Analytic study on pressure drop and heat transfer characteristics for low reynolds number flow in spirally finned tubes. (September 2020) - Yu, Dahm; Jeon, Wonju; Kim, Sung Jin
Highlights: Analytic solutions of the velocity and temperature profiles for a low reynolds number flow in a spirally finned tube are obtained. The coordinate transformation in conjunction with the perturbation method is used to solve the governing equations. Correlations of optimum fin number and twist ratio are presented. Abstract: Analytic solutions of the velocity and temperature profiles for a low Reynolds number flow in a 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 an inner radius ri, an outer radius ro, and an apex angle 2 α . The channel is twisted about its longitudinal axis with a twist length H . To simplify the problem, it is assumed that the swirling effect is negligible, which is valid for low Reynolds number flows. By using an appropriate coordinate transformation, the fully-developed flow in the spirally finned tube can be treated as a quasi-2-dimensional flow. The perturbation method is used to solve the transformed momentum and energy equations for forced convection in the tube subject to the uniform heat flux condition. The Poiseuille and Nusselt numbers are obtained by using the analytic solutions for the velocity and temperature profiles. The values of f Re and Nu are presented in terms of the geometrical parameters, 2 α, R i = r i / r o, and ω = 2 π r o / H . The results obtained from the analytic solutions show good agreement with numerical results for ω ≤ 0.5 and Re < 21 / ω . These analytic solutions are useful for optimizing the thermal performance of the spirally finned tube under various constraints. To illustrate their usefulness, the thermal resistance of a spirally finned tube under the constraint of fixed pumping power is evaluated. Based on the analytic solutions, the optimum fin geometry for which a minimum thermal resistance is attained can be analytically determined for a given non-dimensional pumping power. Furthermore, correlations of the optimum fin number and optimum twist ratio are presented in this study. According to the results, for relatively low pumping power conditions ( P pump * ≤ P pump, crit * ), the straight finned tube has better thermal performance than that of the spirally finned tube, and the optimum fin number increases as the pumping power increases. On the other hand, For relatively high pumping power conditions, ( P pump * > P pump, crit * ), the spirally finned tube has better thermal performance than that of the straight finned tube. The optimum twist ratio and the fin number increase as the pumping power increases.