Constructal entransy dissipation rate minimization for a heat generating volume cooled by forced convection

The geometry of a heat generating volume cooled by forced convection is optimized by applying the entransy dissipation extremum principle and constructal theory, while the optimal spacing between the adjacent tubes and the optimal diameter of each tube are obtained based on entransy dissipation rate minimization. The results of this work show that the optimal constructs based on entransy dissipation rate minimization and maximum temperature difference minimization, respectively, are clearly different. For the former, the porosity of the volume of channels allocated to the heat generating volume is 1/2; while for the latter, the larger the porosity is, the better the performance will be. The optimal construct of the former greatly decreases the mean thermal resistance and improves the global heat transfer performance of the system compared with the optimal construct of the latter. This is identical to the essential requirement of the entransy dissipation extremum principle that the required heat transfer temperature difference is minimal with the same heat transfer rate (the given amount of heat generated in the heat generating volume) based on the entransy dissipation extremum principle.