Analytical Study of Heat Transfer of Falling Liquid Film on a Horizontal Elliptical Tube

An analytical study is made into the process of heat transfer on a horizontal elliptical tube under the simultaneous effects of the forces of surface tension and gravity on the falling liquid film. The analysis is based on the energy integral solution. The falling liquid film at free surface is assumed to be sub-cooled for the case of constant temperature condition imposed at the wall of the tube. The effect of boiling has been ignored. Zoningof heat transfer may be considered as the four distinct regions namely the first two equal stagnation and impingement zones, the thermally developing zone and the fully developed zone which the thermal boundary layer penetrated in the whole thickness of the flow. Analytical expressions for the dimensionless falling film and thermal boundary layer thicknesses and the local and mean heat transfer coefficients around the elliptical periphery have been derived under the effects of gravity and surface tension for various values of ellipticity e, respectively. It is shown that the local heat transfer coefficient increases by increasing the film Reynolds number Ref, in thermal developing region, but decreases in thermal developed region as Ref increased. In addition, while the film Prandtl number Pr, the Archimedes number Ar, and the ellipticity of the tube are increased, the local and mean heat transfer coefficients are increased, either. The dimensionless mean heat transfer coefficient- Nu for both ofdeveloping and fully developed regions has been obtained. For specific object (circular tube e = 0), the results are in very good agreement with the earlier experimental and numerical works.

کلیدواژه ها:

falling film evaporation ، elliptical tube ، analytical study ، heat transfer