The present study analyses the magnetohydrodynamic (MHD) flow of a double stratified micropolar fluid across a vertical stretching/shrinking sheet in the presence of suction, chemical reaction, and heat source effects. The governing equations in the form of partial differential equations are transitioned into coupled nonlinear ordinary differential equations by means of similarity transformation. The numerical solutions are obtained with the aid of the boundary value problem bvp4c solver in the MATLAB software. Numerical results have been confirmed with the previous results for a certain case and the comparison is found to be in an excellent agreement. Results for related profiles and heat transfer characteristics are displayed through plots and tabulated for the governing parameters involved. It is found that the reduced skin friction coefficient and the local Nusselt number increase with the increasing chemical reaction and heat source parameters. The rising values of the chemical reaction parameter have increased the magnitude of the local Sherwood number. In contrary, the heat source parameter has the tendency to decrease the magnitude of the local Sherwood number.

The purpose of this study was to investigate the magnetohydrodynamic (MHD) mixed convection flow and heat transfer of a dual stratified micropolar fluid over a vertical permeable stretching/ shrinking sheet with chemical reaction and heat source. The governing nonlinear partial differential equations are reduced into a system of nonlinear ordinary differential equations using an appropriate similarity transformation. Then, the obtained ordinary differential equations are solved numerically using the boundary value problem solver (bvp4c) in MATLAB software. The numerical results are tabulated and plotted for the heat transfer characteristics, namely, the skin friction coefficient, the local Nusselt number, the local Sherwood number as well as the velocity, temperature and concentration profiles for some values of the governing parameters. The present numerical results also have been compared with the previous reported results for a particular case and the comparisons are found to be in an excellent agreement. The results indicate that the skin friction coefficient and the local Nusselt number increase with chemical reaction and heat source. The magnitude of the local Sherwood number increases with the increasing of chemical reaction parameter. However, the magnitude of the local Sherwood number decreases with heat source effect.

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The numerical investigation of unsteady magnetohydrodynamic (MHD) stagnation point flow of Al2O3-Cu/H2O hybrid nanofluid past a convectively heated permeable stretching/shrinking sheet with suction/injection effect is underlined. The characteristic of MHD and boundary condition with suction/injection has received a lot of consideration due to its across-the-board application in mechanical and chemical engineering. The governing continuity, momentum and energy equations are transformed into a system of nonlinear ordinary differential equations using similarity transformation, which is then solved using the bvp4c routine. Numerical results are obtained for the skin friction coefficient, local Nusselt number as well as the velocity and temperature profiles for certain values of the governing parameters, namely suction/injection parameter, copper nanoparticle volume fraction parameter and MHD parameter. Results showed that both velocity profile and temperature increase as the suction/injection parameter increases for the first solution and decreases for the second solution. Similarly, when increase the value of MHD parameter M, the velocity and temperature profiles are decreases for both solutions. The magnitude of the reduced skin friction coefficient and the local Nusselt number are notably increased for the first solution with increasing values of the suction/injection and MHD parameters. Finding also revealed that the skin friction coefficient is intensified in conjunction with the local Nussel number by adding up the copper nanoparticle volume fraction. In general, dual solutions are found to exist to a particular extent of the stretching/shrinking sheet.