Transient 1D radial conduction

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Discussion Overview

The discussion revolves around a transient heat conduction problem involving a slab of homogeneous material and discretized elements. Participants explore how to estimate the time required for heat transfer between points on the surface of the material under specific conditions, including transient heating scenarios.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant seeks guidance on calculating the time taken to raise the surface temperature at a specific point when another point's temperature is increased, emphasizing the need for a quick estimate.
  • Another participant asks clarifying questions about the nature of the heating scenario, including whether it is a one-time event or ongoing, the arrangement of heat sources, and the thermal diffusivity of the material.
  • The original poster clarifies that the elements are not true heat sources and mentions a more complex bioheat mechanism at play, while still seeking a rough estimate for heat transfer time.
  • There is a discussion about the units of thermal diffusivity, with confirmation that it is expressed in m²/s.
  • A participant references another thread and a textbook on heat conduction for additional resources, suggesting these may provide further insights.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the specifics of the problem, and multiple viewpoints regarding the nature of the heat transfer and the setup remain. The discussion is still open and unresolved.

Contextual Notes

Participants have not fully defined the assumptions regarding the geometry of the heat sources or the exact nature of the transient heating, which may affect the calculations. The complexity of the bioheat mechanism is also not fully explored.

jb26
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Morning all,

This is probably going to seem absurdly simple, however I need to do a very quick conduction calculation as part of a much larger problem I am working on. I was wondering if anyone would be able to give me some pointers as time is of the essence.

The scenario can be simplified as follows: I have a slab of homogeneous material 10mm thick that can be considered semi-inifinite with a series of discretised elements on top of it. The attached (terrible and uninformative) image shows two such elements; let's pretend they are 1mm apart. To further simplify we can consider the elements to not have area and simply act as points. All I need to know is how to calculate the time taken to raise the surface temperature at point 2 by a given amount (lets say 1degree K) when the surface temp of point 1 is raised above the ambient temperature of the bulk material by some amount (lets say 5 degree K) for a known transient heating "on" time (lets say 2s).

You can see I've been quite general, but this is because I need to try some different heating scenarios.

Thanks in advance for any help given.

J

EDIT: I know I put radial in the title, but I simplified the geometry when writing the post an forgot to change it, sorry!
 

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Hi JB26. Welcome to Physics Forums.

Some questions:

Is this a one shot deal, or is there an ongoing cycle?
Is it truly a linear array, or are the sources laid out on an area grid?
Are the elements truly points, or do they have area? This affects the solution.
What is the thermal diffusivity of the slab material?

Chet
 
Cheers chet,

I'm trying to keep it simple tbh as I am just after an estimate. In reality the elements aren't heat sources (there is a more complicated bioheat mechanism generating heat in the material from an external stimulus). The real array elements do have area, but again I am just wanting to estimate the time for heat to transfer from one point to another across the surface of a material for a transient case.

Thermal diffusivity is of the order 1.92E-7

Cheers
 
jb26 said:
Cheers chet,

I'm trying to keep it simple tbh as I am just after an estimate. In reality the elements aren't heat sources (there is a more complicated bioheat mechanism generating heat in the material from an external stimulus). The real array elements do have area, but again I am just wanting to estimate the time for heat to transfer from one point to another across the surface of a material for a transient case.

Thermal diffusivity is of the order 1.92E-7

Cheers

units of thermal diffusivity are m^2/s?
 
yes the thermal diffusivity I stated was in standard SI form of m^2/s

Funnily enough I have a copy of that book sat right next to me. I took it out for some reason a long time ago and only just realized I have it! That said, any help is still very gratefully received as that faster I can get a rough number the better.

I'll have a read of the thread and then try to find a similar problem in the book.

Cheers
 

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