Using primary dimensions, verify that the Rayleigh number (Table 7–5) is indeed dimensionless. What other established non-dimensional parameter is formed by the ratio of Ra and Gr?

Data from Table 7-5

TABLE 7-5 Some common established nondimensional parameters or II's encountered in fluid mechanics and heat transfer* Name Definition Archimedes number Aspect ratio Biot number Bond number Cavitation number Darcy friction factor Drag coefficient Eckert number Euler number Ar = AR = Bi = Bo = f= CD Ec P.8L Ca (sometimes ) sometimes = hL k || 8T pV Eu = -(P, - p) 8(P; - p.)I or V CT D FD pVA PV2 = PP pV 2(PP) pV2 sometimes pV, Ratio of Significance Gravitational force Viscous force Length Length Width Diameter or Surface thermal resistance Internal thermal resistance Gravitational force Surface tension force Pressure - Vapor pressure Inertial pressure Wall friction force Inertial force Drag force Dynamic force Kinetic energy Enthalpy Pressure difference Dynamic pressure