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## Main Question or Discussion Point

Can you derive the heat conduction equation from the navier stokes equations (particularly the energy eqn)?

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- Thread starter pyroknife
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Can you derive the heat conduction equation from the navier stokes equations (particularly the energy eqn)?

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Thanks. Question.

Are equations like potential flow, Euler's, heat conduction equation formulated before the Navier Stokes equations? I see that Euler existed before Navier&Stokes.

If so, then were the Navier Stokes equations formulated on the basis of these simplified equations?

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A minor comment- the Navier Stokes equation(s) is/are concerned with momentum transport. Just as mass transport is handled by a different equation-the continuity equation- energy transport is handled by it's own equation. All three equations are, to some degree, independent:Thanks. Question.

Are equations like potential flow, Euler's, heat conduction equation formulated before the Navier Stokes equations? I see that Euler existed before Navier&Stokes.

If so, then were the Navier Stokes equations formulated on the basis of these simplified equations?

http://www.ldeo.columbia.edu/~mspieg/mmm/Conserveq.pdf

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Wait I thought the Navier Stokes equations refers to the 3 conversation equations for mass, momentum, and energy? And hence the pluralness of "equationS?" If its just the momentum equation then why is it not called the Navier Stokes Equation?A minor comment- the Navier Stokes equation(s) is/are concerned with momentum transport. Just as mass transport is handled by a different equation-the continuity equation- energy transport is handled by it's own equation. All three equations are, to some degree, independent:

http://www.ldeo.columbia.edu/~mspieg/mmm/Conserveq.pdf

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Really it's just a semantics debate, though.

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Oh yeah I forget it is a vector equation. So the NS equations technically include the continuity and energy eqn?

Really it's just a semantics debate, though.

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Chestermiller

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No. It only addresses momentum. The continuity equation can be combined with the NS equation to obtain a different form of the equation, but its primary focus is still momentum. It is also possible to obtain the "mechanical energy balance equation" by dotting the NS equation with the velocity vector. This can be subtracted from the "overall energy balance equation " to yield the so-called "thermal energy balance equation".Oh yeah I forget it is a vector equation. So the NS equations technically include the continuity and energy eqn?

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