- A general method of analysis of heat transfer through a heat sink composed of rectangular fins attached to each other in a tree-like configuration (a stem with branches) is presented. By treating each fin in the array as a single fin and considering its place in the array through the boundary conditions, the analysis of the problem is reduced to the solution of a system of linear algebraic equations. Furthermore, an extensive analysis of fin performance and optimum dimensions is presented. The analysis also illustrates the effect of various ratios between the length of the branch fins and the stem fin. For design purposes, the results are presented graphically and via a simple correlation.