Abstract: The constructal optimization of the control-volume, which generates heat uniformly and is cooled by a single point, is carried out based on constructal volume-point conduction model. The application of constructal theory in conduction is introduced. The forward constructal solution, which is from internal “small” construct to external “big” construct with rectangular element, is researched based on the optimized variable cross-section conducting path of volume-point conduction. Then the control-volume is optimized with inward constructal solution from external “big” construct to internal “small” construct. The optimal thermal resistances of all the constructs are compared with each other under the same values of some parameters. The complete analytical results are obtained. The optimum number of the lower order constructs which formed higher order constructs is determined. The optimum order of the construct with smallest heat resistance is obtained. The results obtained with inward constructal solution show that heat resistance can’t always decrease when the complexity of the control-volume increases. There exists an optimal constructal order corresponding to the minimum heat resistance.

Key words: Constructal theory, Generalized thermodynamic optimization, Volume-point conduction