Analytic study on flow and heat transfer characteristics in channels with axial variations in geometry

Abstract

In this thesis, the analytic solutions of the velocity and the temperature distribution for the fluid flow in channels with axial variations in geometry are obtained. The coordinate transformation in conjunction with the perturbation method is used to solve the governing equations. Two kinds of channels are treated in this thesis. In the first technical chapter, analytic solutions of the Poiseuille and Nusselt numbers for the fluid flow between two wavy plate fins are obtained. The geometric features of the wavy plate fins are described by a sinusoidal variation with three parameters: fin spacing, amplitude of waviness, and period length. The fluid flow between two wavy plate fins is assumed to be a 2-dimensional flow. The coordinate transformation in conjunction with the perturbation method is used to solve the governing equations. The results from the analytic solutions are shown to be in good agreement with those obtained from numerical simulations using a commercial code, FLUENT. The value of the Poiseuille number monotonically increases as the dimensionless waviness increases and the increment is proportional to the square of the dimensionless waviness. On the other hand, the Nusselt number increases to the peak value and then decreases as dimensionless fin spacing increases. Based on the analytic solution, a correlation of the optimum dimensionless fin spacing at which the maximum Nusselt number is attained is presented. In the second technical chapter, analytic solutions of the Poiseuille and Nusselt numbers for the fluid flow in the spirally finned tube are obtained. The cross-sectional shape of the unit channel of the spirally finned tube is described by an annular sector with inner radius, outer radius, and apex angle. The channel is twisted about its longitudinal axis with the twist length. The fully-developed flow is treated as 2-dimensional flow by means of the coordinate transformation. The perturbation method is used to solve the momentum and energy equations for the forced convection in the tube. By using the analytic solutions for the velocity and temperature profiles, the Poiseuille and Nusselt numbers are obtained. The values of the Poiseuille and Nusselt numbers are presented in terms of the geometrical parameters. The results obtained from the analytic solutions are shown to be in close agreement with numerical results. The analytic solutions are very useful in optimizing the thermal performance of the spirally finned tube under various constraints. To illustrate its usefulness, the thermal resistance of the spirally finned tube under the fixed pumping power condition is presented. The optimum number of fins at which the thermal resistance attains its minimum value is presented in this study.