Consider the following Statements:

1) the efficiency of heat transfer in a condenser will improve by increase of the overall heat transfer coefficient.

2) The efficiency of heat transfer in a condenser will improve by increase of the velocity of flow of water in the tube.

3) the difference between the temperature of steam entering the condenser and the inlet water temperature should be maximum for maximum efficiency.

Which of the above statements are correct?

Concept:

Condenser efficiency: The efficiency of a condenser is defined as the ratio of the difference between the outlet and inlet temperatures of cooling water to the difference between the temperature of the steam corresponding to the vacuum in the condenser and inlet temperature of cooling water.

\(\eta = \frac{{{T_{ce}} - {T_{ci}}}}{{{T_s} - {T_{ci}}}}\)

With the increase in the overall heat transfer coefficient the heat transfer rate will increase as the

Q = U × A × ∆Tm

U = overall heat transfer coefficient, A = area, ∆Tm = Logarithmic mean temperature difference

• Therefore the exit temperature of the cold fluid will be more with the increased overall heat transfer coefficient, consequently the efficiency of the condenser will increase.
• Now with the increased velocity of the flow the mass flow rate of the cold fluid will increase which will pick more heat from the steam and again the exit temperature of the cold fluid will be higher which will increase the efficiency of the condenser.

When the temperature difference between the steam entering the condenser and inlet temperature of the cold water is high the efficiency of the condenser will decrease as can be seen from the expression for efficiency.