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Problem 2: Boiler tubes exposed to the products of coal combustion in a power plant are subject to fouling by the ash (mineral) content of the combustion gas. The ash

forms a solid deposit on the tube outer surface, which reduces heat transfer to a pressurized water/steam mixture flowing through the tubes.Consider a thin-walled boiler tube (D=0.05 m) whose surface is maintained at T=600 K by the boiling process. Combustion gases flow over the tube at T=1800K and an average convection coefficient of h=100w/m?-K, while radiation from the gas and boiler walls to the tube may be approximated as that originating from large surroundings at Tsurr=1500 K. (a) If the tube surface is diffuse and gray, with ɛ = 0.8, and there is no ash deposit layer, whatis the rate of heat transfer per unit length (in kW/m) to the boiler tube? Ans: 54 kW/m (b) If a deposit layer of diameter Da=0.06 m and thermal conductivity k=1W/m-K forms on the tube, what is the deposit surface temperature, Ta? The deposit is diffuse and gray, with &a= 0.9,and Tt, To, and T surr remain unchanged. What is the net rate of heat transfer per unit length to the boiler tube?

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