# Tube in tube heat Xchanger

## Main Question or Discussion Point

For internal forced convection in a circular duct, exact solution is available for h, for both constant surface temperature & constant surface flux, Nu being 3.66 for former & 4.36 for latter.
Now if I have a double tube heat exchanger, with inner tube with hot water & annulus with cold water & they both undergo sensible cooling & heating, which Nu am I supposed to use for calculations? Both temperature & heat flux change:grumpy: along the length of heat Xchanger.

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It’s been a while since I did any heat transfer work. But since no one else has responded, here is my opinion.

Heat transfer formulas for engineers are empirical approximations that hide the complexities of the underlying physics. I am not familiar with the formula you are trying to use. The basic formula for convective heat exchangers where both fluids are pumped thru tubes, states that the “rate of heat transfer is proportional to the surface area of the tube between them and the temperature difference between the two fluids”.

You are right is believing that the temperature of both fluids changes along the length of that tube. That’s one reason the fluids are typically pumped in opposite directions. At one end the hot fluid is hottest but the cold fluid has already warmed up a bit. So the temperature difference is less than the nominal difference. At the other end the cold fluid is at its coldest but the hot fluid has cooled off a bit. Again the temperature difference is less than the nominal difference. When the heat exchanger has reached equilibrium, the temperature difference is assumed to be the same along its length.

It is that temperature difference you use in the formula. If you want to derive that temperature difference yourself, you will need to know calculus. But any number you come up with will be an approximation because you are not taking into account the turbulent heat transfer within each fluid. All companies that sell such heat exchangers provide values for the rate of heat transfer as a function of nominal fluid flux, and temperature and tube diameter and length, based upon actual experimental data.

hi mike,
thanks for your time. I actually was referring to heat transfer coefficient which actually remains constant for fully developed internal flows. It is essentially a function of temperature & velocity profile in the boundary layer. Since boundary layer thickness for internal flows is actually the radius of pipe(& doesn't change for the entire length of the developed flow), convective heat transfer coefficient reaches a constant value.

Actually, I hadn't completely understood the problem when i made the post, so it was a lil vague.

For the case I mentioned, heat transfer rate varies, if I can get q" as a function of axial dimension, i can calculate the heat transfer coefficient. Anyway, I used some correlations & was pretty much close to the experimental value, which was calculated using log mean temperature difference.