Abstract: The optimization of the “volume-point” flow problem which generates heat uniformly is repeated based on constructal theory. With help of the simplification method used in the approximate solution that the heat input into the high conductivity channel is uniform, and the calculation in the routine way, a result consistent with the exact result is deduced, and the cause of the error in the approximate solution is not the reasonable simplification is proved. According to the principle that the maximum temperature after and before the equivalent transformation should be the same, the equivalent thermal conductivity put forward in the approximate solution is deduced again, and a correct equivalent thermal conductivity is obtained. Substituting the equivalent thermal conductivity with the original one, a consistent result is obtained, the original equivalent thermal conductivity is not equivalent, which is also the real cause of the error. The cause of the error is clarified, while a new solution which is relatively simple but consistent with the exact solution is obtained.

Key words: “Volume-point” flow problem, Constructal theory, Equivalent thermal conductivity efficient, Generalized thermodynamic optimization, GPU parallel computing, Interaction node pair, Local search, Collocation approach, Coupled FE-EFG method