A hot liquid is being transported inside a long tube with a diameter of 25 mm. The hot liquid causes the tube surface temperature to be 150°C. To prevent thermal burn hazards, the tube is enclosed with a concentric outer cylindrical cover of 5 cm in diameter allowing a vacuumed gap in between the two surfaces. The concentric outer cover has an emissivity of 0.6 and the outer surface is exposed to natural convection with a heat transfer coefficient of 8 W/m2·K and radiation heat transfer with the surrounding at a temperature of 20°C. Determine the necessary emissivity of the inside tube so that the outer cover temperature is below 45°C to prevent thermal burns.
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