Heat transfer coefficient

The term 'U' means the Overall Coefficient Of Heat Transfer of the Heat Exchanger.
The value of 'U' depends on the followinfg factors:

1. The Specific Heats of both the fluids flowing through the heat exchanger.

2. The individual coeff. of heat transfer of the inisde and outside fluid films.

3. The inlet and the outlet tempreatures of the each fluid.

4. The difference in the tempreatures between the entering fluids ( Ti1 and ti1)

5. The flowrate of the fluids passsing.

From the above mentioned factors, it is very clear that when you vary the flowrates of the fluids the value of 'U' will change. This is because the time for heat transfer between the fluids will change due to the changed flowrate.
Secondly, when the inlet tempreature of either of the fluids is changed, the tempeature difference between the fluids is changed and due the varied tempreature gradient created, the rate of heat transfer between them will also change.
Both the things are quite evident feom the above factors of dependency of the overall heat transfer coefficient.
Thus when in your case when you vary either of the factors, the value of 'U' changes accordingly. It is simple physical phenomena. I think the above explaination must have cleared the doubt. There is nothing that you are missing in your calculations.

Maybe we went to different universities, Rohan 😀
The overall coefficient is basically the sum of the film coefficients and the thermal resistance of the tube material.
The overall duty of the exchanger can be calculated by Q = UA(LMTD) where Q is the duty in watt, A is the transfer area and LMTD is the log mean temperature difference. Since you did not respond to Rohan I'd need to see what you did with your calcs first.