The numerical computations are carried out using the well-established Crank-Nicolson method. Validation of numerical computations is carried out by comparing the results of computations with analytic solutions at a steady state for applicable cases. Our results are in good agreement with the analytic solutions. Plots for Horizontal velocity, Vertical velocity, Temperature field, local Skin friction, and local Nusselt number are described. Transient progressive profiles of the dependent variables are described to understand the nature of unsteadiness. The results show that the Quadratic free convection can be utilized to control the fluid flow to obtain finer results.