Geometric Optimization of Periodic Flow and Heat Transfer in a Volume Cooled by Parallel Tubes

Abstract

This paper addresses the fundamental problem of maximizing the thermal contact between an entire heat-generating volume and a pulsating stream of coolant that bathes the volume. The coolant flows through an array of round and equidistant tubes. Two laminar flow configurations are considered: stop-and-go flow, where the reservoir of coolant is on one side of the volume, and back-and-forth flow, where the volume is sandwiched between two reservoirs of coolant. The total heat transfer rate between the volume and the coolant is determined numerically for many geometric configurations in the pressure drop number range 102⩽B⩽106, and Pr⩾1. The optimal tube radius and the maximum volumetric heat transfer rate are determined numerically. The numerical optimization results are later predicted based on scale analysis by matching the longitudinal and transversal time scales of the temperature field in each tube, for each pulsation stroke. The predicted scales lead to power-law formulas that correlate the results and summarize the optimal geometry. The optimal tube size is nearly the same in stop-and-go flow and back-and-forth flow, and is independent of the pulsation frequency.