Two coaxial cylinders of diameters D₁ = 0.10 m and D₂ = 0.50 m and emissivities ε₁ = 0.7 and ε₂ = 0.4 are maintained at uniform temperatures of T₁ = 750 K and T₂ = 500 K, respectively. Now a coaxial radiation shield of diameter D₃ = 0.20 m and emissivity ε₃ = 0.2 is placed between the two cylinders. Determine the net rate of radiation heat transfer between the two cylinders per unit length of the cylinders and compare the result with that without the shield.