Enhanced Longitudinal Heat Transfer in Oscillatory Channel Flow—A Theoretical Perspective

Abstract

Enhanced longitudinal heat transfer in viscous, laminar, single-phase, oscillatory channel flow is investigated in this paper. Kurzweg (ASME J. Heat Transfer-Trans. ASME. 107, 1985) analyzed this case theoretically and derived a correlation for a nondimensionalized effective thermal conductivity in terms of Prandtl and Womersley numbers. The present investigation contributes analysis of limiting cases and physical interpretation to the results of Kurzweg. A simplified model with isothermal walls is proposed, applicable if working fluid and channel wall material exhibit sufficiently large differences in thermal inertia. Examined over a wide range of Womersley numbers, this model reveals six distinct regimes characterized by the Prandtl number of the fluid. The respective thickness of hydrodynamic and thermal boundary layers relative to the channel width is relevant in this context. Maximum effective thermal conductivity is attained when the thermal boundary layer expands over the full channel width. The influence of Womersley number is discussed and explained in terms of the interplay of hydrodynamic and thermal flow characteristics. These patterns reveal either quasi-steady parabolic or oscillating bulk characteristics. The importance of the thermal boundary layer thickness motivates the introduction of a new nondimensional group, making it easier to classify the various regimes of enhanced longitudinal heat transfer.