An analytical investigation of heat and mass transfer under conditions of film cooling of bodies

An analytical investigation is performed of heat and mass transfer under conditions of film cooling by liquids which exhibit the properties of abrupt variation of dynamic viscosity with a moderate variation of temperature (by three to five orders of magnitude with the temperature varying by $150$–$200$ degrees). The coolant under constant pressure on the inner boundary of the body is filtered through specifically organized pores and forms an evaporating liquid film on the outer boundary. This organization of heat shielding makes it possible to automatically control the feed of coolant depending on the varying external heat fluxes and related temperatures of the body and coolant, as well as to maintain the initial geometry of the body (no carry-over of mass of the body material occurs). A simplified mathematical model of heat shielding is suggested, and analytical solutions are obtained for the body temperature and for the rates of coolant flow rate and evaporation. The relevant results are discussed.