In this current paper, an investigation has been conducted on the magnetohydrodynamic boundary layer flow of non-Newtonian Casson fluids on magnetized sheet with an exponentially stretching sheet. The similarity approach has been used to transform the governing models for Casson fluid to ordinary differential equations. We presented numerical results for momentum, energy and concentration equation parameters. Effects of the magnetized sheet and varying all the emerged parameters on the flow of Casson fluid with respect to the friction between the fluid and the surface, temperature and concentration are presented in tables. As a result of the induced magnetization of the sheet, the thickness of the thermal boundary layer has been enhanced. This behaviour brings a considerable reduction to the heat transfer. The induced magnetized sheet has a similar influence on the skin friction, Nusselt number and the Sherwood number. We however proposed incorporation of magnetized surfaces in MHD flows for controlling the flow rate of the fluid and heat transfer characteristics.

This paper aims at comparing the performance in relation to the rate of convergence of five numerical methods namely, the Bisection method, Newton Raphson method, Regula Falsi method, Secant method, and Fixed Point Iteration method. A manual computational algorithm is developed for each of the methods and each one of them is employed to solve a root-finding problem manually with the help of an TI-inspire instrument. The outcome of the computations showed that all methods converged to an exact root of 1.56155, however the Bisection method converged at the 14th iteration, Fixed Point Iterative Method converged at 7th iteration, Secant method converged at the 5th iteration and Regula Falsi and Newton Raphson methods converged at the 2nd iteration, suggesting that Newton Raphson and Regula Falsi methods are more efficient in computing the roots of a nonlinear quadratic equation.

An analysis of aCasson fluid flowing over a porous exponentially stretching surface with radiation has been studied. A non-Newtonian fluid model was developed for the flow and similarity analysis used in the transformation process. The model of partial differential equations was transformed into ordinary differential equations and reduced into a system of first order differential equations which was then solved using the Fourth-order Runge-Kutta algorithm alongside the Newton Raphson shooting method. The results have been presented graphically and in tabular form for various controlling parameters of the problem. It is observed that general control can be achieved by the permeability of the surface and the value of the Casson parameter.

The fourth order Runge-Kutta integration scheme coupled with numerical shooting algorithm is employed to examine heat and mass transfer in a steady two-dimensional Magnetohydrodynamic non-Newtonian fluid flow over a stretching vertical surface with suction by considering radiation, viscous dissipation, Soret and Dufour effects. A steady twodimensional magneto hydrodynamic non-Newtonian fluid flow over a flat surface with suction has been studied. The boundary layer governing partial differential equations are derived by considering the Bossiness approximations. These equations are transformed to nonlinear ordinary differential equations by the techniques of similarity variables and are solved analytically in the presence of buoyancy forces. The effects of different parameters such as magnetic field parameter, Prandtl number, buoyancy parameter, Soret number, Dufour number, radiation parameter, Brinkmann number, suction parameter and Lewis number on velocity, temperature, and concentration profiles are presented graphically and in tables and discussed quantitatively. Results show that the effect of increasing Soret number or decreasing Dufour number tends to decrease the velocity and temperature profiles (increase in Soret cools the fluid and reduces the temperature) while enhancing the concentration. Among the many importance of the fluid in chemical engineering, metallurgy, polymer extrusion process will definitely require cooling the molten liquid to further cool the system, for the production of paper and glass. In this process, the rate of cooling and shrinking influences very much on the final quality of the product.

An extensive investigation into heat transfer through Casson fluid on a stretched magnetized surface with presence of chemical reactants has been conducted. The magnetic strength influence at the plate surface and within the body of the fluid has been analysed as well as effects of radiation and convection fields are considered. The methods of similarity analysis have been used to transform the multivariable dependent equations modelling the flow to a single variable dependent equation. The emerged dimensionless parameters describing the flow have been presented numerically. The effects of magnetization of the surface along with the bulk fluid are presented in tables and graphs. It is evident that magnetizing the surface enhances the temperature distribution near the surface. Similar results can be seen with the coefficient of wall resistance, and the mass and transfer rate on the magnitised plate. From the study, it is recommended that surface magnetization can influence flow kinematics involving Casson fluids for efficient control.