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.