Consider a tube for transporting steam that is not centered properly in a cylindrical insulation material (k = 0.73 W/m ∙ K). The tube diameter is D₁ = 20 cm and the insulation diameter is D₂ = 40 cm. The distance between the center of the tube and the center of the insulation is z = 5 mm. If the surface of the tube maintains a temperature of 100°C and the outer surface temperature of the insulation is constant at 30°C, determine the rate of heat transfer per unit length of the tube through the insulation.

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D₂ T₂ L