Water is heated by hot air in a heat exchanger. The flow rate of the water is 12 kg/s and that of the air is 2 kg/s. The water enters at 40°C and the air enters at 460°C. The overall heat transfer coefficient of the heat exchanger is 275 W/(m2 K) based on a surface area of 14 m2. Determine the effectiveness of the heat exchanger if it is (a) parallel-flow type or(b) a cross-flow type (both fluids unmixed). Then calculate the heat transfer rate for the two types of heat exchangers described and the outlet temperatures of the hot and cold fluids for the conditions given.
GIVEN
• Water heated by air in a heat exchanger
• Water flow rate m w= 12 kg/s
• Air flow rate m a= 2 kg/s
• Inlet temperatures
? Water (Tw,in) = 40°C
? Air (Ta,in) = 460°C
• Overall heat transfer coefficient (U) = 275 W/(m2 K)
• Transfer area (A) = 14 m2
FIND
(a) The effectiveness (e)
(b) The heat transfer rate (q)
(c) The outlet temperature (Tw,out, Ta,out) for: 1. parallel-flow 2. cross-flow
ASSUMPTIONS
• Steady state
SKETCH
PROPERTIES AND CONSTANTS
the specific heat of dry air (cpa) = 1059 J/(kg K) at 400°C
the specific heat of water (cpw) = 4178 J/(kg K) at 50°C
The heat capacity rates are
(a) The effectiveness for parallel-flow geometry is
For cross-flow, the effectiveness can be taken
e ? 0.83
(b) The rate of heat transfer is
For parallel-flow
For cross-flow
(c) The outlet temperatures can be calculated from
Parallel-flow
Cross-flow
COMMENTS
The cross-flow arrangement improves the heat transfer rate by 1.8%.
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