Closed-Form Solution of Temperature and Heat Flux in Embedded Cooling Channels

An analytical method is discussed for predicting temperature in a material layer with embedded cooling channels to control material temperature. Problems of this type are encountered in the aerospace industry and include high-temperature or high-heat-flux protection for advanced composite-material skins of high-speed air vehicles, thermal laminar flow control on supersonic civil transports, or infrared signal suppression on military vehicles. A Green’s function solution of the diffusion equation is used to simultaneously predict the localized and global effects of temperature in the material and embedded cooling channels. The integral method is used to calculate temperature in the cooling fluid and material simultaneously. This method of calculation preserves the three-dimensional nature of this problem.