Optimum geometric arrangement of vertical rectangular fin arrays in natural convection

The optimal spacing between isothermal laminar natural convection plates cooled by air for maximal heat transfer has been determined analytically and numerically. It is found that the optimal plate’s allocation spacing is different from the conventional way, where the boundary layers of the plates merge early, it is the distinguishing feature of the outlet velocity that causes an enhancement of heat transfer. Further comparison results verify that our expression and numerical results and Rohsenow expression are very consistent. In the general condition, an optimized spacing expression of the maximum heat transfer density for a given volume is derived. It may be expected that the heat transfer enhancement can be accomplished by inserting multi-scale plates into the boundary layer according to the constructal theory.