lumped parameter method, with flux at surface

ecocanuck · Feb 1, 2007

Is there a criterion for determining when the lumped parameter method will work for bodies with a constant temperature or flux at the surface?

I understand the Biot criterion can be used if you can calculate a heat transfer coefficient at the surface (i.e. convective resistance dominates total resistance so that conduction in the body can be ignored), but it is not clear to me under what conditions conduction can be ignored when you have a temperature or flux at the surface, because there is only one resistance from conduction in the body. Clearly, if the body is very small and has a moderately high conductivity, you would not expect a large temperature gradient in the body, but is there a formal criterion to show this?

Thanks for any adivce.

torpen · Feb 2, 2007

Hello,

The lumped capacitance method supposes negligible gradients at any instant during time (spatially uniform temperature). With the Fourier’s law this condition is impossible unless the thermal conductivity is infinite.
However this condition is approximately satisfied if the resistance to conduction is much less than the resistance to heat transfer between the solid and its surroundings.
If you impose a temperature the lumped capacitance method is then inappropriate.
If you apply a heat flux you can estimate the global heat transfer coefficient h (with the fluid temperature and an estimation of the range of the wall temperature) and then calculate the Biot number Bi.

The assumption of a uniform temperature across a solid is valid if the Biot number Bi satisfies the following condition
Bi << 1 (< 0.1 for example)

Regards,

Torpen

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lumped parameter method, with flux at surface

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