Transient conduction in solid

[smukthiHT]

I am trying to compute the time taken by a solid to reach steady state(30cmX30cmX0.5cm) if I have constant heat flux bc on one of the surafaces of the solid(30cmX30cm on bottom) that is placed in an open ambient environment where there is only convection between other 5 faces of solid and fluid air.
The analytical formula from heat transfer text books for time constant if for a constant temperature bc on the fluid. Is there any analytical model to figure what I need?

Thanks
Sridhar

 

[DmitryKalganov]

I think it is not calculate analytically , use the CAE

 

[IRstuff]

You should read up on Biot Number:

https://en.wikipedia.org/wiki/Biot_number

TTFN
faq731-376
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[GregLocock]

Your first problem is in your phrasing- it'll take forever to reach steady state, In practice you can bound the problem by considering how long it would take to heat the block in the absence of cooling, and say 100 times that. I'm assuming (by observation of real life) the system is overdamped, otherwise you'll be having much more fun.

Cheers

Greg Locock


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[DmitryKalganov]

By the way, it can be simplified to calculate , without convective heat flow at the edges. If the assume that heat flow only on the bottom you can use the equation for the plane wall

 

[chicopee]

Get a heat transfer book and learn numerical analysis that could get a little complicated when you try to apply it into a computer program.

 

[davefitz]

The significant length parameter "s" is 0.5cm. The time constant is s^2/a, where a is the thermal diffusivity. You should be close to steady state after 4 time constants. Most thermocouples have a 2-4 C error , so that should take you to within measurement accuracy.

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