A numerical solution for temperature distributions in a discrete injection transpiration-cooled nosetip system

An analysis is performed to describe the thermodynamics behavior of 'fin' and fluid components of a transpiration-cooled nosetip system. Partial differential equations governing fin and fluid temperatures are derived and solved numerically to yield time-dependent distributions. Correlations used for the subcooled boiling heat transfer mechanism are found to over-predict the amount of heat removed from the fin in depth. A comparison of temperature distributions indicates that the fluid equation may be considered as steady state with a negligible effect on the solution. The numerical scheme used to solve the governing equations is strongly stable, even when drastic changes in parameters occur.