An integral approach for hydromagnetic natural convection heat and mass transfer from vertical surfaces with power-law variation in wall temperature and concentration in porous media

This work uses the integral method to study the heat and mass transfer by natural convection from vertical plates with variable wall temperature and concentration in porous media saturated with an electrically conducting fluid in the presence of a transverse magnetic field. The surface temperature and concentration are assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. The approximate solutions are found to be in reasonable agreement with the similarity solutions. Results are plotted for the local Nusselt number, the local Sherwood number, and the reciprocal of the ratio of the thermal boundary-layer thickness to the concentration boundary-layer thickness. Increasing the power-law exponents tends to increase the local Nusselt number and the local Sherwood number. Increasing the magnetic parameter decreases the local Nusselt number and the local Sherwood number. Moreover, the ratio of the thermal boundary-layer thickness to the concentration boundary-layer thickness increases with the Lewis number, and it also increases with the buoyancy ratio when the Lewis number is not equal to one.