Electronic Thesis and Dissertation Repository

Degree

Master of Engineering Science

Program

Mechanical and Materials Engineering

Supervisor

J.M. Floryan

Abstract

This thesis consists of two parts. The first part deals with the development of proper methodology, i.e. a spectrally accurate algorithm suitable for analysis of convection problems in corrugated slots. The second part is devoted to the study of natural convection in corrugated slots.

The algorithm uses the immersed boundary conditions (IBC) concept to deal with the irregular form of the solution domain associated with the presence of corrugated plates. The field equations are discretized on a regular domain surrounding the flow domain using Fourier expansions in the horizontal direction and Chebyshev expansions in the vertical direction. The boundary conditions are expressed in the form of constraints and the spectrally accurate discretization of these constraints has been proposed.

The buoyancy forces associated with the temperature difference between isothermal plates drive the natural convection. This temperature difference is expressed in terms of the Rayleigh number Ra and the analysis is limited to its subcritical values where no secondary motion takes place in the absence of corrugation. Corrugations have a sinusoidal form characterized by the wave number a, the upper and lower amplitudes and the phase difference between the upper and lower corrugation systems. They create horizontal temperature gradients which lead to the formation of vertical and horizontal pressure gradients which drive the motion regardless of the intensity of the heating. Presence of corrugations affects the conductive heat flow and creates the convective heat flow. The increase of the heat flow induced by the corrugations has been determined. The convection is qualitatively similar for all Prandtl numbers with the intensity of convection increasing for smaller Pr’s and with the heat transfer augmentation increasing for larger Pr’s.

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