Heat transfer augmentation in unsteady conjugate thermal systems – Part II: Applications

Abstract

Many energy conversion and other thermal-fluid systems exhibit unsteady convective heat exchange. In such systems, generic spatiotemporal variations in the flow give rise to variations in the heat flux for a given fluid–solid temperature difference, which can be interpreted as spatiotemporal fluctuations of the instantaneous heat transfer coefficient. These variations can lead to unsteady conjugate heat transfer, in which the exchanged heat flux arises from an interaction between the bulk fluid temperature and the temperature in the solid. Further, the nonlinear coupling between the fluctuating temperature differences and the heat transfer coefficient can lead to an effect we refer to as augmentation, which quantitatively describes the ability of a particular arrangement to have a different time-mean heat flux from the product between the mean heat transfer coefficient and the mean temperature difference across the fluid. It is important to be able to understand and to model in a simple framework the effects of the material properties, the geometry and the character of the heat transfer coefficient on the thermal response of the fluid–solid system, and consequently to predict the overall heat transfer performance of these systems.This paper, which follows on from its predecessor [1], is concerned with the phenomenon of augmentation in simple, one-dimensional, unsteady and conjugate fluid–solid systems. A simple semi-analytical one-dimensional model of heat transfer with a time-varying heat transfer coefficient, which was presented in Mathie and Markides [1], is applied herein to two different paradigm problems. Such a model can be an important tool in the design of improved heat exchangers and thermal insulation, through for example, the novel selection of materials to exploit these augmentation effects. The first flow considered is a thin, wavy fluid film flowing over a heated plate. This film flow exhibits a periodic fluctuation in the heat transfer coefficient, that is linked to the wavy interfacial deformations of free surface of the liquid film. The second flow considered concerns the heat transfer behind a backwards-facing step, which exhibits broadband fluctuations in the heat transfer coefficient due to the flow separation and turbulence behind the step. The model predictions of the augmentation ratio for these problems are also compared to direct measurements from each case. Good agreement is observed with the experimental results for the global heat transfer trends. In both cases the augmentation ratio was negative, reflecting a reduction in time-averaged heat transfer. For the backwards-facing step flow a low magnitude of augmentation ratio was observed, however, the thin film flows exhibited augmentation ratios of as high as 10%.