Water-vapor Transfer by Forced-convection from a Leaf-shaped Plane Surface with Temperature-distribution

Abstract

Fundamental analyses and some experiments regarding to water-vapor transfer by foced convection over a wetted leaf-shaped plane surface were made.In general, for a leaf-shaped plate, local water-vapor transfer coefficient (Dx) which is a function of wind velocity (u) and distance (x) over the surface from the leading edge in the direction of air-flow is written as follows:Dx=Bum2x-n2, where, B is a numerical coefficient affected by the shape of the plate, its relative position to wind, natures of air-flow and the boundary-layer, the vapor-concentration distribution over the surface, properties of air and so on; m1 and n1 are exponents related to the structure of the boundary-layer, respectively.Water-vapor concentration departure (ΔCx) of the surface from the air outside the boundary-layer is generally expressed as follows;ΔCx=Co+bu-m2xn2, where, b is a numerical coefficient and Co is a constant. When the temperature of the leading edge of the plate is identical to the air temperature, Co is the saturation deficit of air in vapor-concentration.A local evaporation-rate is obtained as the product of the local values of vapor transfer coefficient and vapor-concentration departure.Then, the relationships between a local and the average values of transfer coefficient, concentration departure and evaporation-rate were theoretically analysed and the effect of the surface-temperature distribution in the air-flow direction upon the convection vapor transfer coefficients was experimentally examined.I. For the plane-surface with the above described transfer coefficient and the distribution of vapor-concentration departure, each correction factor for obtaining the average value of transfer coefficient, concentration departure or evaporation-rate from each local value was calculated. These results are shown in figures (Figs. 1, 2-A and 3). For example, the correction factor of vapor transfer coefficient at the point where the distance from the leading edge in the air-flow direction is 40% of the surface dimension are 1.26 and 1.04 for laminar and turbulent boundary-layer, respectively.Further, the positions where a local value coincided with the average value for each quantity were derived. The distance of the position where a local vapor-concentration departure agrees with its average is about 40% of the surface dimension from the leading edge in the flow direction.The position for evaporation-rate is complicated as it is related to air-temperature, humidity, wind velocity, surface dimension and temperature departure of the surface from air. However, under moderate air conditions local evaporation-rates at positions whose distance from the leading edge being between about 26 and 30% of the surface-dimension in the flow direction agrees with the average rate for a flat leaf.II. Three representations of average evaporation-rate were shown in the cases of using (i) both local values of transfer coefficient and vapor-concentration departure, (ii) the average transfer coefficient and a local concentration departure, (iii) both average values of transfer coefficient and concentration departure.