The paper is connected to investigate numerical simulation of two-dimensional laminar steady-state on MHD free convection within trapezoidal cavity with non-uniformly heated bottom wall. The cavity consists of non-uniformly heated bottom wall, insulated top wall and isothermal side walls with inclination angles (phi). Heat flow patterns in the presence of free convection within trapezoidal enclosures have been analyzed with heatlines concept. The fluid is concerned for the wide range of Rayleigh number (Ra) from 10(3) to 10(7) and Prandtl number (Pr) from 0.026, 0.7, 1000 with various tilt angles Phi = 45 degrees, 30 degrees and 0 degrees (square). The physical problems are represented by non-dimensional governing equations along with the corresponding boundary conditions and discretized by using Galerkin weighted residual method of finite element formulation. Results are presented in terms of streamlines, isotherms, local Nusselt number along distance and average Nusselt number along Rayleigh number, Ra for non-uniform heating of the bottom wall, governing parameters namely, Prandtl number Pr, and at the three values of Rayleigh number Ra, varying from 10(3) to 10(7), covering free convection dominated regimes. It is shown that the average and local Nusselt number at the non-uniform heating of bottom wall of the cavity is depending on the dimensionless parameters and also tilts angles. Crown Copyright (C) 2013 Published by Elsevier Ltd. All rights reserved.