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_xRe_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_xRe_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_xRe_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_xRe_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.