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I'm at little rusty on my heat transfer and could use some help.

I'm trying to calculate the approximate time to freeze standing water in a 18inch steel pipe. I have some parameters and made some assumptions and they are:

The pipe is 18inch carbon steel

The standing water is initially around 68^{o}F

The outside temp is around 0^{o}F

There is a constant breeze around 5mph

No insulation around pipe

The pipe is exsposed to the air and not buried

The pipe is completely filled with water

I've calculated this two different ways and came up with two completely different time values. One was around 8.7hrs and the other was around 4.8hrs.

For the first method, I calculated the surface heat transfer coefficient (h) at the wind/pipe interface by:

First calculating the Reynolds number (R_{e}) of the wind/pipe interface from R_{e}=VD/v_{(kinematic viscosity of air)}

Then I found the Prandtl number (P_{r}) for air at 0^{o}F

Then I calculated the Nusselt number (N_{u}) by N_{u}=0.023 x (R_{e})^{4/3}x (P_{r})^{1/3}

Then I found the thermal conductivity of the air k_{f}

Then I calculated the surface heat transfer coefficient(h) by h=(N_{u}x k_{f})/D_{pipe}

I came up with h~11 W/(m^{2}K)

Once I found the surface heat transfer coefficient, I calculated the Biot number (B_{i}) by B_{i}=hD/k_{s}, where k_{s}is the thermal conductivity of the carbon steel pipe.

I found B_{i}=0.003364666 , and with B_{i}<0.1 I figured could use the lumped capacitance method.

Note: density=rho=p

p_{s}=density of steel

p_{w}=density of water

c_{s}=heat capacitance of steel

c_{w}=heat capacitance of water

T_{i}=initial water temp

T_{inf}=air temp

T=water at 32^{o}F or 273.15 K

Using the lumped capacitance method, time (t) in secs can be found from t=[(pVc)_{tot}/(hA_{s})]*ln[(T_{i}-T_{inf})/(T-T_{inf})]

Where (pVc)_{tot}=[((p_{s}c_{s}(D_{o}-D_{i}))/4)_{s}+((p_{w}c_{w}(D_{i}))/4)_{w}]

and so ((pVc)_{tot})*(1/h)*ln[(T_{i}-T_{inf})/(T-T_{inf})]=t

This method is how I came up with 8.7hrs. I came up with 4.8hrs using a method out of an ASHRAE handbook.

Is the method okay for a good approximation? Is 8.7hrs a good approximation? If there's something I'm doing wrong or a better approach, please let me know.

Thanks for the help.

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# How long to freeze standing water in steel pipe

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