Optimum geometry of fixed volume plate fin for maximizing heat transfer

A method is presented for finding the plate fin geometry for maximizing total heat transfer when cooled by forced or natural convection. The method is based on an approximate treatment of conjugated heat transfer in which analytical results are utilized. As a result of this type of approach, non-dimensional variables have been found that contain the geometrical and thermal properties of a fin and the flow. An essential fact is that there is no need to evaluate convection heat transfer coefficients. Only one variable with a fixed value is needed to determine the geometry of a fixed volume fin that gives the maximum heat transfer.