A numerical study of laminar and turbulent natural convective flow through a vertical symmetrically heated channel with wavy walls

Abstract

Paper presented at the 8th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Mauritius, 11-13 July, 2011.

Natural convective flow through a vertical plane channel has been considered. Both of the heated walls are kept at the same temperature. These heated walls have sharp-edged wavy surfaces. Conditions under which both laminar and turbulent flow exists in the channel have been considered. Now using a wavy heated wall can increase the heat transfer rate in external natural convective flows. Using wavy heated walls in vertical channel flows could therefore potentially also increase the heat transfer rate. However the added flow resistance resulting from the wall waviness will normally decrease the flow through the channel which would tend to decrease the heat transfer rate from the heated walls. Therefore a need existed to examine what effect the wall waviness does have on the heat transfer rate in natural convective flow through a vertical channel and it was for this reason that the present study was undertaken. The flow has been assumed to be steady and the Boussinesq approximation has been adopted. The basic k-epsilon turbulence model with the effects of the buoyancy forces fully accounted for has been used. The solution has the Rayleigh number, the Prandtl number, the ratio of channel width to the heated channel height, the ratio of the amplitude of the wall waviness to the heated channel height, and the ratio of the pitch of the wall waviness to the heated channel height as parameters. Results have only been obtained for a Prandtl number of 0.74 (the value for air at temperatures near ambient) and for a single value of the dimensionless pitch of the wall waviness. This leaves the Rayleigh number, the width to heated height ratio of the channel, and the amplitude of the wall waviness to the heated channel height ratio as parameters. Results have been obtained for a range of values of these parameters and the effect of these parameters on the mean Nusselt number has been studied.