Vertical Parallel-Plate Channel — Isothermal
Calculates the average convective heat transfer coefficient and total heat rate for a symmetric vertical channel: two parallel isothermal plates separated by a spacing S, open to ambient at both ends. Buoyancy drives a chimney-like flow up the gap. When the plates are close together the flow becomes fully developed (the Elenbaas limit); when they are far apart each plate behaves as an isolated vertical plate. The Bar-Cohen & Rohsenow composite correlation bridges the two limits smoothly.
Channel Rayleigh Number
Properties are evaluated at the film temperature Tf=(Ts+T∞)/2. The spacing S is the characteristic length:
RaS=ν2gβ(Ts−T∞)S3Pr,El=RaSHSNusselt Number (composite)
NuS=[El2576+El1/22.873]−1/2The first term dominates at small El (fully-developed flow) and the second at large El (isolated-plate limit).
Heat Transfer Coefficient and Heat Rate
h=SNuS⋅k,Q=hA(Ts−T∞),A=2HWReferences
- Bar-Cohen, A. and Rohsenow, W. M., Thermally Optimum Spacing of Vertical, Natural Convection Cooled, Parallel Plates, J. Heat Transfer, 106, 116, 1984.
- Incropera, F. P. and DeWitt, D. P., Fundamentals of Heat and Mass Transfer, eq. 9.45.