An effective method for predicting the optimal thermal performance of partially-confined compact heat sinks under multi-constraints of pressure drop and heat sink mass has been successfully developed. The design variables of PPF compact heat sinks include: heat sink fin and base material, thickness of heat sink base, heat flux, channel top bypass and inlet flow velocity. A total of 108 experimental cases for confined forced convection are designed by the Central Composite Design (CCD) method. According to the results in ANOVA, a sensitivity analysis for the design factors is performed. From the analysis, the effect of inlet flow velocity, which has the contribution percentage of 86.24%, dominates the thermal performance. The accuracies of the quadratic RSM models for both thermal resistance and pressure drop have been verified by comparing the predicted response values to the actual experimental data. The maximum deviations of thermal resistance and pressure drop are 9.41% and 7.20% respectively. The Response Surface Methodology is applied to establish analytical models of the thermal resistance and pressure drop constraints in terms of the key design factors with a CCD experimental design. By employing the Sequential Quadratic Programming technique, a series of constrained optimal designs can be efficiently performed. The numerical optimization results for four cases under different constraints are obtained, and the comparisons between these predicted optimal designs and those measured by the experimental data are made with a satisfactory agreement.

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