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)
Finite element analysis of triangular fins attached to a thick wall
Heat conduction in an array of triangular fins with an attached wall is modeled using the finite element method. An adaptive mesh refinement technique is developed giving accuracy comparable to uniform mesh refinement and much increased computational efficiency. The effects of wall thickness and fin spacing are examined for various Biot numbers. It is shown that for low Biot numbers (Bi < 0.1), the one-dimensional assumption is valid but for higher Biot numbers (Bi ⪢ 0.1), two-dimensional heat conduction must be considered, temperature distributions at the fin root are always non-uniform and the fin is found not to be effective.
Simplified solutions to circular annular fins with contact resistance and end cooling
Oneand two-dimensional solutions are obtained for circular annular fins of constant cross-section having uniform base, end, and side conductances. The solutions are dependent upon one geometric parameter and three fin parameters which relate the internal conductive resistance to the three boundary resistances. The two arid one-dimensional solutions are compared by means of their fin efficiency ratios. For fins used in typical microelectronic applications, the analytical expressions are also reduced to simple polynomial expressions which converge to unity for large values of the arguments. Numerical computations were performed on an IBM-PC and some typical results are reported in graphical form. These plots give the heat loss ratio as a function of the dimensionless geometric and fin parameters.