Analytic solutions of the friction factor and the Nusselt number for the low-Reynolds number flow between two wavy plate fins

Abstract

Analytic solutions of the Fanning friction factor and the Nusselt number for the low-Reynolds number flow between two wavy plate fins are obtained. The geometric features of the wavy plate fins are described by a sinusoidal variation with three parameters: fin spacing 2H, amplitude of waviness a, and period length L. The fluid flow between two wavy plate fins is assumed to be a 2-D flow. The coordinate transformation in conjunction with the perturbation method is used to solve the governing equations. The results from the analytic solutions are shown to be in close agreement with those obtained from numerical simulations using a commercial code, FLUENT. The applicable range of the present solutions is as follows: a/H⩽0.5, H/L⩽0.33, Pe⩽100. The value of fRe monotonically increases as the dimensionless waviness (a/L) increases and the increment is proportional to the square of a/L. On the other hand, the Nusselt number increases to the peak value and then decreases as H/L increases. Based on the analytic solution, a correlation of (H/L)max for which the Nusselt number attains a maximum is presented.