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Notes: Summary This is the second of a series of two papers in which the steady state velocity and temperature distributions in a liquid film are analytically investigated. The liquid is assumed to appear on a flat surface due to transpiration through a porous medium or the melting of a solid material. The liquid is considered to be introduced into the film at the solid-liquid interface, in a direction normal to the interface, such that mass is continually being added to the film along the longitudinal path of flow. The flow, which is assumed to be laminar, occurs under the influence of gravity or an externally applied shear stress at the film surface. Heat transfer takes place into the film by convection from an atmosphere which is at a higher temperature than the liquid. Evaporation and gaseous boundary layer effects are not considered. Physical properties of the liquid, such as density, viscosity, and thermal conductivity are considered constant. In the first paper, an investigation is made of the velocity distribution for a liquid film which is subjected to a uniform body force. In this paper, the velocity distribution is determined for a film which is subjected to an externally applied shear stress at the film surface. In addition, temperature distributions are determined for a film subjected to either a gravity body force or a surface shear stress. The externally applied surface shear stress, and the rate at which liquid is introduced into the film are, in general, considered independent of position. The continuity, momentum, and energy equations are set up in integral form. Then, the problems of determining the film thicknesses, velocity distributions, and temperature distributions are approached in four different ways, referred to as Case I, II, III and IV. These four cases differ from one another by the simplifying assumptions made. These assumptions are made in such a way that each successive case takes different effects into account, and yields a solution based on a somewhat more accurate analysis. Comparing the solutions resulting from the four cases, it is found that where the liquid film thicknesses are relatively small, for each individual problem the results of all four cases converge to the same expression. This tends to justify the use of certain simplifying assumptions even though one would not initially regard them reasonable.