A numerical investigation of natural convective heat transfer from a horizontal upward facing isothermal heated surface having a series of equally spaced triangular shaped waves and imbedded in a flat adiabatic surface was undertaken. Most previous studies of this situation dealt with the case of waves of constant height. The possibility of increasing the heat transfer rate enhancement of surface waves by using waves of varying height was numerically investigated. Waves decreasing linearly in height from the center of the surface to the edge of the surface and waves increasing linearly in height from its center to the edge of the surface were considered. Two-dimensional steady flow was assumed. The Boussinesq assumption was adopted in dealing with the buoyancy forces. The solution was obtained using the commercial CFD solver ANSYS FLUENT^©. Laminar, transitional, and turbulent flow conditions were considered. The k-epsilon turbulence model was applied with account being taken of buoyancy force effects. The mean heat transfer rate from the surface expressed in terms of a Nusselt number is dependent on the Rayleigh number, the number of surface waves, the average height of the waves relative to their width, the form of the wave height variation, and the Prandtl number. Results were obtained for a Prandtl number of 0.74 and for the case where there are ten waves across the surface. Variations of the Nusselt number with Rayleigh number for various wave height distributions were studied. Results indicate that non-constant wave heights do not significantly increase the heat transfer rate.