Effects of surface tension and non-isothermal wall temperature variation upon filmwise condensation on vertical ellipsoids/sphere

Abstract

An analytical study is made into the process of heat transfer with the vapour condensation on non-isothermal vertical ellipsoids/sphere. The mathematical treatment leads to explicit expressions for local condensate film thickness and local heat transfer coefficients around the ellipsoidal periphery in terms of the parameters of the configuration shape - ellipticity ‘ e ’ and process – the inverse Bond numbers, and the non-isothermal wall temperature variation amplitude ‘ A ’. The result indicates that these parameters have significant effects on the local heat transfer coefficients. The dimensionless mean heat transfer coefficient, Nu ¯ , has been explicitly showed to be increased as ellipticity of vertical ellipsoids increases. However, it is nearly unaffected by both surface temperature non-uniformity with a cosine distribution and surface tension effect due to the non-uniform surface curvature. For a special object, the isothermal sphere ( e = 0, A = 0 ), the reduced result agrees well with finite difference m ethod’s solution by Karimi. The present solutions are explicit for the heat and momentum transfer parameters bringing some convenience in practical applications.