Oil c p2.1 kJ/(kg K) is used to heat water in a shell and tube heat exchanger with a single shell and two tube passes. The overall heat transfer coefficient is 525 W/(m2 K). The mass flow rates are 7 kg/s for the oil and 10 kg/s for the water. The oil and water enter the heat exchanger at 240°C and 20°C, respectively. The heat exchanger is to be designed so that the water leaves the heat exchanger with a minimum temperature of 80°C. Calculate the heat transfer surface area required to achieve this temperature.
GIVEN
• Oil heats water in a heat exchanger with one shell pass and two tube passes
• Oil specific heat (cpo) = 2.1 kJ/(kg K) = 2100 J/(kg K)
• Overall heat transfer coefficient (U) = 525 W/(m2 K)
• Oil mass flow rate m o= 7 kg/s
• Water mass flow rate m w= 10 kg/s
• Inlet temperatures: Oil (To,in) = 240° Water (Tw,in) = 20°C
• Minimum water outlet temperature (Tw,out) = 80°C
FIND
• The heat transfer area (A) required
ASSUMPTIONS
• Oil is in the tubes
SKETCH
PROPERTIES AND CONSTANTS
the specific heat of water at the average temperature of 50°C (cpw)= 4178 J/(kg K)
The heat capacity rates are
The effectiveness required to achieve Tw,out = 80°C is
The number of transfer units, NTU, NTU = (U A)/Cmin ? 2.5
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Hot water is used to heat air in a double pipe heat exchanger as shown in the following sketch. If the heat transfer coefficients on the water side and on the air side are 550 W/(m2K) and 55 W/(m2 K), respectively, calculate the overall heat transfer coefficient based on the outer diameter. The heat exchanger pipe is 5 cm, schedule 40 steel (k = 54 W/m K), with water inside but assume that a fouling factor of 0.173 (m2 K ) /kW based on the tube outside diameter has developed over time.
GIVEN • A double pipe heat exchanger with water in inner tube and air in the annulus • Heat transfer coefficients ? Water side h i= 550 W/(m2 K) ? Air side h o= 55 W/(m2 K) • Inner pipe: 2 in., schedule 40, made of steel • Pipe thermal conductivity (k) = 54 W/(m K) • Fouling factor (Rd) = 0.173 (m2 K )/kW= 1.73*10-4 (m2 K )/kW, based on the tube outside area FIND • The overall heat transfer coefficient based on the outer diameter (Uo) ASSUMPTIONS • Uniform heat transfer coefficients • The given fouling factor is based on the outer tube diameter (Do)