Equation of Heat: Meaning of ζ

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Discussion Overview

The discussion revolves around the physical meaning of the symbol ζ in the context of a heat equation, particularly focusing on its values when heating from below or above. Participants explore the implications of ζ being +1 or -1 based on temperature differences.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant states that ζ represents the heat flux across a plane, referencing a source.
  • Another participant clarifies that ζ equals +1 when the temperature of the fluid is lower than the external temperature of the heater and -1 when the fluid is cooling down.
  • There is confusion regarding the physical meaning of ζ, particularly why it takes on the values +1 and -1.
  • A participant suggests that the position of the heater (top or bottom) may not be as significant as the relative temperatures of the fluid and the environment.

Areas of Agreement / Disagreement

Participants express confusion and seek clarification on the meaning of ζ, indicating that there is no consensus on its physical interpretation or the conditions under which it takes specific values.

Contextual Notes

Participants have not fully defined the symbols used in the equation, which may contribute to the confusion. The discussion also highlights the dependence on the definitions of temperature conditions.

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]
 
Last edited by a moderator:
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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:
 
Last edited by a moderator:
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.
 
Last edited by a moderator:

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