A theoretical study has been conducted for evaporative heating of turbulent free-falling liquid films inside long vertical tubes. The methodology of the present work is based on splitting the energy equation into homogeneous and nonhomogeneous problems. Solving these simple problems yields a rapidly converging solution, which is convenient for computational purposes. The eigenvalues associated with the homogeneous problem can be computed efficiently, without missing any one of them, by the sign-count algorithm. A new correlation for the local evaporative heat transfer coefficient along the tube length is developed over wide ranges of Reynolds and Prandtl numbers. Furthermore, the average heat transfer coefficient is correlated as a function of Reynolds and Prandtl numbers as well as the interfacial shear stress. A correlation for the heat transfer coefficient in the fully developed region is also presented in terms of Reynolds and Prandtl numbers. Typical numerical results showed excellent agreement of the present approach with the available data in the literature. Moreover, a parametric study is made to illustrate the general effects of various variables on the velocity and temperature profiles.

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