Heat transfer in the flow of a cold, two-dimensional draining sheet over   a hot, horizontal cylinder
  An accurate and comprehensive numerical solution to the parabolic free boundary problem arising from thin film flow with both velocity and temperature distribution at large Reynolds numbers is obtained using a modified Keller box method. A detailed numerical solution scheme is presented to establish the flow and heat transfer characteristics of the draining film flow. A solution is obtained for selecting representative values for the basic parameters of heat transfer in the flow of a cold two-dimensional draining sheet over a hot horizontal cylinder. These indicate the underlying features of developing film thickness, velocity, and temperature distribution. Good agreement with the approximations is obtained, providing basic confirmation of the validity of the numerical results presented. Numerical solutions, supplemented with parameter values associated with specified configurations and operating conditions, can be readily invoked to establish the details of engineering practice. 
Jian-Jun Shu and Graham Wilks
physics.flu-dyn