numerical and analytical approach for film condensation on different forms of surfaces

This paper tries to achieve a solution for problems that concern condensation around a flat plate, circular and elliptical tube in by numerical and analytical methods. also, it calculates entropy production rates. at first, a problem was solved with mesh dynamic and rational assumptions; next it was compared with the numerical solution that the result had acceptable errors. an additional supporting relation is applied based on the characteristic of the condensation phenomenon for condensing elements. as it is shown here, due to higher rates of heat transfer for elliptical tubes, they have more entropy production rates, in comparison to circular ones. findings showed that the two methods were efficient. furthermore, analytical methods can be used to optimize the problem and reduce the entropy production rate