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2-dimensional transient Conduction in a Cylindrical Workpiece

2-dimensional transient Conduction in a Cylindrical Workpiece

(OP)
Hey Guys,

I am trying to figure out the best design for a new test bench and stuck with a interesting question. I try to analyse the resulting heat flow of a cylindrical specimen (bearing) with a diameter of about 90 mm. This bearing has in the load zone a higher heat dissipation than in the opposite zone. My goal is to analyse this difference. So there will be a different heat generation depending on the angle. My approch is the following: The Bearing is fitted in another cylinder made of steel. For the temperature measurement there are thermocouples insight the outer ring of the bearing. I made a sketch and added it to the post. The Heat which is locally generated will firstly increase the temperature in the direct environment. With advance of time the heat will of course dissipate to zones with lower temperatures.
For Analysing the different heat generation the temperature change with time will be evaluated. This heat change is proportional to the heat flow.(see attached equation).Unfortunately the heat convection must therefore be negligible in a period of time. I think for a few seconds it will be negligible but of course i want to estimate this time. Is there any way to estimate this time?


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