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# Heat source location in 1D and 2D models - Conduction

## Heat source location in 1D and 2D models - Conduction

(OP)
Hello,

I need guidance to formulate a methodology to solve the heat transfer problem. I am interested to determine the strength and location of heat source in 1D and 2D domains.
The known parameters include the material conductivity, the geometry of the domain, boundary temperatures changing with time, and insulated boundaries so conduction only.
I have already applied analytical methods but they work on simplified geometry and central position of heat source so there is symmetry in the temperature profile. This means that boundary temperatures will be equal.
I am interested to find the location of a heat source when boundary temperatures are not equal and therefore heat source will be in a non-central position. Also, the temperature inside the domain will be unknown, the problem needs to be solved using only boundary temperatures. I am supposed to look into numerical techniques but some guidance will be really helpful. Please let me know if something is missing from the explanation and not making sense. Thanks

### RE: Heat source location in 1D and 2D models - Conduction

You could use Finite Element Analysis for that (there are many programms that can perform thermal analysis, some even free). But in FEA when you solve time-dependent problem you have to define initial temperature. If you ignore this setting, default value of 0 or room temperature (usually around 293.15 K) will be used by the solver.

### RE: Heat source location in 1D and 2D models - Conduction

(OP)
Hi, thanks for the response.
I have been using FEA to obtain the temperature profile at the boundary walls and there is no issue in running transient thermal simulations. I am using Abaqus to perform FEA analysis rather than physical experimental work.

I want to use the obtained temperature profile from the simulation so it is realistic. Then using the temperature data changing over time, would like to determine the unknown location of the heat source within that domain.

In other words, if I have a heat source in a cuboid body and I can only measure the surface temperature. Temperature measurements limited to any two adjacent surfaces or even just one surface. Using this data how can I estimate how far or how deep is the heat source from the surface.

Known parameters would include temperature change over time, thermal conductivity and geometry of the domain.
Thank you. Looking forward to the response.

### RE: Heat source location in 1D and 2D models - Conduction

I don't understand your problem; you have the tool, so why not just move the source around in the simulation and analyze the results? For a cuboid, you'd need 3D FEA.

TTFN (ta ta for now)
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### RE: Heat source location in 1D and 2D models - Conduction

(OP)
The issue is I don't know the location of the heat source within the structure. For example, if I am measuring the temperature at the surface of any machine tool, can I manipulate that data to find out the depth (spatial location of heat source). This is a common issue when access to the geometry is restricted, you don't know the exact location of the heat sources and cannot accurately simulate the thermal modelling. Therefore, I want to use just the surface temperature and find out where could heat source possibly be at and match the thermal behaviour as well. I hope this clears up the problem.

### RE: Heat source location in 1D and 2D models - Conduction

(OP)
IRstuff,
Yes that's one way to go, but if the structure is a complicated one, running thermal simulations and comparing results until matching results are obtained will take a lot of time. I have done that but its not useful when the geometry is not fully known, that's why I am looking to develop an algorithm that can predict location just by using the transient temperature at the surface.

### RE: Heat source location in 1D and 2D models - Conduction

Syed,

You can solve your 1D and 2D problems analytically. Open any heat transfer textbook and you will find examples of asymmetrical heating.

For complex 3D models, you are going to have a heck of a time developing a method from scratch, in which case you probably want to solicit help from a PhD skilled in heat transfer and numerical methods. I happen to know one; he charges \$1000/hour for a phone call.

It sounds like your problem is a bit like looking at shards of broken glass on the floor and demanding to know the precise location, velocity, and orientation with which the wine glass hit the floor. Sure, in a deterministic universe it is possible in theory, but good luck.

Perhaps you just need to use IRstuff's method. If it takes too long, write a script to automate it. From a practical sense, I am extremely interested in exactly what this mysterious black box is that you are trying to look inside of.

-Chris

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