MHD flow of water-based Brinkman type nanofluid over a vertical plate embedded in a porous medium with variable surface velocity, temperature and concentration

The aim of this paper is to investigate the unsteady magnetohydrodynamic (MHD) flow of Brinkman type nanofluid over a vertical plate embedded in a porous medium with variable surface velocity, temperature and concentration. The thermal radiation effect in the energy equation and chemical reaction in the concentration are also considered. Four different types of nanoparticles of spherical shape namely Silver (Ag), Copper (Cu), Titanium oxide (TiO2) and Aluminum oxide (Al2O3) are suspended in water taken as conventional base fluid. The problem is modeled in terms of partial differential equations with physical boundary conditions. Closed form solutions are obtained for velocity, temperature and concentration, using the Laplace transform technique. Graphical results for different physical parameters such as Brinkman parameter, volume fraction and radiation parameter are presented. Corresponding expressions for skin-friction, Nusselt number and Sherwood number are also evaluated. The present solutions are reduced to some well-known results in the published literature and are found in an excellent agreement.