A study of the effect of triangular and rectangular surface waves on the natural convective heat transfer from a circular upward facing heated horizontal isothermal surface

Abstract

Natural convective heat transfer from a horizontal, upward facing circular isothermal heated surface imbedded in a large flat adiabatic surface has been numerically studied. The heated circular surface is covered with a series of waves which are arranged in an axially-symmetric (concentric) manner around the vertical axis of the horizontal circular surface. Surface waves with a triangular cross-sectional shape and with a rectangular cross-sectional shape have been considered. Conditions under which the flow is laminar, transitional, and turbulent have been considered. The flow has been assumed to be axially-symmetric and steady. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces which has been treated using the Boussinesq approach. The commercial CFD solver ANSYS FLUENT© was used to obtain the numerical solutions. The standard k-epsilon turbulence model was employed with full account being taken of buoyancy force effects. The heat transfer rate from the heated surface expressed in terms of the Nusselt number is dependent on the Rayleigh number, the number of surface waves, the shape of the surface waves, the dimensionless height of the surface waves, and the Prandtl number. Results have only been obtained for the case where there are five surface waves and for a Prandtl number of 0.74. A detailed study of the variation of the Nusselt number with Rayleigh number for various dimensionless surface wave heights has been undertaken. The heat transfer rates for the wavy surface have been compared with those which would exist in the case of a non-wavy (wave height of zero) surface.