Analysis and optimization of convective pin fins with trapezoidal profile having internal heat generation density

An analysis of the thermal performance for convective pin fins, having a trapezoidal profile and internal heat generation density is presented. The solution of the optimal problem is also given, when either the desired heat dissipation rate or the volume of the pin is specified. An additional optimum solution is given for spines located in limited spaces, and is necessary to specify the height. The results are presented graphically and in polynomial form which are particularly useful for computerized calculations. The effect of the finʹs profile and thermal conductivity upon the optimum dimensions is discussed. Furthermore, certain limiting values of the heat generation imposed on the pin fins for a feasible optimization are also derived. The usefulness of the method is demonstrated with two examples.