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liquid oil is used in the tube side of a shell-and-tube heat exchanger with two shell...

liquid oil is used in the tube side of a shell-and-tube heat exchanger with two shell passes and four tube passes. water is heated in the shell side from 10°C to 50°C while the oil is cooled from 90°C to 60°C. the overall heat transfer coefficient is 53 W/m^2*K. the specific heat of the oil is 2.0 kJ/kg*K. Using the NTU - effectiveness method, calculate the area of the heat exchanger for a total energy transfer of 500 kW. what is the water flow rate for this heat transfer?

Solutions

Expert Solution

Here water is cold fluid which flows in shell side and oil is a hot fluid that flows in tube side.

Given: Initial and final temperature of water respectively, t1=100C=283.15 K and t2= 500C=323.15 K

Initial and final temperature of oil respectively, T1=900C=363.15 K and T2=600C= 333.15 K

Overall heat transfer coefficient, U=53 W/m2K

Specific heat of oil, Cpo= 2 kJ/kg K= 2000 J/kg K

Total energy transfer, q= 500 kW

For water, tc = t2-t1= 323.15 K-283.15 K= 40 K

For oil, Th= T1-T2= 363.15 K-333.15 K= 30 K

As the temperature difference for water is higher, it is the minimum fluid.

If the cold fluid is minimum fluid, effectiveness is calculated as

The energy transfer rate, q is given by

q=Co(Th)=Cw(tc)

where Cw is the Heat Capacity flow rate of water, which is the product of mass flow rate of water, w and specific heat of water, Cpw

Co is the Heat Capacity flow rate of oil, which is the product of mass flow rate of oil, o and specific heat of oil, Cpo

Consider q=Cw(tc)

Substitute the values of q and tc

Consider q=Co(Th)

Substitute for q and Th

Hence Cmin=Cw=12.5 kW/K and Cmax=Co=16.66 kW/K

Thus the capacity ratio, C is

Area of Heat Exchanger, A is obtained from the expression

where NTU is the Number of Transfer Units

From the Figure, Effectiveness of 2,4 Multipass Counterflow Exchanger Performance, the NTU corresponding to C=0.75 and =0.5 is 0.9.

Thus the area of heat exchanger is

Water Flow Rate, w is obtained using the expression

where Cw is the Heat Capacity flow rate of water

Cpw is the Specific Heat of water, Cpw=4.18 kJ/kg K

(W can be expressed as J/s)

Area of Heat Exchanger, A=212.26 m2 and Water Flow Rate, = 2.9904 kg/s


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