Mode of heat transfer between two cubes and to its surroundings 1

[purpleb]

Hi all,

I am trying to mathematically proof that one can neglect convection and radiation when two cubes (paraffin-based, 1x1x1cm) are in direct contact on one side whilst the other 5 sides are perfectly insulated. Any ideas on how to calculate the Nusselt number here?

How do you justify that radiation can be neglected? Can they actually be neglected?

How would the mode of heat transfer be changed if the cubes were not perfectly insulated, but instead were surrounded by air?

It would be fantastic if anyone could give me any hint! Many warm wishes and thanks so much in advance!

 

[IRstuff]

You need to explain more. From what to what is the radiation you are trying to ignore? Note that even a perfect insulator will radiate. Convection is easier to deal with; if there's no air, there's no convection.

TTFN
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[purpleb]

Hi, thanks a lot for your reply and for your help, which I appreciate.

How could I mathematically (with a formula) explain that convection does not play a role here?

I am trying to determine whether heat radiates from the hot paraffin cube (ca. 100°C) to the other cube or to the surrounding air and whether it is significant with regards to conduction?

Does this answer your question? Thanks again so much for your help!

 

[IRstuff]

> How could I mathematically (with a formula) explain that convection does not play a role here?

There are equations for convection, based on Raleigh and Nusselt numbers; when graphed as a function of separation, the convection coefficient is inversely proportional to the Rayleigh number. At some separation, however, I think the standard equations break down, since it becomes strictly conduction, rather than convection. You'll need to consult someone or some book that is better versed in convection in small gaps.

> I am trying to determine whether heat radiates from the hot paraffin cube (ca. 100°C) to the other cube or to the surrounding air and whether it is significant with regards to conduction?

You'll have to do the numbers, but given that paraffin is essentially a thermal insulator, conduction and radiation are probably comparable. You are just going to have to create a model that can given you a live estimate of what's going on.

TTFN
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[dvd]

Convection of/with what? Does the paraffin exist as a solid at 100C? Is there a convection loop of liquid paraffin at the interface? Does liquid paraffin have optical properties which allow it to transmit radiation? This whole post seems way too academic for it to be much else than that.

 

[IRstuff]

Is this for school?

TTFN
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