Water flowing at a rate of 12.6 kg/s is to be cooled from 90 to 65°C by means of an equal flow rate of cold water entering at 40°C. The water velocity with the such that the overall coefficient of heat transfer U is 2300 W/(m2 K). Calculate the heat-exchanger surface area (in square meters) needed for each of the following arrangements: (a) parallel flow, (b) counterflow, (c) a multi-pass heat exchanger with the hot water making one pass through a well-baffled shell and the cold water making two passes through the tubes, and (d) a crossflow heat exchanger with both sides unmixed.
GIVEN
• Warm water cooled by cold water in a heat exchanger
• Both flow rates ( m c) = 12.6 kg/s
• Water temperatures
? Th,in = 90°C
? Th,out = 65°C
? Tc,in = 40°C
• Overall heat transfer coefficient (U) = 2300 W/(m2 K)
FIND
The transfer area (A) for (a) Parallel flow (c) Tube-and-shell; 1 hot shell pass, 2 cold tube passes (b) Counterflow (d) Crossflow–both unmixed
ASSUMPTIONS
• The specific heat is constant
SKETCH
PROPERTIES AND CONSTANTS
the specific heat of water in the temperature range of interest (cp) = 4187 J/(kg K)
The effectiveness of the heat exchanger, is
(a) that infinite NTU would be required to reach e = 0.5 for Cmin/Cmax = 1 with a
parallel flow configuration. Therefore, parallel flow is not practical. For Cmin/Cmax = 1, reduce to
However, for practical purposes, e = 0.5 at NTU = 2.5
(b) for e = 0.5 and Cmin/Cmax = 1.0: NTU = 1.1
Solving for the area
(c) NTU = 1.3
(d) NTU = 1.2
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