Radiation models for thermal flows at low Mach number

Simplified approximate models for radiation are proposed to study thermal effects in low Mach flow in open tunnels. The governing equations for fluid dynamics are derived by applying a low Mach asymptotic in the compressible Navier-Stokes problem. Based on an asymptotic analysis we show that the integro-differential equation for radiative transfer can be replaced by a set of differential equations which are independent of angle variable and easy to solve using standard numerical discretizations. As an application we consider a simplified fire model in vehicular tunnels. The results presented in this paper show that the proposed models are able to predict temperature in the tunnels accurately with low computational cost.