A transient heat convection and thermal expansion problem 1

[ringo9857]

A wire with finite length moves planarly in an air with temperature, which is distributed in the plane of motion Oxy nonlinearly. The distribution of the temperature T=T(x,y) is known function. How to find the transient temperature of the wire and its thermal expansion?

 

[IRstuff]

Sounds like homework. If so, please delete and repost in the Student Engineering forum

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[ringo9857]

The problem is part of an engineering project. It will be very difficult for a student to solve it. Please see the file attached here.

 

[goutam_freelance]

Analytical solution is very difficult if not impossible. FEA or finite difference solution can be attempted.

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[LittleInch]

That appears to be quite complex with many variables. Some experiments may be needed.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[ringo9857]

Thank you for the answer. We have some experiments. But I need to express the heat transfer in 2D space. What is the governing equation for 2D (or maybe 3D) heat convection for the considering case?

 

[goutam_freelance]

Here is a derivation with assumption of constant physical parameters. Further simplification has been applied at the end for calculation of thermal expansion like temperature invariance with r and phi at any z and time(axisymmetric).

Engineers, think what we have done to the environment !

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[ringo9857]

Perfect answer!!! Thank you very much goutam_freelance!!! I need time to realize how to apply these equations into my dynamic model, which is more complex. By the way, can't we initially assume that the temperature in the radial direction is constant. For example at a very small radius.

 

[goutam_freelance]

Yes. In fact I have already mentioned this possibility.

Engineers, think what we have done to the environment !

https://www.linkedin.com/in/goutam-das-59743b30/