In this work, the effects of radiation optical properties and Lorentz force on the 2D unsteady laminar boundary magnetohydrodynamic (MHD) fluid flow and heat transfer along a semi-infinite stretching plate are numerically investigated, the Joule heating effect and viscous dissipation are considered. The heat flux caused by the thermal radiation is obtained by solving the radiation transfer equation (RTE) instead of the Rosseland approximation. All the governing equations, including continuous equation, momentum equation, energy equation, and RTE subject to the boundary radiative emission, are transformed into dimensionless forms. The dimensionless governing equations together with the corresponding boundary conditions are solved numerically via Chebyshev collocation spectral method (CCSM). The effects of various physical parameters, say, Ha, Pr, Ec and Pl, especially the optical properties such as the optical thickness, the scattering albedo, and the wall emissivity of the plate, on the flow and heat transfer are depicted graphically and analyzed in detail. It is found that, due to the thermal radiation, the overall average temperature within the boundary layer becomes much higher and the boundary layer becomes thicker. The magnetic force can suppress the fluid flow significantly and stop the convective heat transfer effectively. Viscous dissipation and Joule heating greatly enhance the temperature distribution with the help of the magnetic field. (C) 2016 Elsevier Ltd. All rights reserved.