The current study aims to study the magnetohydrodynamics (MHD) Casson kind nanofluid stream through a permeable medium above a nonlinear extending surface considered along with Darcy‐Forchimer relation and chemical reaction. Thermophoresis and Brownian diffusion effects are considered. The MHD effect is used to highlight the physical and thermal properties of the nanofluid. The Keller Box scheme is used to solve the guiding equations numerically. Graphs are plotted for various nondimensional parameters. To justify the method, the used local parameters are calculated and compared with the existing literature. The results specify that a decreasing tendency is observed in the velocity profile for Forchiemer, magnetic, and stretching rate parameters, whereas the opposite tendency is noted for the Casson parameter. On observing temperature profiles, declination is noticed for Casson, thermal slip parameters and raising nature is detected for increasing values of Brownian diffusion, and thermophoresis, radiation parameters. From the results, it is observed that the momentum boundary layer diminishes for a higher inertial influence and the opposing force offered by the porous media to the fluid flow.

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The main resource of this paper is to establish over fluid flows sheet using mathematical modeling for constant and variable thickness by including magnetic fields, electric fields, porous medium, heat propagation/immersion, and radiative heat relocation. The Implicit Finite Difference Method (IFDM) is applied to simplify using similarity conversions to implicate partial differential equations to convert into ordinary differential equations. IFDM has been implemented in MATLAB to tabulate numerical observations of the local parameters. Nusselt and Sherwood numbers are analyzed and measured for different parameters in different constant and variable thickness conditions of fluid properties. The influence of various parameters is explained through temperature, velocity, concentration, and nanoparticle volume fraction graphical representations. The coefficient of the skin friction for irregular fluid properties is shown to have a greater influence than that compared for constant fluid properties. Nevertheless, there is a reverse case in the local Nusselt number that is lower for the fluctuating fluid properties than with constant fluid properties. The results showed high‐exactness computational outcomes are attained from the IFDM.

In this paper, heat and mass transfer of MHD Casson fluid under radiation over an exponentially permeable stretching sheet with chemical reaction and Hall Effect investigated numerically. Suitable similarity transformations are used to convert the governing partial differential equations to nonlinear ordinary differential equations. Using a numerical technique named Keller box method the equations are then solved. Study of various effects such as chemical reaction, hall effect, suction /injection on magneto hydrodynamic Casson fluid along with radiation the heat source parameter, chemical reaction parameter, Schmidt number are tabulated for various parameters. Also local parameters are calculated and compared with previous literature the results are found to be in good agreement. The velocity, temperature, concentration visual representations are plotted for various parameters using matlab. Skin friction coefficient, Nusselt number and Sherwood number are calculated in both cases of Newtonian and non-Newtonian it is observed that the friction factor and the heat and mass transfer rates reduces for increase in magnetic parameter. Also for progressive values of radiation parameter, thermal grashof number, concentration grashof number and hall parameter, skin friction coefficient, heat and mass transfer rates increases where as they decreases for chemical reaction parameter, Schmidt number.

In the current workflow and heat exchange of a Casson nanoliquid across a penetrable media above a moving plate with variable thermal conductivity, adaptive thickness and chemical reaction are analyzed. First, the governing nonlinear equations of partial derivative terms with proper extreme conditions are changed into equations of ordinary derivative terms with suitable similarity conversions. Then the resulting equations are worked out using the Keller box method. The effects of various appropriate parameters are analyzed by constructing the visual representations of velocity, thermal, and fluid concentration. The velocity profile increased for shape parameter, and the opposite trend is observed for magnetic, Casson, porosity parameters. Temperature profile increases for magnetic, Casson, Brownian motion parameter, and thermophoresis parameters. Concentration profiles show a decreasing trend for wall thickness, Brownian movement, chemical reaction parameters. Also, skin friction values and calculated and matched with previous literature found in accordance. Also, local parameters Nusselt and Sherwood numbers are calculated and analyzed in detail.