Optimum Plate Spacings for Laminar Natural Convection Heat Transfer From Parallel Vertical Isothermal Flat Plates

The problem of determining the optimum spacings between parallel vertical isothermal flat plates which are dissipating heat by natural convection to the environment is discussed. One optimum, first suggested by experimental data of Elenbaas with air and later derived theoretically by Bodoia, corresponds to the spacing between parallel vertical plates attached to a surface which will permit the maximum rate of heat transfer from that surface. A different optimum is derived in this paper which for a given heat flux gives the minimum plate spacing required to minimize the temperature difference between the plates and the fluid. The minimum temperature difference is shown to occur when the plate spacing is made sufficiently large that the wall boundary layers do not merge. It is shown that Elenbaas’ optimum, although requiring a plate spacing only 54 percent of that for minimum ΔT, produces a temperature difference which is 38 percent higher than the minimum.