Containers of circular cross section filled with humid air and walls subjected to varying temperatures are commonly used in practice. Circular ducts containing humid air can be also considered as containers when out of service. Gradients of density, induced by gradients of temperature and water vapor concentration, lead to double-diffusive natural convection in the container. Under such conditions, condensed water could exist at the wall, evaporation of condensed water could occur for increasing wall temperatures, or additional condensation could occur for decreasing wall temperatures. Due to heating (and possible evaporation) or cooling (and possible condensation), significant changes could occur on the pressure level and also on density, and the Boussinesq approximation cannot be used. Mass, momentum and energy conservation equations, including the water mass conservation equation and the possible phase change at the wall are considered in the physical model. Possible fog formation is not considered, but integral mass and energy conservations are guaranteed. Very specific issues when the water mass conservation equation shifts from or to the saturation condition at the wall are discussed in detail. An equal order control volume based finite element method for two dimensional combined heat and vapor transfer by natural convection, including phase change at the wall, is proposed and used to solve the problem. Solutions for the cooling (and condensation) and heating (and evaporation) situations are obtained. Results show how the stream function, temperature, vapor concentration and relative humidity change with space and time, how absolute pressure level and the overall Nusselt and Sherwood numbers vary with time, and how the thickness of condensate varies over the wall for the cooling (and condensation) situation.
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