Question 13.9: Sensible Heating Moist air enters a steam-heating coil at 40......
Sensible Heating
Moist air enters a steam-heating coil at 40°F (4.4°C) dry-bulb temperature and 36°F (2.2°C) wet-bulb temperature at a rate of 2000 ft³/min (943.8 L/s). The air leaves the coil at a dry-bulb temperature of 90°F (32.2°C). Determine
(a) The heat transfer rate that occurs at the coil
(b) The amount of steam needed if saturated steam at 220°F (100°C) enters the coil and leaves as a condensate at 220°F
Given: \dot{V}_{1} = 2000 cfm, T_{db1} = 40°F, T_{wb1} = 36°F, and T_{db2} = 90°F.
Figure: See Figure 13.11, process 1–2.
Find: \dot{Q}_{h}.
Assumptions: Thermodynamic equilibrium exists. The local atmospheric pressure is 1 atm, or 14.696 psia.
Lookup values: Let states 1 and 2 represent the entering and exiting airstream conditions, respectively. From the psychrometric chart, v_{1} = 13.66 ft^{3}/lb_{a}, h_{1} = 13.47 Btu/lb_{a}, and h_{2} = 26.5 Btu/lb_{a}.
From the steam tables, h_{3} = 1153.4 Btu/lb_{w}, and h_{4} = 168.1 Btu/lb_{w}.
The mass flow rate of moist air is
Finally, from Equation 13.36,
\dot{Q}_{sen} = \dot{m}_{a} (h_{2} – h_{1} ) (13.36)
\dot{Q}_{h} = 9,479 lb_{a}/h \times (26.5 – 13.47) Btu/lb_{a} =123,511 Btu/h (36.2 kW).
The amount of steam required is easily determined from an energy balance on the heating coil:
\dot{m}_{steam} = \dot{m}_{a} \frac{(h_{2} – h_{1})}{(h_{3} – h_{4})} = 9479 \times \left\lgroup \frac{26.5 – 13.47 }{1153.4 – 168.1} \right\rgroup= 125.3 lb_{w}/h (56.5 kg_{w}/h)