Heat transfer in the thermally developing region of a laminar oscillating pipe flow

Abstract

A theoretical analysis was performed focusing on the heat transfer associated with the laminar oscillating flow in a tube. This situation finds applications in the Stirling engines or regenerative-type refrigerators where the working fluid in the heat exchanger undergoes an oscillatory motion. Such an oscillating flow conceivably entails the thermally developing region, not only because the swept length of working fluid is roughly equal to or longer than. the characteristic length of the heat exchanger, but also because the wall temperature changes abruptly along the longitudinal direction. For simulation of the practical heat exchanger composed of cooler and heater, two types of thermal boundary conditions are taken into account; either wall temperature or wall heat flux has a square-wave distribution. It is found that the thermally developing length increases in proportion to the oscillation frequency at slow oscillation but eventually approaches an.asymptotic value at high frequency. The local average Nusselt number in the developing region is observed to be inversely proportional to the square root of the distance measured from the thermal discontinuity. Out of the thermally developing region, the local Nusselt number is determined only by the oscillation frequency regardless of axial position. (C) 1998 Elsevier Science Ltd. All rights reserved.