Fully developed laminar flow in trapezoidal grooves with shear stress at the liquid–vapor interface

Abstract

This paper discusses the behavior of liquid flowing in a groove with a trapezoidal cross-section. For fully developed laminar flow, the conservation of mass and momentum equations reduce to the classic Poisson equation in terms of the liquid velocity. A finite difference solution was employed to determine the mean velocity, volumetric flow rate, and Poiseuille number ( Po= fRe) as functions of the groove aspect ratio, groove-half angle, meniscus contact angle and imposed shear stress at the liquid–vapor interface. Comparisons with existing solutions for fully developed flow in rectangular ducts and rectangular and triangular grooves are provided. The volumetric flow rate in a groove in which the fill amount varies is discussed. A semi-analytical solution and a two-point numerical solution for the mean velocity in a groove are presented and used to determine the capillary limit for a revolving helically grooved heat pipe. The effects of interfacial shear stress and groove fill ratio on heat pipe performance are investigated.