Vertical Plate in Natural Convection — Isothermal
Calculates the average convective heat transfer coefficient and total heat rate for a vertical plate held at a uniform surface temperature in an otherwise quiescent fluid. Buoyancy drives a free-convection boundary layer up the heated face. The plate is assumed to exchange heat from one side only.
Rayleigh Number
Fluid properties are evaluated at the film temperature Tf=(Ts+T∞)/2. The Rayleigh number uses the plate height as the characteristic length:
RaH=ναgβ(Ts−T∞)H3=ν2gβ(Ts−T∞)H3Prwhere β is the volumetric thermal expansion coefficient, ν the kinematic viscosity and α=ν/Pr the thermal diffusivity.
Nusselt Number (Churchill–Chu)
For the laminar regime (RaH<109):
Nu=0.68+[1+(0.492/Pr)9/16]4/90.670RaH1/4For the turbulent regime (RaH≥109) the all-regime form is used:
Nu={0.825+[1+(0.492/Pr)9/16]8/270.387RaH1/6}2Heat Transfer Coefficient and Heat Rate
h=HNu⋅k,Q=hA(Ts−T∞),A=HWValidity
- Valid across the full laminar-to-turbulent range of Rayleigh numbers.
- Applies to gases and liquids with Prandtl numbers from roughly 0.01 upward.
References
- Churchill, S. W. and Chu, H. H. S., Correlating Equations for Laminar and Turbulent Free Convection from a Vertical Plate, Int. J. Heat Mass Transfer, 18, 1323, 1975.
- Incropera, F. P. and DeWitt, D. P., Fundamentals of Heat and Mass Transfer, eqs. 9.26 & 9.27.