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# Heating calculations of flow in a pipe

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## Heating calculations of flow in a pipe

(OP)
Hey All,

We want to design a water heater that works with a constant water flow in a pipe.
The pipe run in circles inside a water tank, the water in the tank is the heating medium.
We want to get an estimate of the required length pipe.

For this I take few assumptions:
• surface temperature is the same at all length pipe
Water mass flow is constant
Water inlet and outlet is constant
And I am using these two equations:

Can I get an indication more or less or am I missing something?
Thanks!
Liad

### RE: Heating calculations of flow in a pipe

Yes, basically correct. Theoretically, that assumes 100% efficiency. It will define how much heat you need, but not the time you will need to heat the water. That will depend on heat rate, flow rate and the type of flow you have in the pipe and if the contact time of water against the pipe walls and the interfacial conduction and/or convection that may have to happen to ensure all the water gets heated to full temperature during the time the water's mass has to pass through the heat exchanger. For example, if flow is laminar, you may only heat the water particles flowing very near the pipe walls while a central core of fluid remains cooler. All of which may de categorised by a judicial choice of efficiency factor.

### RE: Heating calculations of flow in a pipe

I assume you're chopping this into several sections as the the inner temperature goes up so Q does down.

in practice it's difficult to get less than 7-10 C difference between tank temperature and outlet temperature. To get it less than that you need to have a very length length that becomes impractical.

What value of Cp are you thinking of?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Heating calculations of flow in a pipe

There are other factors to consider, possibly:
> Variability of outlet temperature -- if the flow stops for significant amount of time, the temperature of the immersed section will equilibrate with the tank, but after flow starts up, that section of immersed pipe will clear, and the outlet temperature will drop down to the steady-state flow outlet temperature
> The length of pipe and flow will dictate how much lag there will be before the outlet temperature reaches the steady-state flow temperature
> Thermal transfer efficiency to the tank water might require having fins on the immersed pipe, to decrease thermal resistance and engage more of the tank water in the heat transfer

TTFN (ta ta for now)
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### RE: Heating calculations of flow in a pipe

Q = U A LMTD.

1/U = 1/hi + 1/ho + 1/hfo + 1/hfi

In this case, ho is the external htc due to natural convection of hot water on the outside of these tubes; hi the internal htc due to forced convection of the flow of cold water inside the tubes; hfi and hfo are fouling htc contributions for the tube od and tube id. You will find that the value of ho governs the resultant value of U in this case.

See your Uni heat transfer text for methods to derive these values.

### RE: Heating calculations of flow in a pipe

Your first assumption is wrong "•surface temperature is the same at all length pipe". Second assumption is correct. Third assumption "Water inlet and outlet is constant" does not make sense

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