Unsteady magnetohydrodynamic stagnation point flowclosed-form analytical solutions

This paper investigates the unsteady stagnation point flow and heat transfer of magnetohydrodynamic (MHD) fluids over a moving permeable flat surface. The unsteady Navier-Stokes (NS) equations are transformed into a similarity nonlinear ordinary differential equation, and a closed form solution is obtained for the unsteadiness parameter of 2. The boundary layer energy equation is transformed into a similarity equation, and is solved for a constant wall temperature and a time-dependent uniform wall heat flux case. The solution domain, velocity, and temperature profiles are calculated for different combinations of parameters including the Prandtl number, mass transfer parameter, wall moving parameter, and magnetic parameter. Two solution branches are obtained for certain combinations of the controlling parameters, and a stability analysis demonstrates that the lower solution branch is not stable. The present solutions provide an exact solution to the entire unsteady MHD NS equations, which can be used for validating the numerical code of computational fluid dynamics.