The problem of steady, laminar and incompressible natural convection flow in an octagonalenclosure was studied. In this investigation, two horizontal walls were maintained at a constant hightemperature, two vertical walls were kept at a constant low temperature and all inclined walls wereconsidered adiabatic. The enclosure was assumed to be filled with a Bousinessq fluid. The studyincludes computations for different Prandtl numbers Pr such as 0.71, 7, 20 and 50 whereas the Rayleighnumber Ra was varied from 103 to 106. The pressure-velocity form of Navier-Stokes equations andenergy equation was used to represent the mass, momentum and energy conservations of the fluidmedium in the enclosure. The governing equations and boundary conditions were converted todimentionless form and solved numerically by penalty finite element method with discretization bytriangular mesh elements. Flow and heat transfer characteristics were presented in terms of streamlines, isotherms and average Nusselt number Nu. Results showed that the effect of Ra on the convection heattransfer phenomenon inside the enclosure was significant for all values of Pr studied (0.71-50). It wasalso found that, Pr influence natural convection inside the enclosure at high Ra (Ra > 104).