Periodic, fully developed, natural convection in a channel with corrugated confining walls

Numerical solutions are obtained for natural convection heat transfer in an open channel with corrugated, isothermal confining walls. The channel is very long so that the fluid temperature approaches the wall temperature and the flow can be assumed to be periodically fully developed. The solutions are obtained by solving the full elliptic governing equations in a transformed coordinate system which maps the channel with corrugated walls onto a channel with flat walls. The periodic, fully developed Nusselt number for the corrugated channel is expressed by the relation Nu = CGrPr/(L/W) where Gr, Pr and L/W are the Grashof number, the Prandtl number and the aspect ratio, respectively, and C is a parameter which is a function of Gr, L/W and the corrugation angle θ. In the limiting case of θ = 0° (two flat walls), the parameter C approaches a constant value. This value is within 1.6% of the exact analytical result.