The area–point constructal entransy dissipation rate minimization for a discrete variable cross-section conducting path

According to the constructal area–point heat conduction model, the thermal current in the high-conductive path 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 path increases discretely. The cross-section of the high-conductive path should be adapted to the change of the thermal current through it. The area–point heat conduction problem is re-optimized based on entransy dissipation rate minimization using a discrete variable cross-section conducting path. The optimization process confirms that the mean temperature difference will decrease by resembling constructs which is expected by the constructal theory. Constructing the next assemble by a four optimization unit and making the high-conductive path cross-section scale by 2:1 will decrease the mean temperature difference regularly at an interval of two assembly levels, and the mean temperature difference will approach a constant. Optimization results show that the minimum mean temperature difference of the ninth assembly level decreases further by 2.84% compared with the optimization result without the premise of an optimized last-order construct.