It is common practice to recover waste heat from an oil-or gas-fired furnace by using the exhaust gases to preheat the combustion air. A device commonly used for this purpose consists of a concentric pipe arrangement for which the exhaust gases are passed through the inner pipe, while the cooler combustion air flows through an annular passage around the pipe.

Consider conditions for which there is a uniform heat transfer rate per unit length. q"i = 1.25 x 105 W/m, from the exhaust gases to the pipe inner surface, while air flows through the annular passage at a rate of ma = 2.1 kg/s. The thin-walled inner pipe is of diameter Di = 2m while the outer pipe which is well insulated from the surroundings, is of diameter Do = 2.05 m. The air properties may be taken to be cp = 1030 J/kg ∙ K, JL = 270 x 10-7 N ∙ s/m2, k = 0.041 W/m ∙ K, and Pr = 0.68.

(a) If air enters at Ta,1 = 300 K and L = 7 m, what is the air outlet temperature Ta.2?

(b) If the airflow is fully developed throughout the annular region, what is the temperature of the inner pipe at the inlet (Ts, i,1) and outlet (Ts,i,2) sections of the device? What is the outer surface temperature Ts,o,1 at the inlet?

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Air Taz a.2 Ti2 D, Do -Inner pipe wall Annular passage T,0.1 Furnace exhaust Air gases