Infrared Heaters-Problem

Question: An infrared radiator is designed by placing an electric heater inside a solid cylinder of radius R1 = 10 mm length L = 100mm. Then a hollow cylinder of radius R2 and length L is placed coaxially around it with this outer cylinder and the top part of opening ideally insulated. The infrared radiation is leaving through the opening at the bottom at the bottom spacing between the cylinders. This results in surface 1 being the high temperature surface with direct and reradiation exchange with surface 2. Determine how the radiative heat flux flowing through the bottom opening depends on radius of the hollow cylinder. Temperature of the inner cylinder is T1 = 800K while emissivity of the inner and hollow cylinder are ∈ 1 = 0.8 and ∈2 = 0, respectively.