Procyon001
Mechanical
Hi all,
I've been working an old problem for a couple weeks now, have ended up confusing myself and now need some advice.
Here's the break down:
[ul]
[li]A lumped system (sub millimeter volume / confirmed Bi <<< 0.1) is held on top of a hot plate during dt[/li]
[li]Heat is transferred to the system from the hot plate during dt[/li]
[li]Heat is lost to ambient during dt[/li]
[li]Only the initial temperatures of the two surfaces are known[/li]
[li]Ignoring point loading/contact resistance to simplify the analysis - I will consider them once the main analysis is determined[/li]
[/ul]
I used the semi-infinite solid Fourier model to determine the contact surface temperature between the two materials, considering k, p and c, and assuming perfect contact.
Main question: Because the system is lumped, does this surface temperature actually characterize the system temperature at Ti (lumped)? or T(t) (SIS)?
If so, I can then use Q = hA[T(t)-Ti)] to determine the temperature loss after dt and I'm done.
If not, what model is most appropriate here? I have been studying Cengel and McGraw-Hill and my analysis is limited to these methods.
It really seems like the definitions of the two models contradict each other, so this is where my confidence in the analysis drops.
All comments and help are welcomed.
I've been working an old problem for a couple weeks now, have ended up confusing myself and now need some advice.
Here's the break down:
[ul]
[li]A lumped system (sub millimeter volume / confirmed Bi <<< 0.1) is held on top of a hot plate during dt[/li]
[li]Heat is transferred to the system from the hot plate during dt[/li]
[li]Heat is lost to ambient during dt[/li]
[li]Only the initial temperatures of the two surfaces are known[/li]
[li]Ignoring point loading/contact resistance to simplify the analysis - I will consider them once the main analysis is determined[/li]
[/ul]
I used the semi-infinite solid Fourier model to determine the contact surface temperature between the two materials, considering k, p and c, and assuming perfect contact.
Main question: Because the system is lumped, does this surface temperature actually characterize the system temperature at Ti (lumped)? or T(t) (SIS)?
If so, I can then use Q = hA[T(t)-Ti)] to determine the temperature loss after dt and I'm done.
If not, what model is most appropriate here? I have been studying Cengel and McGraw-Hill and my analysis is limited to these methods.
It really seems like the definitions of the two models contradict each other, so this is where my confidence in the analysis drops.
All comments and help are welcomed.
