To overcome the computational mesh quality difficulties, mesh-free methods have been developed. One of the most popular mesh-free kernel approximation techniques is radial basis functions (RBFs). Initially, RBFs were developed for multivariate data and function interpolation. It is well-known that a good interpolation scheme also has great potential for solving partial differential equations. In the present study, the RBFs are used to interpolate stream-function and temperature in a two-dimensional thermal buoyancy flow acted upon by an externally applied steady magnetic field. Use of mesh-free methods promises to significantly reduce the computing time, especially for the complex classes of problems such as magnetohydrodynamics. (C) 2009 Elsevier Ltd. All rights reserved.