Semi-Analytical Solution for Heat Transfer in a Water Film Flowing Over a Heated Plane

Film flow coupled with heat and mass transfer is a widely open domain due to the range of its applications. However, the coupling between the different phenomena makes the analytical resolution difficult, and thus, coerces most authors into performing numerical studies. Although efficient, the numerical approach does not reveal the real link between the different parameters when studying heat transfer. This lack of meaningful formulation motivates the present paper, which proposes a semi-analytical solution for the establishment of the thermal boundary layer of a film flowing down an inclinated heated plane. The formula is obtained by a truncated sum of Whittaker’s functions, and is validated by comparison with a full numerical solution of the problem (assuming the same hypotheses). The semi-analytical nature of the equation provides better understanding of the physical phenomena and could help in reducing numerical computational time.