Heat transfer and effective thermal conductivity analyses in carbon-based foams for use in thermal protection systems

The applicability of carbon-based foams as an insulation material in the thermal protection systems (TPSs) of space vehicles is considered using a physical analysis and computer modelling. The heat transfer through the foam is considered through its solid phase and the gas residing in the foam pores via conduction and radiation. As the cellular structure of the foam prevents a large-scale motion of the gas, thermal convection is neglected as a heat transfer mode. The results obtained show that, although the gas-phase conduction and radiation can be ignored at near-room temperatures and at sub-atmospheric pressures, their contributions at high temperatures and at near-atmospheric pressure become very significant. It is also found that one can derive an analytical expression for the effective thermal conductivity (a parameter that combines the contributions of both conduction and radiation) as a function of temperature and pressure. Such an expression is shown to be valid for quite large ranges of temperature, pressure, and insulation thickness and, due to its mathematical simplicity, is very suitable for use in computationally intensive large-scale thermo-mechanical analyses of the entire TPS of a space vehicle.