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

Abstract

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 ( Pr m ) is found to strongly enhance wall heat transfer rate ( Nu x Re x − 1 / 2 ), 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. Nu x Re x − 1 / 2 , but reduces magnetic field function, g and temperature, θ. Increasing ordinary Prandtl number ( Pr), decreases temperature, θ, but increases wall heat transfer rate ( Nu x Re x − 1 / 2 ). 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, Nu x Re x − 1 / 2 . The model has potential applications in astronautical magneto-thermo-aerodynamics, nuclear reactor channel flow control with magnetic fields and MHD (magnetohydrodynamic) energy generators.