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I am doing an experiment to see how does the thickness of the cup affect its heat transfer.

I need to find a theoretical equation that shows me the amount of heat transfer in a certain time for the cup.

The only equation I have found is this equation:

enter image description here

But it is only 1 dimension form, I am concerned if I could use it for the cup. Could I use it ?

The another general equation that I find is:

𝑞=−𝑘∇𝑇

But I am not pretty sure how do I calculate the temperature gradient (∇𝑇) in this case and local heat flux density. Search online, but have no luck with that.

So I am wondering if there is any equation that could be used for combing the time needed for the heat transfer and thickness of the material.

Any help and suggestion will be appreciated

The cup looks something like this:

enter image description here

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I think using the cylindrical coordinate system will be more convenient than the rectangular one. And also using the concept of thermal resistance will help in this type of problem. Don't forget taking the convection and heat radiation in consideration.

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  • $\begingroup$ Thanks, but if it is possible, could you show me an example of how to combine cylindrical coordinate system with the thermal resistance? $\endgroup$
    – James
    Commented Jan 23, 2023 at 17:12
  • $\begingroup$ youtu.be/6x-jdCGWuHI (watch this video) $\endgroup$
    – Muhammed
    Commented Jan 23, 2023 at 17:29

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