Marangoni effects in condensation of vapors. In many situations the heat transfer coefficient for condensing vapors is given as h = k/& where k is the thermal conductivity of the condensate film, and 8 is the film thickness. Correlations available in the literature are normally based on the assumption of zero shear stress at the free surface of the film, but if the surface temperature decreases downward, there will be a shear stress τ_s = ∂σ/∂z, where σ is the surface tension, and z is measured downward, that is, in the direction of flow. How much will this effect change a heat transfer coefficient of 5000 kcal/hr ∙ m² ∙ C for a water film? The kinematic viscosity of water may be assumed to be 0.0029 cm2/s, the density is 0.96 g/cm³, the thermal conductivity 0.713 kcal/hr ∙ m ∙ C, and dσ/dT = –0.2 dynes/cm ∙ C for the purposes of this problem The term in τ_s, represents the effect of surface tension gradients, and when this term is small, its denominator will be near the value for no gradient. For the conditions of this problem, pgδ = 14.3dyn/cm². Surface tension effects will thus be small for systems such as the one under consideration, where the surface tension increases downward. In the opposite case, however, even small gradients can cause hydrodynamic instabilities and thus can have major effects.