Constructal optimization of a disc-shaped body with cooling channels for specified power pumping

The thermal performance of a disc-shaped heat generation body with cooling channels is investigated by using constructal theory based on previous model of heat convection on a disc and previous analytical method of heat conduction on a disc. By taking minimum dimensionless maximum thermal resistance as optimization objective, the optimal aspect ratio of the elemental sector in the radial-pattern disc is obtained for the specified power pumping of the elemental sector; the optimal width ratio of the first-order and elemental cooling channels and the optimal dimensionless radius of the elemental sector are obtained for the specified power pumping of the disc. There exists a critical radius of the disc to determine whether the radial-pattern design and branched-pattern design should be adopted. These conclusions are different from those obtained by Wechsatol et al.'s model, and the essential reason for these differences is that the power pumping is specified in this article, but not the specified flow rate number in Wechsatol et al.'s model. Finally, the assumption about the heat capacity of the coolant and the thermal conductivity of the disc is validated. An analytical method is introduced in this article, which can provide another thought for the constructal optimization of disc with heat convection. The optimal constructs of the discs are obtained for the specified power pumping, which provides some different guidelines for the design of disc with heat convection.