Exhaust gas from a furnace is used to preheat the combustion air supplied to the furnace burners. The gas, which has a flow rate of 15 kg/s and an inlet temperature of 1100 K, passes through a bundle of tubes, while the air, which has a flow rate of 10 kg/s and an inlet temperature of 300 K, is in cross flow over the tubes. The tubes are unfinned, and the overall heat transfer coefficient is 90 W/m2·K.

Determine the total tube surface area, in m2, required to achieve an air outlet temperature of 850 K. The exhaust gas and the air may each be assumed to have a specific heat of 1075 J/kg·K.

The total tube surface area in m² required to achieve an air outlet temperature of 850 K is 192.3 m²

Explanation:

Here we have the heat Q given as follows;

Q = 15 × 1075 × (1100 - ) = 10 × 1075 × (850 - 300) = 5912500 J

∴ 1100 - = 1100/3

 = 733.33 K

Where

= Arithmetic mean temperature difference

= Inlet temperature of the gas = 1100 K

= Outlet temperature of the gas = 733.33 K

=  Inlet temperature of the air = 300 K

= Outlet temperature of the air = 850 K

Hence, plugging in the values, we have;

Hence, from;

, we have

5912500  = 90 × A × 341.67

Hence, the total tube surface area in m² required to achieve an air outlet temperature of 850 K = 192.3 m².