e - Propulsion and Combustion Laboratory

Combined Conduction and Radiation – Formulations‣ Governing Equations2Rk T q∇ −∇⋅ = 0Introduce the nondimensional variables( ) ( )x , y = x, y L , Θ= T T , G= I I =πI σT* * 4ref ref b,HOT HOT3( ) L L , , N k 4 Tτ = κ + σ = β ω = σ β = β σL a s ref 0 ref 0 s 0 0 HOTFinal nondimensional G.E. becomes‣ Dimensionless RTE 1 dG( r , s ) 1 −ω4 ω =− Grs ( , ) + 0 Θ ( r) + 0 Grs ( , ′) Φ( ssd ′,) Ω′τ dsπ 4π ∫Ω=′ 4πL∂Θ 2 2 2τL4 1+ ∂Θ =*2 *2( 1 −ω0)⎛ ⎜Θ − GdΩ⎞ ⎟∂x ∂y N 4π4π⎝∫⎠31 Propulsion and Combustion Lab.