It is common practice to recover waste heat from an oil-or

Chapter 8, Problem 8.98

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It is common practice to recover waste heat from an oil-or gas-fired furnace by using the exhaust gases to preheatthe combustion air. A device commonly used for thispurpose consists of a concentric pipe arrangement forwhich the exhaust gases are passed through the inner pipe, while the cooler combustion air flows through anannular passage around the pipe.Consider conditions for which there is a uniform heat transfer rate per unit length, q?i?1.25?105W/m,from the exhaust gases to the pipe inner surface, while air flows through the annular passage at a rate of m?a?2.1 kg/s. The thin-walled inner pipe is ofdiameter Di?2 m, while the outer pipe, which is well insulated from the surroundings, is of diameterDo?2.05 m. The air properties may be taken to becp?1030 J/kg?K, ??270?10?7N?s/m2, k?0.041W/m?K, and Pr?0.68.(a) If air enters at Ta,1?300 K and L?7 m, what isthe air outlet temperature Ta,2?(b) If the airflow is fully developed throughout theannular region, what is the temperature of the innerpipe at the inlet (Ts,i,1) and outlet (Ts,i,2) sections ofthe device? What is the outer surface temperatureTs,o,1at the inlet?