Insight into thermal dynamic of stagnated flow of MHD Jeffery fluid when the joule heating, viscous dissipation and Soret effect are present: A multistep Milne's approach

The purpose of this work is to use the RK approach in conjunction with Milne's Predictor Corrector method to investigate the numerical solution of the magnetohydrodynamic Jeffery fluid passing over the upper horizontal parabolic surface. Milne's predictor-corrector methodology is highly important since it increases result accuracy when compared to either approach alone. The physical aspects are investigated by using the variable fluid properties, and consider the stagnation point and boundary layer flow of the MHD Jeffery fluid, which flows on the upper horizontal parabolic surface. The influence of Jeffery fluid flowing the paraboloid surface is ascertained by measuring the velocity slip and melting surface effects. We examined both the heat and mass transfer rates with the effects of viscous dissipation, Joule heating, heat source/sink, activation energy, and the Soret effect because these rates are important in chemical reactions, electronic devices, climate change, separation and distillation processes, and water and air pollution. The governing equations in the form of PDEs are obtained by implementing all of the assumptions on the fundamental conservation laws. These equations are then converted into ODEs by using the similarity variables. The "Milne's Predictor-Corrector Method" is a numerical strategy used to solve numerical problems and the results are analyzed both graphically and numerically manners with this numerical technique. Analysis is done on the graphical behavior of many parameters on the temperature, concentration, and velocity regions. The numerical findings of skin friction and Nusselt number are also presented here, and the outcomes are compared with the results of the BVP5c and Milne's (Predictor-Corrector) methods. The obtained results indicated that the motion (velocity) of Jeffery fluid is restricted by the enhancement in Deborah number, retardation to relaxation parameter, Hartmann number, and viscosity parameter, whereas augmentation happens in fluid velocity due to melting parameter and stretching ratio parameter. The temperature region can be increased by the source of the viscosity parameter, Hartmann number, heat source/sink parameters, and Eckert number. The decline in the concentration distribution is noted due to activation energy and the reaction rate parameter, while an upsurge in concentration occurs due to the Soret number.