Heat Flow to ground 3

[corus]

In calculating heat transfer of an object sat on the ground, what assumptions can be made as to the heat flow into the ground? I would assume that at an infinite distance then there would be no heat flow, however I'd also expect the temperature to tend to a constant value. What temperature and at what distance from ground level is it constant?

corus

 

[willard3]

There will be conductive, convective and radiant exchange if is is ON the ground. There will be no conductive exchange if it is ABOVE the ground.

Neither the ground surface nor the space above it will have unchanging temperatures because of wind, moisture changes, radiant flux and etc.

The problem is wayyyyyy too unspecific.

 

[corus]

The object is sat on the ground as I have said. The problem isn't the heat flow into the ground, which I assume there is perfect conduction, but through the ground to infinity below ground surface level.

corus

 

[vpl]

corus

Are you asking "At what depth does the ground reach an equalibrium temperature?"

I know here in the Chicago USA area, it's about 3.5 feet down and the temperature is around 50^oF.

Patricia Lougheed

Please see FAQ731-376 for tips on how to make the best use of the Eng-Tips Forums.

 

[CarlB]

What assumptions you can make depends on the size of the object, its thermal resistance, period of evaluation, etc.
For some cases you can assume a constant ground temperature. For long term operation of buried pipes, to model the ground's resistance there are certain "shape factors" that are based on flow lines that curve to the surface. There probably is something similar for your case. There may be cases where you model deep into the ground, then you may need to include the temperature gradient (you know, the deeper the warmer).

 

[CarlB]

I found the following document which presents the basic equation for heat transfer through a floor/slab, which shouls be applicable for an "object on the ground".

http://www.buildingphysics.com/slab.htm

 

[Clay1969]

Corus
When you are establishing heat BCs through the ground. You have to have some info regarding the existing thermal gradient in that region. Every region has different thermal gradient (which represents the steady state condition at that region). So if you have no measured data within the earth, you can know the thermal gradient and the surface temperature you can get the ground temperature at any desired depth. I beleive that The temperature below the ground surface will never reach a constant value with depth by going deeper within the earth. You have to assume an ending depth to your model

 

[IRstuff]

How much heat are you talking about? That makes a big difference as to when the diffused heat becomes negligible to the temperature of the region. It's essentially Fick's Law.

TTFN

 

[corus]

CarlB,
The software looks good, however I don't know what assumptions are being made in the calculation. The program assumes semi-infinte ground and hence I would presume that the assumption is being made that there is no heat loss at infinity (or some large distance). For a fixed temperature at the surface, such as a hot slab, then with no heat loss at infinity, then the ground would be at the same temperature as the slab for an infinite depth.
I would presume that heat flow in the ground would be characterised by a heat sink to some fixed temperature (as Patricia says) so that at infinity there is no heat flow, but the temperature tends to some fixed value. Are there referenced guidelines as to the heat sink, whether it's in Chicago or otherwise?

IRstuff,
I'd never heard of Fick's law, however without the transient term then the equation is just Laplace's equation for heat transfer.

corus

 

[IRstuff]

Probably similar...

Fick's law is d^2N/dx^2 ~ dN/dt, the concentration drives the diffusion

Since the heat is spreading in two dimensions, assuming negligible gradients lengthwise to the pipe, the expanding front eventually drops the "concentration" of heat to the point where heat transfer is neligigle and the ground is close to its normal temperature. For example, if at a certain radius of expansion, the further increase in temperature of the ground is less than, say, 0.1ºC, you could consider that as having reached the background temperature, since the change is smaller than the local variations in temperature, probably smaller than the measurement accuracy, and smaller than the temperature variations of the pipe itself.

TTFN

 

[corus]

Interesting IRstuff. To rephrase your suggestion, what you propose is to consider no heat flow at some large distance and then look at the temperature change and assume that when the dT/dx is small, say 0.1C/m then at that point the temperature could be assumed to be fixed at, say, a ground temperature of 55F (as patricia suggests). This might get round the problem that it can't be assumed that the temperature of the ground is constant at 3.5 feet below if you've got a red hot slab sat on it, for instance. This might be the best approximation to use.
Thanks

corus

 

[BigInch]

Assume a constant earth temperature, equal to the average yearly temperature exists at about 6 feet below the Earth's surface. That will work for almost any area, except near arctic climates, where it may be several feet deeper. Below say a 10-12 foot depth, the temperature does change, but for all practical intents and purposes remains essentially constant at yearly avg temp for quite a way down, unless the area has some near surface geothermal activity.


BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[Tremolo]

A model presented at the following web site:

http://soilphysics.okstate.edu/toolkit/temperature/index0.html

will show the soil temperature variation as a function of depth. According to the model, the soil temperature is essentially constant beyond depths of 10 feet at a value equal to the average of the annual maximum and minimum air temperatures. The temperature at depths of 10 feet or more typically vary less than 1 degree from the annual average temperature.

Heat transfer to the soil is dependent on the soil temperature which changes depending on the time of the year (for depths less than 10 ft), the soil moisture content, soil type, whether the soil is underneath an object (such as a floor) or adjacent to the side of the object (such as a basement wall), object shape, (flat slab, corner of a building, pipe), soil surface orientation (north vs south), ground cover type. So, the calculation of heat transfer can carry a significant uncertainty.

A report from the US Department of Energy (

http://www.nrel.gov/docs/fy03osti/33954.pdf)

discusses the modeling of heat transfer from buildings to the ground. Although the report relies on a sophisticated numerical model, key conclusions are 1) “soil thermal conductivity is the most important parameter in determining” ground heat transfer; 2) the soil thermal conductivity can change by a factor of 10 based on soil moisture content; 3) the soil moisture content varies significantly only near the surface of the soil.

A simplified method for heat transfer calculations from the University of Colorado can be found here:

http://www.ibpsa.org/proceedings/BS1997/BS97_P046.pdf

The key parameter in this simplified model is the soil thermal conductivity.

A paper from University of California, Berkeley (

http://www.cnr.berkeley.edu/biometlab/espm129/pdf/Lecture 34 espm 129.pdf

) estimates thermal conductivities as a function of soil mineral content and moisture content. The reported thermal conductivities range from about 0.25 W/m/K for 0% water content to 1.0 W/m/K for 50% water content.

Hope this helps.

 

[corus]

It did, thanks

corus