A hot liquid (c p = 1000 J/kg K) flows at a flow rate of 0.028

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A hot liquid (cp = 1000 J/kg ∙ K) flows at a flow rate of 0.028 kg/s inside a 5-m-long pipe with an inner diameter of 45 mm and a wall thickness of 5 mm. At the pipe exit, the liquid temperature decreases by 10°C from its inlet temperature. The pipe is located in a surrounding with air at 10°C. To prevent thermal burn hazards, the pipe outer surface temperature should be at 45°C or lower. Instead of covering the pipe with insulation, a colleague has suggested to paint the pipe outer surface with black paint (ε = 0.88). Determine whether or not painting the pipe outer surface black is sufficient to keep the temperature below 45°C. Evaluate the properties of air at 25°C and 1 atm pressure. Is this a good assumption?

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