The area-point constructal optimization for discrete variable cross-section conducting path

According to constructal area-point heat conduction model, the thermal current in the high conductive link increases only at conjunction points. If the optimum number of the lower order constructs which formed higher order constructs is finite, the number of the conjunction points is finite and the thermal current in the high conductive link increases discretely. The cross-section of the high conductive link should be adapted with the change of the thermal current through it. For minimizing the thermal resistance, the more thermal current flows into the high conducting path, the wider the cross-section of the high conducting path should be. A new method based on discrete variable cross-section conducting path is introduced in this paper. Both the case of the elemental area with constant cross-section conducting path and the case of the elemental area with variable cross-section conducting path are discussed. The results show that the minimum of maximum thermal resistance which is obtained through assembling can be obtained by changing the cross-section conducting path based on constructal theory and in each assembly, the optimized minimum thermal resistance based on variable cross-section conducting path element is smaller than that based on constant cross-section conducting path element. When the optimum number of the lower order constructs (ni ⩾ 4) which formed higher order constructs is fixed, at the same construct, the constructal optimal method based on discrete variable cross-section conducting path can reduce the thermal resistance further.