Thermal Characteristics in a Curved Rectangular Channel With Variable Cross-Sectional Area

Abstract

Heat transfer due to steady, laminar air flow through a curved rectangular channel with a variable cross-sectional (c/s) area is investigated computationally. Such a flow passage is formed between two fin walls of a curved fin heat sink with a 90 deg bend, used in avionics cooling. Simulations are carried out for two different configurations: (a) a variable c/s area curved channel with inlet and outlet sections (entry and exit lengths) that are straight and constant c/s area—termed as the long channel and (b) a variable c/s area curved channel with no entry and exit lengths—termed as the short channel. Multiple secondary flow patterns develop in the curved section of the channel, which in conjunction with the bulk axial flow, lead to the formation of multiple vortices and separation bubbles. The complex 3-D flow structures, as well as the variable c/s area of the curved channel (diverging–converging) significantly alter the heat transfer characteristics, compared to the straight fin heat sink. Secondary flow strengthens with increasing axial (bulk) flow velocity, or Dean number in dimensionless form. This in turn improves heat transfer from all walls, particularly, the outer curvature (concave) wall and the heat sink base. At the highest Dean number condition, the local heat transfer coefficient at certain locations of the outer curvature wall is augmented by as much as 3.5 times, compared to the straight fin walls. The overall channel average heat transfer coefficient is improved by about 40% for the long channels, and about 10% for the short ones. However, the heat transfer enhancement is associated with a penalty of higher pressure drop, compared to the straight channels. To quantify the effectiveness of thermal performance enhancement a system Figure of Merit (FOM) is defined. A greater than unity FOM value is observed for all curved channel geometries and flow rate conditions. This indicates that heat transfer enhancement in the variable c/s area curved channel outweighs the penalty of additional pressure drop, compared to a straight channel of similar length.