Equation of Heat: Meaning of ζ

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The discussion centers on the physical meaning of the Greek letter zeta (ζ) in the context of heat equations. It is defined as ζ = sign(T₀ - Tₑ), where ζ equals +1 when heating from below and -1 when heating from above. Participants express confusion about why ζ takes these specific values and the implications for heat flux across a plane. The key point is that the sign of ζ indicates whether the fluid temperature is above or below the external temperature, influencing the direction of heat transfer. Understanding this distinction is crucial for interpreting heat flow dynamics in various heating scenarios.
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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