Nonsimilar, laminar, steady, electrically-conducting forced convection liquid metal boundary layer flow with induced magnetic field effects

A nonsimilar steady laminar boundary layer model is described for the hydromagnetic convection flow of a Newtonian, electrically-conducting liquid metal past a translating, non-conducting plate with a magnetic field aligned with the plate direction. The non-dimensional boundary layer equations are solved with the Sparrow–Quack–Boerner local nonsimilarity method (LNM). An increase in magnetic Prandtl number (Prm) is found to strongly enhance wall heat transfer rate (), velocity (f′) and induced magnetic field function (g), but exerts negligible influence on the temperature (θ) in the boundary layer. A rise in magnetic force number (β) increases velocity, f′, shear stress function, f″, and wall heat transfer gradient, i.e. , but reduces magnetic field function, g and temperature, θ. Increasing ordinary Prandtl number (Pr), decreases temperature, θ, but increases wall heat transfer rate (). An increase in wall to free stream velocity ratio parameter, ζ, increases flow velocity, f′, and induced magnetic field gradient, g′ for small ξ but reduces g′ for larger ξ, and also boosts the wall temperature gradient, . The model has potential applications in astronautical magneto-thermo-aerodynamics, nuclear reactor channel flow control with magnetic fields and MHD (magnetohydrodynamic) energy generators.