Computational Study on MHD Nanofluid Free Convection in a Porous Medium with the Impact of Brownian and Thermophoretic: Analysis of Homotopy Perturbation Approach

In the present study, magnetohydrodynamic (MHD) nanofluid free convective flow past a vertical permeable plate is investigated, considering thermophoretic effects, Brownian motion, and thermal radiation. The solution of the governing equations of the nanofluid model proposed by Buongiorno analytically is done through the Homotopy Perturbation Method (HPM), which generates closed-form expressions for the temperature, velocity & nanoparticle concentration profile. Also, Nusselt number, Sherwood number and skin friction coefficient are established explicitly. The literature has a relatively few explicit analytical solutions, which explicitly consider Brownian motion, thermophoresis, magnetic effects, porous resistance, and thermal radiation. The results show that radiation reinforces the thermal boundary layer, magnetic and porous resistances prevent flow, and Brownian and thermophoretic forces have a considerable influence on the distribution and transport rates of nanoparticles. The consistency of HPM is supported by agreement with well-established physical tendencies reported in past studies.