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)
Application of Adomian's decomposition procedure to the analysis of convective-radiative fins
We present a method which may be used to determine the temperature distribution within a convective-radiative longitudinal fin of variable thermal conductivity, subject to convection heat transfer from a fluid of known temperature T f through the inside face of the primary surface, and which experiences convection-radiation heat dissipation into the environment at its tip. We demonstrate the use of the Adomian decomposition method in generating an analytical solution of the resulting nonlinear energy balance equation with nonlinear boundary conditions
A Least Weight Circular Cooling Fin
The design of the least weight circular cooling fin is obtained through an application of the Minimum Principle. The fin temperature, thickness, and heat flux are considered to be functions only of the radius. Solutions are obtained for the exact one-dimensional representation and also for the approximate case where the profile curvature is neglected in the convection calculation. A regularization technique is used to avoid computational difficulties, especially near the tip where the fin thickness becomes vanishingly small. In the exact case, an additional degree of freedom allows the selection of the fin root dimension. This flexibility suggests the possibility of optimization in a parameter, the root dimension; this was done by using a pattern search technique. Closed form results are given for the approximate case. For kθo /qo = 100, the fin design obtained in the exact case is about 20 percent shorter and contains about 1 percent to 2 percent less material than the fin obtained in the approximate case.