Definition and Determination of Fin Substitution Factors Accelerating Thermal Simulations

The effort of numerical heat transfer calculations increases with the complexity and size of the domains and surfaces under consideration. When calculating heat transfers on finned arrays, one way to reduce this effort is to substitute the fins. Therefore, this work defines the fin substitution factor by considering that a smooth surface behaves thermally sufficiently similar to a specific finned array. A process for determining the case-specific most accurate analytical computation path for fin substitution factors is also defined. The performance of the process and the resulting solution is demonstrated using the example of vertical rectangular finned arrays under natural convective heat transfer with a constant fin base temperature and air as the surrounding fluid. The heat flows determined in solid-state simulations of flat plates considering fin substitution factors deviated by an average of 6.2% from the heat flows resulting from detailed CFD simulations of the corresponding finned arrays.