The phenomena of natural convection in a right-angled triangular enclosure is studied numerically. A penalty finite element analysis with bi-quadratic elements is used for solving the Navier-Stokes and energy balance equations. The detailed study is carried out in two cases depending on various thermal boundary conditions: (a) Vertical wall is uniformly or linearly heated while inclined wall is cold isothermal. (b) Inclined wall is uniformly or linearly heated while vertical wall is cold isothermal. In all the cases horizontal bottom wall is adiabatic and the aspect ratio of the lengths of base and height is considered to be one. The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters of Rayleigh number Ra (10(3) <= Ra <= 10(5)) and Prandtl number Pr (0.07 <= Pr <= 1000) in all the cases mentioned above. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. It has been found that at low Rayleigh numbers (Ra <= 10(4)), the isotherms are almost parallel near the bottom portion of the triangular enclosure while at Ra = 10(5), the isotherms are more distorted. This is because the heat transfer is primarily due to conduction for lower values of Rayleigh number. As Rayleigh number increases, there is a change from conduction dominant region to convection dominant region, and the critical Rayleigh number corresponding to on-set of convection is obtained. It has been shown that the average Nusselt number for vertical wall is root(2) over bar times that of the inclined wall as the bottom wall is adiabatic and that verifies the thermal equilibrium of the system for all case studies. (C) 2007 Elsevier Ltd. All rights reserved.