A 2-D boundary-layer flow induced by non-linear (quadratic) stretching of a curved surface of an incompressible MHD viscous fluid is investigated. Heat transfer analysis is presented including viscous dissipation and thermal radiation. A radially variable magnetic field is applied that satisfies Maxwell's equation and incorporates the curvature effects. A new similarity variable and similarity transformation are introduced to reduce the governing PDE's into ODE's. A numerical procedure is adopted to find the solution of momentum and energy equations. The numerical scheme is validated with the existing data. The results are illustrated graphically and discussed physically. Comparison with the literature shows a significant improvement compared to existing studies.