Question

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?

Answer 1

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, C_po= 2 kJ/kg K= 2000 J/kg K

Total energy transfer, q= 500 kW

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

For oil, T_h= 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=C_o(T_h)=C_w(t_c)

where C_w is the Heat Capacity flow rate of water, which is the product of mass flow rate of water, _w and specific heat of water, C_pw

C_o is the Heat Capacity flow rate of oil, which is the product of mass flow rate of oil, _o and specific heat of oil, C_po

Consider q=C_w(t_c)

Substitute the values of q and t_c

Consider q=C_o(T_h)

Substitute for q and T_h

Hence C_min=C_w=12.5 kW/K and C_max=C_o=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 C_w is the Heat Capacity flow rate of water

C_pw is the Specific Heat of water, C_pw=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