Studies on buoyancy-induced open flows : plane thermal plume

Abstract

In the present thesis, the natural convection flow over a line heat source is studied for the mean flow and the linear stability characteristics at different Prandtl numbers. This flow is purely driven by buoyancy and called a thermal plume. The temperature of the fluid is more at the line heat source than the surrounding fluid - the resulting density difference generates buoyancy force which drives the plume through the ambient fluid. The stability and the transition behaviour of a thermal plume are not well understood at high Prandtl numbers which is the focus of the present thesis. Understanding natural convection is very important for environmental problems, like atmospheric and oceanic circulations, as well as for a vast number of engineering and industrial applications. The mean flow of a plane thermal plume is analysed for the leading-order and the higher-order terms by using boundary-layer approximations. The leading-order mean flow equations are solved by using the Runge-Kutta method with the NewtonRaphson correction. The computed results have been validated by comparing them with known analytical results. With increasing Prandtl number (P), the thermal boundary layer becomes thinner and the velocity levels are decreased in the plume. Since the viscous diffusion is more for high Prandtl number fluids, the velocity profile becomes flatter with increasing P. For a given Prandtl number, the maximum temperature in the plume decreases as minus three-fifth power of the height. The first-order correction for the mean flow equations are also solved by the RungeKutta method with the Newton-Raphson correction. The mean flow results after adding higher-order correction terms suggest that the center-line temperature decreases and the flow velocity increases near edge of the boundary layer. The magnitudes of first-order correction terms for both velocity and temperature become progressively smaller with increasing Prandtl number.