Simple formulae for the overall heat and moisture transport rates due to laminar natural convection in a rectangular cavity are obtained by scale analysis from the governing differential equations and a simplified picture of the flow. The two formulae contain a single unknown proportionality constant, which is determined by a least squares fit to the results of a series of numerical solutions. The relations apply for the case of isothermal vertical walls at constant, unsaturated relative humidity, and adiabatic, impermeable horizontal walls. The heat transfer formula agrees well with published data for the square cavity with zero humidity gradient.

Index Terms: Natural convection; Atmospheric humidity; Mathematical models; Heat transfer; Mass transfer; Moisture; Numerical analysis; Differential equations; Laminar flow; Least squares approximations; Prandtl number; Transport rates; Scale analysis; Proportionality constant

• cavity wall