Existence Theory for Radiative Flows

Abstract

We consider the coupling of radiative heat transfer equations and the energy equation for the temperature Tof a compressible fluid occupying a bounded convex region D with smooth boundary. Using the technique of upper and lower sequences associated with integro-parabolic equations, we establish the existence and uniqueness of a solution T, 0 ≤ Λ₋ ≤ T(x,t) ≤ Λ₊ < ∞ with corresponding radiative intensity I(x,Ω,ν,t) where the total incident radiation satifies ∫_S² I(x,Ω,ν,t)dΩ = S_g B(ν,t)+S_b B(ν,T_b), and where S_b and S_g are positivity preserving linear operator, T_b is the external temperature of the boundary, and B is Planck's function. We also establish certain energy estimates for T.

Keywords:

• Conductive-radiative heat transfer
• Fluid flows
• Upper and lower solutions
• Parabolic integro-differential evolution equations