Heat through a semi-infinity solid

  • Thread starter Thread starter davidgruty
  • Start date Start date
  • Tags Tags
    Heat Solid
Click For Summary
SUMMARY

This discussion focuses on thermal analysis of a metallic bar embedded in soil, initially at 100ºC, with the surrounding soil at 20ºC. The key equation used for heat conduction is q = 2 π k (ti - to) / ln(ro / ri), where the user seeks to determine the distance at which the temperature gradient in the soil reaches 20ºC and the time required for the bar to return to 20ºC. The analysis neglects convection and radiation effects, emphasizing conduction as the primary heat transfer mechanism.

PREREQUISITES
  • Understanding of heat conduction principles
  • Familiarity with thermal analysis software, specifically Ansys
  • Knowledge of material properties relevant to thermal conductivity
  • Basic mathematical skills for logarithmic calculations
NEXT STEPS
  • Research the derivation and application of the heat conduction equation in cylindrical coordinates
  • Explore transient heat conduction analysis techniques
  • Study the concept of thermal diffusivity and its impact on heat transfer
  • Learn about numerical methods for solving heat transfer problems, such as finite element analysis
USEFUL FOR

Engineers, thermal analysts, and researchers involved in heat transfer studies, particularly those working with conduction in solid materials.

davidgruty
Messages
20
Reaction score
0
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,
 

Attachments

  • Layout.jpg
    Layout.jpg
    11.4 KB · Views: 468
Engineering news on Phys.org

Similar threads

  • · Replies 6 ·
Replies
6
Views
12K
Replies
12
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 7 ·
Replies
7
Views
7K
Replies
2
Views
2K
  • · Replies 16 ·
Replies
16
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K