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# Heat Loss from a Buried Pipe | Stagnant/No Flow Condition

## Heat Loss from a Buried Pipe | Stagnant/No Flow Condition

(OP)
I have a transient pipe model (internal flow of water inside the pipe) that can calculate the water temperature distribution through the pipe length over time (solving convection-diffusion equation with heat sink).

This pipe model considers the heat transfer (as loss from the water to the surrounding ground) at turbulent and laminar flow conditions (using Gnielinski correlation, and Mills correlation to obtain the water thermal resistance, respectively).

My Question: How can I calculate the water thermal resistance when there is no flow condition?

“In life, the truest guide is science” – Mustafa Kemal Atatürk

### RE: Heat Loss from a Buried Pipe | Stagnant/No Flow Condition

Is the heat sink at constant temperature or is it increasing in temperature when water is cooling down?

### RE: Heat Loss from a Buried Pipe | Stagnant/No Flow Condition

Like IRstuff recommended, why not just input the lowest possible velocity your model will accept (ideally 0).

Also, what are you trying to actually determine. To get the average temperature of the water that isn't flowing, is a very basic heat transfer/resistance calculation that you wouldn't need a model for.

### RE: Heat Loss from a Buried Pipe | Stagnant/No Flow Condition

At zero flow, internal htc will be purely by natural convection currents - see Perry Chem Engg Handbook for these correlations at the approximately limiting value of the Nusselt number under laminar flow - in the 7th edition, refer to page 5-15 table 5-4 which suggests the Nusselt number reaches a limiting value of 3.66 for long pipes.

### RE: Heat Loss from a Buried Pipe | Stagnant/No Flow Condition

(OP)

#### Quote (IRstuff)

Is the model known to be invalid at zero velocity?

I didn't understand well enough your question but the model shall answer zero velocity condition. I model district heating piping network so there are conditions (at spring and summer) that the end-users do not consume heat so the water content in the end pipes becomes zero-velocity so my model has to handle such conditions. If your question is if Mills correlation for laminar flow condition can be used for zero-flow condition: I must say that I don't know.

#### Quote (chicopee)

Is the heat sink at constant temperature or is it increasing in temperature when water is cooling down?

I consider the layers of the pipe sections so for water volume the pipe wall material is the heat sink while solving pure-diffusion equation with heat sink (this time the heat sink for the pipe wall material is the insulation material). I solve the numerical models for each of the layers (water, pipe wall, insulation, casing). So, yes, the sink temperature increases with time when the water temperature is increased).

#### Quote (GT-EGR)

Like IRstuff recommended, why not just input the lowest possible velocity your model will accept (ideally 0).

Also, what are you trying to actually determine. To get the average temperature of the water that isn't flowing, is a very basic heat transfer/resistance calculation that you wouldn't need a model for.

It was my first attempt to just applying zero-flow (then Mills correlation was used to find the water-resistance as partial in the overall thermal resistance (water,steel,insulation,casing,ground). It works but the problem is that I have no idea what the water resistance is when at natural convection (at zero flow) exists. So I have doubt in the validity of the results obtained.

#### Quote (georgeverghese)

At zero flow, internal htc will be purely by natural convection currents - see Perry Chem Engg Handbook for these correlations at the approximately limiting value of the Nusselt number under laminar flow - in the 7th edition, refer to page 5-15 table 5-4 which suggests the Nusselt number reaches a limiting value of 3.66 for long pipes.

I don't have this handbook. But laminar flow?

“In life, the truest guide is science” – Mustafa Kemal Atatürk

### RE: Heat Loss from a Buried Pipe | Stagnant/No Flow Condition

(OP)
I could find a correlation for completely filled horizontal cylinder at the book chapter by Martynenko OG, Khramtsov PP. Chapter 4 - Natural convection in enclosures. In: Free-Convective Heat Transfer. Springer. pp. 279-343.

“In life, the truest guide is science” – Mustafa Kemal Atatürk

### RE: Heat Loss from a Buried Pipe | Stagnant/No Flow Condition

That is the closest I can find for this case. It appararently is valid for NGr as low as 0.10.

### RE: Heat Loss from a Buried Pipe | Stagnant/No Flow Condition

Don't bother calculating, just use the established coefficient of conductive heat transfer for water thereby dismissing the effect of convection. Afterall you stated that there is no flow and I don't think that convection in the radial direction of the pipe will be significant unless you have a pipe diameter of several feet.

### RE: Heat Loss from a Buried Pipe | Stagnant/No Flow Condition

Why not assume that the water temperature will equal the ground temperature after a small enough interval that no user will notice the difference? For certain thermal diffusion through the ground of varying air temperature will start to have a noticeable effect on the few degrees of temperature difference between the actual temp and the former assumption.

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