This paper mainly deals with conjugate heat transfer problem pertinent to rectangular fuel clement of a nuclear reactor dissipating heat into an upward moving stream of liquid sodium. Introducing boundary layer approximations, the equations governing the flow and thermal fields in the fluid domain are solved simultaneously along with two-dimensional energy equation in the solid domain by satisfying the continuity of temperature and heat flux at the solid-fluid interface. The boundary layer equations are discretized using fully implicit finite difference scheme so as to adopt marching technique solution procedure, while second-order central difference scheme is employed to discretize the energy equation in the solid domain and the resulting system of finite difference equations are solved using Line-by-Line Gauss-Seidel iterative solution procedure. Numerical results are presented for a wide range of parameters such as aspect ratio, A(r), conduction-convection parameter, N-cc, heat generation parameter, Q, and flow Reynolds number, Re. It is concluded that there exist an upper or a lower limiting value of these parameters above or below which the temperature in the fuel element crosses its allowable limit. It is also found that an increase in Re results in considerable increase in overall heat dissipation rate from the fuel element. (c) 2006 Elsevier Ltd. All rights reserved.