Heat through a semi-infinity solid

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In summary, the conversation is about a thermal analysis that involves a metallic bar inside soil at different temperatures. The speaker is looking for a way to calculate the gradient of temperature and the distance up to the 20ºC point. They also want to know how long it would take for the bar to return to 20ºC. They have neglected superficial conditions and have access to all material properties. The attached paper on shape factors may provide some helpful information.
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davidgruty
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Hi there!

I run into a situation where I can't go on. It's about a thermal analysis, I already made a simulation using Ansys but I also want an approach made "by hand".

In order to simplify the case I made this example:

We have a metallic bar inside the soil. The bar is at 100ºC and the soil at 20ºC. Check the attached picture.

Once we stick the bar on the ground I understand there is a gradient of temperature radially in the soil, from 100ºC (perfect contact, Point A) to 20ºC (Point B).

I know all the heat goes by conduction according to:
q = 2 π k (ti - to) / ln(ro / ri), but I don't know the distance.

My two questions are:

1) where does the gradient in the soil stops? what's the distance up to the 20ºC? Where is the point B located? (ok, these are 3 questions, but it's always the same!)

2) How long does it take to the point A to get back to 20ºC?

We neglect the superficial conditions (convection, radiation)
We know all the material properties

Thank you
regards,
 

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Engineering news on Phys.org

1. What is "heat through a semi-infinity solid"?

"Heat through a semi-infinity solid" refers to the process of heat transfer through a solid material that has one side exposed to a heat source and the other side exposed to a colder environment, while the remaining sides are infinite in extent.

2. How does heat transfer occur in a semi-infinity solid?

Heat transfer in a semi-infinity solid occurs through a process called conduction, where heat energy is transferred from the hot side of the solid to the cold side through molecular vibrations and collisions.

3. What factors affect heat transfer in a semi-infinity solid?

The rate of heat transfer in a semi-infinity solid is affected by the thermal conductivity of the material, the temperature difference between the hot and cold sides, and the thickness and surface area of the solid.

4. How is heat flow calculated in a semi-infinity solid?

The rate of heat flow through a semi-infinity solid can be calculated using Fourier's Law, which states that the heat flux (or rate of heat transfer per unit area) is equal to the product of the thermal conductivity, temperature gradient, and surface area of the solid.

5. What are some real-world applications of heat transfer in semi-infinity solids?

One common application of heat transfer in semi-infinity solids is in building insulation, where heat flow through walls and roofs must be controlled to maintain a comfortable temperature inside. Other examples include heat transfer in cooking utensils, electronic devices, and industrial processes.

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