Equation of Heat: Meaning of ζ

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SUMMARY

The discussion centers on the physical meaning of the Greek letter ζ (zeta) in the context of heat transfer equations. Specifically, ζ = sign(T₀ - Tₑ) = +1 indicates heating from below, while ζ = sign(T₀ - Tₑ) = -1 indicates heating from above. The participants clarify that ζ represents the heat flux across a plane, emphasizing the importance of the temperature difference between the fluid and its environment. Understanding the sign of ζ is crucial for interpreting heat transfer dynamics in various heating scenarios.

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ssky
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Hi,

I have an equation of heat, as the form

gif.latex?\frac{\partial%20\theta%20}{\partial%20t}-\zeta%20w=\bigtriangledown%20^{2}\theta.gif

where,

[PLAIN]http://latex.codecogs.com/gif.latex?\zeta = +1 when heating from below
and
[PLAIN]http://latex.codecogs.com/gif.latex?\zeta = -1 when heating from above

what is the physical meaning of [URL]http://latex.codecogs.com/gif.latex?\zeta?[/URL]
 
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That symbol represents the heat flux across or through a plane, according to wiki. The symbol is a greek letter zeta.
 
sorry,

i forget to write that

[URL]http://latex.codecogs.com/gif.latex?\zeta[/URL] =sign (T_{0}-T_{u})=+1

when heating from below

[URL]http://astro.temple.edu/~davatzes/Geothermal/Geothermal/What_is_Energy_files/Fig33.png[/URL]

and

[URL]http://latex.codecogs.com/gif.latex?\zeta[/URL] =sign (T_{0}-T_{u})=-1

when heating from above

why equal 1 and -1 ?
what is the physical meaning ?
 
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artikk said:
That symbol represents the heat flux across or through a plane, according to wiki. The symbol is a greek letter zeta.

Yes, but I'm confused about the[URL]http://latex.codecogs.com/gif.latex?\zeta[/URL] [/URL]

what is the physical meaning of

[URL]http://latex.codecogs.com/gif.latex?\zeta[/URL] =sign (T_{0}-T_{u})=+1 ?

and why equal +1?

pleas help me :cry:
 
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ssky said:
Yes, but I'm confused about the[URL]http://latex.codecogs.com/gif.latex?\zeta[/URL] [/URL]

what is the physical meaning of

[URL]http://latex.codecogs.com/gif.latex?\zeta[/URL] =sign (T_{0}-T_{u})=+1 ?

and why equal +1?

pleas help me :cry:

You have left out what your various symbols stand for, which made me reluctant to answer since I have to guess.

Well, here's my guess.
It makes a difference whether the fluid is heated with a heater, so the temperature of the fluid starts being lower than the external temperature of the heater.
Or whether the fluid is not heated, but is cooling down.

Note that is won't matter if you have the heater on the bottom or on the top (it seems you're saying that).
What matters is whether the fluid temperature is above the temperature of the environment, or below.
 
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