Core Annular Flow Theory as Applied to the Adiabatic Section of Heat Pipe
The core annular flow (CAF) theory is used to model the parallel flow of fluids of different phases. CAF theory has been applied to a lot of industrial applications from bitumen hydro transport to sub-aqueous drag reduction. Here we consider the extension of core annular flow theory to the study of the adiabatic section of heat pipes as heat pipes deal with the two-phase flow of fluids in parallel, flowing in opposite direction. We aim to develop a first-principles estimate of the conditions
... essary to maximize the (counter) flow of liquid and vapor and, which by extension, maximizes the axial flow of heat. This work investigates a model of the heat pipe in both planar geometry and cylindrical geometry. Moreover, both the geometries considered the heat pipes either containing or devoid of a wick. In these two respective cases, the peripheral return flow of liquid is driven by capillarity and by gravity. Our model can predict velocity profiles and the appropriate pressure gradient ratio (vapor-to-liquid). We further obtain estimates for the optimum thickness of the liquid layer which is required to obtain the maximum mass flow rate. In the case of wick based heat pipe when the liquid flow occurs via capillary pumping, there is a minimum surface tension below which the wick cannot supply a sufficient flow of liquid. We have characterized this critical point in terms of e.g. the viscosity ratio, the density ratio, and the wick depth, porosity, and permeability. We have compared the pressure gradient ratio (vapor-to-liquid) obtained from our model to experimental data from Shafahi et al. (2010) . One inconsistency that our model contains is that the interface is assumed to be flat insofar as using the shear-stress boundary condition but curved insofar as supporting the capillary pressure required by the heat pipe to drive the flow of liquid. We have explored this discrepancy addressed in chapter 2 by using the perturbation theory in chapter 3. Chapter 3 considers two-phase flow in a porous medium extending infinitely and ii curved meniscus at the liquid-vapor interface. Using such a model we have preserved the essential features required to study the effect of a curved interface. Chapter 3 shows the effect of using a deflected interface in the porous medium on the velocity profiles. Finally, we characterize the magnitude of the effect of using a curved interface for liquid vapor parallel flow in the porous medium when compared against the model considering a flat interface.