Analysis of a Reversed Trapezoidal Fin with Fluid in the Inside Wall
Q : dimensionless heat loss from the fin, q/(klw f φ ) Abstract Rt: dimensionless thermal resistance A reversed trapezoidal fin with fluid in the inside wall is analyzed using a two-dimensional analytical method. Thermal resistance for the reversed trapezoidal fin is presented as a function of the fin length and fin base height. The relationship between the inside fluid convection characteristic number and convection characteristic number over the fin for the same amount of heat loss is analyzed. One of the results shows that the thermal resistance decreases parabolically with the increase of fin base height. s: fin lateral surface slope, {(1ξ )lh}/(le-lb)
Optimization of a Thermally Asymmetric Convective and Radiating Annular Fin
In this study, convective and radiating annular fins of rectangular profile under thermally asymmetric conditions are examined using an analytical method. For the fin base condition, it is assumed that heat transfer from the fluid to the inside surface of the pipe is equal to the heat transfer through the fin base. The temperature distribution along the fin height at the fin tip is presented to demonstrate the effects of the thermally asymmetric condition. The heat loss and fin tip radius for fixed fin height are optimized as a function of the fin top convection characteristic number. Also, for fixed fin volume, the heat loss and fin dimensions are optimized based on the top, bottom, and tip convection characteristic numbers, radiation characteristic numbers, fin base radius, and fin volume. The fin effectiveness as a function of the top convection characteristic number and annular fin length are also presented.
Minimum mass convective fins with variable heat transfer coefficients
Abstract Pontryagin's maximum principles are applied to obtain the solution of minimum mass convective fins with variable heat transfer coefficients. It is shown that the volume and the width of the fin are uniquely related to the specified heat transfer rate and the properties of the material. For a power law spatial variation of the heat transfer coefficient, the results are set forth in a dimensionless form and they are given in tables or graphs, in order to aid design procedures. Several properties relating to the optimum volume, base thickness and the width of the fins with the properties of the material are also discussed. The method can also be used to solve problems of minimum mass fins having restricted width, often encountered in practice.