Heat transfer in the flow of a cold, axisymmetric vertical liquid jet   against a hot, horizontal plate
  The paper considers the heat transfer characteristics of a thin film flow over a hot horizontal flat plate resulting from a cold vertical liquid jet falling onto a surface. A numerical solution of high accuracy is obtained for large Reynolds numbers using the modified Keller box method. For the flat plate, solutions for axisymmetric jets are obtained. In parallel approximation theory, an advanced polynomial approximation of the velocity and temperature distributions is employed, and results are in good agreement with those obtained using a simple Pohlhausen polynomial and numerical solutions. 
Jian-Jun Shu and Graham Wilks
physics.flu-dyn