This paper aims to examine the Darcy–Brinkman flow over a stretching sheet in the presence of frictional heating and porous dissipation. The governing equations are modeled and simplified under boundary layer approximations, which are then transformed into system of self-similar equations using appropriate transformations. The resulting system of nonlinear equations was solved numerically under velocity and thermal slip conditions, by fourth-order Runge–Kutta method and built-in routine bvp4c in Matlab. Under special conditions, the obtained results were compared with the results available in the literature. An excellent agreement was observed. The variation of parameters was studied for different flow quantities of interest and results are presented in the form of tables and graphs.

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An analysis is discussed of the heat and mass transfer for micropolar nanofluid in presence of natural convection from a spherical body with magneto-hydrodynamic (MHD) effects. The constant wall temperature boundary condition is also studied. By employing proper similarity transformations, the governing equations are converted into a set of partial differential equations (PDEs) with the used boundary conditions, which can then be solved numerically via the efficient Keller-box implicit numerical finite difference method. The numerical results of impacts of the controlling parameters on heat transfer physical quantities have been presented, tabular and graphically, by MATLAB symbolic software. Comparisons of the current study results to previously published results show good agreement, indicating that our numerical computations are legitimate and accurate. Increasing nanoparticle volume fraction is observed to depress local skin friction, Nusselt number, and angular velocity while the reverse effects are observed for velocity and temperature.

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