Optimization of Plate Fin Arrays with Laminar and Turbulent Forced Convection

The minimum thermal resistance for isothermal plate fin arrays with array volume, number of the fins and either fan power or pressure drop fixed can be found in the literature. We solve the same fundamental problems for non-isothermal fin arrays by using a one-dimensional fin theory. Both laminar and turbulent cases are solved for coolants with Prandtl number equal to 0.7. The ratio of the fin to coolant thermal conductivity is 600, 6000 or 14000. Isothermal boundary condition is used at the fin base. The contraction and expansion losses at the inlet and exit are taken into account in the calculation of the pressure drop. The optimal design is characterized by various non-dimensional variables. The most important non-dimensional variable combines the three criteria and the thermal properties of the coolant and the fin material.