Total surface area, fluid inlet temperature (both tube and shell), flow rate are given. I had try compute it using P-NTU method. First I assume U then I will got NTU, R and calculate P. Finally I will get both fluid outlet temperature. Then I calculate new value of U using m*Cp*(Tc,o-Tc,i)=U*A*F*LMTD (F is correction factor, c= cold, m= mass flow rate).
But from this iteration, the value of U become divergent. Then I try to calculate by assume outlet temperature of cold fluid. But the error form assumed value and calculated value always 5-6% and not become smaller. Step which I used is first assume cold fluid outlet temperature, then calculate hot fluid outlet temperature. After that calculate LMTD, and then i wil get U from heat balance. and then compute NTU-> R -> P -> outlet temperature.
Is there any mistake in my calculation or should I use E-NTU ?
I am not sure if I understand your problem. If both U and both fluid exit temperatures are unknown, your system is undetermined. If you are able to calculate U from appropriate correlations, the P-NTU Method is straight forward and solved as you described it. No iterations are necessary (unless physical prperties vary significantly). If the U-value is unknown, and you have measurements (i.e. you know the fluid exit temperatures, use the LMTD-F-factor method. Again, no iterations are required.
A word of caution: The P-NTU Method differs from the effectiveness-NTU Method in that you need to be consistent in determining R and P (it is not necessarily R=Cmin/Cmax and P=Q/Qmax, as in the effectiveness-NTU Method). Also, note that the correction factor F in the LMTD-Method may become very sensitive if F becomes low (say less than ca 0.75). Also, there are different formulations for F, some of them being inaccurate in given situations.
My suggestion to you is to use the P-NTU (or E-NTU) Method consistently, as they tend to be more robust. Several textbooks also provide invertions of the E-NTU Method (i.e. NTU=f(R,E,configuration) ) which makes the LMTD-F-factor method superfluous.
https://www.sciencedirect.com/search?qs=outlet%20temperature%20of%201-2%20shell%20and%20tube%20heat%20exchanger%20using%20NTU%20method&show=25&sortBy=relevance
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