Dear Bal:
@srfish you mean we calculate U shell and U tube using the respective dimensionless numbers for each?
That's correct, we generally call these the respective "h" values, be aware that the form of the correlation can also be different if the fluid runs inside the shell or tube side.
Also, does Q in the shell = Q tube? If that's correct and logarithmic mean temperature difference is the same for each.
Then using Q=U*A*LMTD:
Would that imply that (U*A) shell= (U*A) tube?
Q Shell=Q tube is an assumption.
U is an overall resistance to heat transfer, so it doesn't belong solely to the tubes or side shell, it is calculated like this (some assumptions are involved in this formula, like neglecting curvature and the resistance of the tube wall):
U=(1/h_tube+1/h_shell)^(-1)
If Q in the shell = Q tube, how do we account for the losses?
As I said before, Q Shell=Q tube is an assumption. If you want to account for losses, you would need a model for them (which can be some simple like, 10% of QShell for example), and in that case, you will have:
QShell+QLoss+Qtube=0
Taking proper account of the signs of course.
Bal, you seem just starting with these topics, I recommend you to read an introductory chapter of some heat transfer book, where these concepts are explained in a simple manner.
Best regards.