Natural Convection Adjacent to Horizontal Surface of Various Planforms

Abstract

Natural convection adjacent to horizontal surfaces of circular, square, rectangular, and right triangular planforms has been studied experimentally. Electrochemical techniques were employed involving a fluid with a Schmidt number of about 2200. The results encompass a wide range of Rayleigh numbers thus providing information on both the laminar and the turbulent regimes. The data for all planforms are reduced to a single correlation in the laminar and turbulent regimes using the characteristic length, as recommended by Goldstein, Sparrow, and Jones. L* = A/p, where A is the surface area and p is the surface perimeter. The laminar data for all planforms are correlated by the expression Sh=0.54Ra1/4(2.2×104≤Ra≤8×106) and the data for the turbulent regime are correlated by the expression Sh=0.15Ra1/3(8×106≤1.6×109) Transition is found to occur at about Ra = 8 × 106. The present work thus significantly extends the Rayleigh number range of validity for the use of L* through the 1/4 power laminar regime into the turbulent 1/3 power regime. It also demonstrates the validity of the use of L* to correlate natural convection transfer coefficients for highly unsymmetrical planforms, which heretofore had not been demonstrated. Comparisons to analytical solutions and other experimental heat and mass transfer data are presented.