The Study of an Inclined Internally Heated Fluid Flow

Abstract

The subject of this dissertation is an analysis of fluid flow stability. Early transitions of convection are theoretically modelled when considering an internal heat source and asymmetric boundary conditions. The motivation of this study is to analyse the bifurcation sequence of the specified model. Physical properties of the flow are varied through control parameters such as: Reynolds number, Prandtl number and the angle of inclination. A number of cases are compared and numerically analysed in order to pinpoint regions where stability of the basic configuration breaks down. Furthermore, a non-linear analysis is done within the found regions in the interest of identifying further structural instabilities. The model defined in this dissertation is applicable to a number of natural and industrial processes; the focus is to define a model that mirrors the cooling process within the shut down of a nuclear reactor. In such cases the source of the internal heat is the radioactive decay of molten nuclear fuel within the nuclear reactors. By modelling such a system, we aim to study the effects of convection with internally heated systems. In the present study, we have identified the boundaries between a laminar and convective state for varying Prandtl number; so far we can deduce that as the Reynolds number is increased slightly, the critical Grashof number becomes more positive, suggesting that for small variations in the Reynolds number our fluid is stable in a greater region. The angle also has a similar effect for small variations, although we find when both the angle and Reynolds number are increased further this behaviour changes and the fluid in fact becomes less stable. Through the non-linear analysis performed, we identify the parameter space of the thermal flow patterns and enforce small disturbances to the states to determine their stability.