Laminar mixed convection heat transfer in a horizontal isothermal cooled tube for high Rayleigh numbers and Prandtl numbers is investigated numerically in the present study. The inlet fluid with a fully developed inlet velocity and a constant inlet temperature T0 is cooled in the tube with a constant wall temperature T(w). Variation of the fluid and wall temperature difference and the heat transfer are governed by the Rayleigh number and the Graetz number. To achieve the high Rayleigh number solution in a sufficiently long range of z, a robust scheme of weighting function for solving the energy equation and a control volume method for evaluating the wall temperature gradient are employed. The varying Nu with Ra = 0 approximately 5 x 10(8) in the range of z = 0-0.8 is obtained. This extends the solution to three orders higher in Ra and one order longer in z than those in the literature. Several axial positions characterizing the Nusselt number curve for each Ra are identified and correlated. Comparisons of Nu with the existing experimental data for Ra in the orders of 10(3)-10(8) are made.