Given data:
- Temperature of saturated vapor: 200°C
- Rate of condensation: 150 kg/s
- Enthalpy of condensation: 2400 kJ/kg
- Fluid entering on the tube side:
- Temperature: 100°C
- Specific heat capacity: 4 kJ/kgK
- Effectiveness of the heat exchanger: 0.9

To find: Mass flow rate of fluid on the tube side

First, let's calculate the heat transfer rate on the shell side using the rate of condensation and the enthalpy of condensation.

1. Calculate the heat transfer rate on the shell side:
- Heat transfer rate = Mass flow rate of condensate x Enthalpy of condensation
- Heat transfer rate = 150 kg/s x 2400 kJ/kg
- Heat transfer rate = 360,000 kJ/s

Next, let's calculate the temperature change of the fluid on the tube side using the heat transfer rate and the effectiveness of the heat exchanger.

2. Calculate the temperature change of the fluid on the tube side:
- Heat transfer rate = Mass flow rate of fluid on the tube side x Specific heat capacity x Temperature change
- 360,000 kJ/s = Mass flow rate of fluid on the tube side x 4 kJ/kgK x Temperature change
- Temperature change = 360,000 kJ/s / (Mass flow rate of fluid on the tube side x 4 kJ/kgK)
- Temperature change = 90,000 / (Mass flow rate of fluid on the tube side) K

Since the temperature change is from 100°C to the final temperature of the fluid on the tube side, the temperature change can be expressed as:

3. Temperature change = Final temperature - Initial temperature
Temperature change = (Final temperature - 100)°C

Now, we can equate the two equations:

90,000 / (Mass flow rate of fluid on the tube side) = (Final temperature - 100)°C

Since the effectiveness of the heat exchanger is given as 0.9, the final temperature can be expressed as:

4. Final temperature = Initial temperature + (Effectiveness x Temperature change)
Final temperature = 100°C + (0.9 x Temperature change)°C
Final temperature = 100°C + 0.9 x (Final temperature - 100)°C

Now, we can solve these equations to find the mass flow rate of fluid on the tube side.

Let's substitute equation (4) into equation (3):

90,000 / (Mass flow rate of fluid on the tube side) = (100 + 0.9 x (Final temperature - 100)) - 100
90,000 / (Mass flow rate of fluid on the tube side) = 0.9 x (Final temperature - 100)

Simplifying the equation:

90,000 = 0.9 x (Final temperature - 100) x (Mass flow rate of fluid on the tube side)
90,000 = 0.9 x (Final temperature - 100) x Mass flow rate of fluid on the tube side

Since Mass flow rate of fluid on the tube side is in the denominator, we can rewrite the equation as:

Mass flow rate of fluid on the tube side = 90,000 / (0.9 x