Heat Flux Across Viscous Flow in Wavy Channels

Abstract

The heat flux across a fluid layer flowing between two sinusoidal walls is theoretically investigated. The surfaces of those walls are assumed to be maintained at constant and different temperatures. Specifically attention is given to the convective heat transfer due to a flow induced by the wavy walls. In the case of the sinusoidal walls with small amplitude, the heat flux integrated over one wavelength of the walls is proportional to the square of that amplitude and the proportional constant depends on the wave number, the phase difference, the Reynolds number, the Prandtl number and the Grashof number. When the wave numbers are from 2 to 3, the convective heat transfer becomes maximum. The heat flux in the case with no phase difference is larger than that in the case with a phase difference, except the case that the Reynolds number is large and the wave number is comparatively small.