The forward constructal solution with rectangular elements is researched based on the optimized variable cross section conducting path of volume-point heat conduction. Complete analytical results are obtained. Then, the inward constructal solution is researched on the basis of the analytical relations. The results obtained herein show that the heat resistance can not always decrease when the complexity of the control volume increases. There exists an optimal constructal order corresponding to the minimum heat resistance. (c) 2006 Elsevier Ltd. All rights reserved.