Title:

Unsteady and conjugate heat transfer in convectiveconductive systems

Unsteady (timevarying) heat transfer is an important transport phenomenon that is found in many engineering and industrial applications. In such systems, generic spatiotemporal variations in the flow give rise to variations in the heat flux for a given fluidsolid temperature difference, which can be interpreted as spatiotemporal fluctuations of the instantaneous heat transfer coefficient. These variations can lead to unsteady and 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 coefficients can lead to an effect we refer to as augmentation, which quantitatively describes the ability of a particular arrangement to have a different timemean heat flux from the product between the mean heat transfer coefficient and the mean temperature difference across the fluid. In this thesis we investigate unsteady conductiveconvective heat transfer, and the resulting augmentative and conjugate effects. The overriding purpose is to propose a simple framework for the description of the effect of unsteadiness on the overall heat exchange performance, leading to the improved understanding and prediction of related processes. An analytical model is developed that describes the thermal interaction between the solid and the fluid domains with the use of a timevarying heat transfer coefficient, and assuming 1D conductive heat transfer in the solid. It is found that the degree of augmentation can be defined in terms of key independent problem variables, including: a timeaveraged Biot number, a dimensionless solid thickness (normalised by an unsteady thermal diffusion length), a heat transfer coefficient fluctuation intensity (amplitude normalised by the mean), and a heat capacity ratio between the fluid and solid domains. The model is used to produce regime maps that describe the range of conditions in which augmentation effects are exhibited. Such maps can be used in the design of improved heat exchangers or thermal insulation, for example through the novel selection of materials that can exploit these augmentation effects. Cases are considered for which the bulk fluid temperature is fixed, and for which the bulk fluid temperature is allowed to respond to the solid, both in thermally developing and fully developed flows. Generally the augmentation effect is found to be negative, reflecting a reduction in the heat exchange capability. However, regions of positive augmentation are uncovered in thermally developing convective flows, which has important implications for heat exchanger design. The approach is used to model two different thermodynamic cycles; gas springs and twophase thermodynamic oscillator engines. Firstly, for the gas spring it is found that at low Peclet numbers the addition of an insulating layer exacerbates the thermal losses in the spring as it shifts the system away from the isothermal ideal operation. Conversely at high Peclet numbers thicker insulating layers reduces the loss as it shifts the system towards the adiabatic ideal. It is also found that there is an intermediate thickness of material thickness which maximises the loss in the gas spring, by up to 20 % of the nominal maximum loss for an isothermal cylinder lining. Secondly the heat transfer and resulting shuttle loss in the vapour space of a twophase thermofluidic oscillator was studied. This model was compared to experimental data from a working test bed and resulted in a substantial improvement in the calculation of the cycle efficiency of the engine. Detailed flow measurements were also conducted on a fluid film flowing down a heated incline, to investigate the effects of unsteady heat transfer in these flows. These wavy interfacial flows exhibit large and periodic fluctuations in heat transfer and the frequency and amplitude of the waves was controlled by a specially constructed flow preparation arrangement. To enable the temperature and heat flux measurements the heated incline consisted of a thin titanium foil. A novel measurement technique was developed (here, for the first time) to measure the film interface height (film thickness), film temperature and instantaneous heat flux through the heated surface. This was achieved with a combination of spatiotemporally resolved Laser Induced Florescence (LIF) measurements and Infrared (IR) thermography. In the case of steady flow conditions (without forced waves) the formation of Marangoni driven rivulet structures are observed on the film surface. In the case of unsteady flow the formation of waves on the film surface result in visible mixing of the rivulet structures. The mixing and the unsteady motion of the waves give rise to a periodic fluctuation in the heat transfer coefficient, with fluctuation intensities of up to 35 % being recorded. 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 is negative, reflecting a reduction in timeaveraged heat transfer. Finally, a backwardsfacing step flow is also studied, for which a low magnitude of augmentation was observed (< 1 %), considerably lower than the augmentation measured in the thin film flows which were up to 10 %.
