Some optimal body shapes for laminar film condensation

The geometry of the condensing surface affects the thermal performance of a condenser. Optimizing the surface shape to maximize the condensation heat transfer offers potential for increased performance and/or reduced condenser cost. Thus, the condensation model developed by Dhir and Lienhard (1971, 1973) for bodies of arbitrary shape is used in the present study to determine two-dimensional and axisymmetric body shapes that maximize the rate of heat transfer by laminar film condensation, subject to certain constraints. The optimal body shapes are obtained as solutions of classical isoperimetric problems in the calculus of variations using both indirect and direct (Rayleigh-Ritz) techniques. Extensions of the present results to film boiling and natural convection are discussed.