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 _t = 0.05 m) whose surface is maintained at T _t = 600 K by the boiling process. Combustion gases flowing over the tube at T_? = 1800 K provide a convection coefficient of h = 100 W/m² ? K while radiation from the gas and boiler walls to the tube may be approximated as that originating from large surroundings at T_sut = 1500 K.

(a) If the tube surface is diffuse and gray, with ? _t = 0.8, and there is no ash deposit layer, what is the rate of heat transfer per unit length, q', to the boiler tube?

(b) If a deposit layer of diameter D _d = 0.06 m and thermal conductivity k = 1 W/m ? K forms on the tube, what is the deposit surface temperature, T_d? The deposit is diffuse and gray, with ?_d = 0.9, and T_t, T₉₉, h, and T_sut remain unchanged. What is the net rate of heat transfer per unit length, q', to the boiler tube?

(c) Explore the effect of variations in D_d and h on q', as well as on relative contributions of convection and radiation to the net heat transfer rate. Represent your results graphically.

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Combustion gas Ash deposit Tu