... | @@ -20,7 +20,7 @@ We indicate with $`\kappa_p`$ and $`\kappa_r`$ respectively the Planck and t |
... | @@ -20,7 +20,7 @@ We indicate with $`\kappa_p`$ and $`\kappa_r`$ respectively the Planck and t |
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We consider an ideal gas of pressure $`P`$ with equation of state:
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We consider an ideal gas of pressure $`P`$ with equation of state:
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$`P = (\gamma-1)e`$ for a gas with adiabatic index $`\gamma`$.
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$`P = (\gamma-1)e`$ for a gas with adiabatic index $`\gamma`$.
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The terms $`P \nabla \cdot \vec v `$ and $`Q^+$ are respectively the compressional heating and the viscous heating ( see Mihalas and Mihalas 1984).
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The terms $`P \nabla \cdot \vec v `$ and $`Q^+`$ are respectively the compressional heating and the viscous heating ( see Mihalas and Mihalas 1984).
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In order to compute the viscous heating we need to know the viscous stress tensor :
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In order to compute the viscous heating we need to know the viscous stress tensor :
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... | @@ -39,9 +39,12 @@ $`\left\lbrace \begin{array}{lllll} |
... | @@ -39,9 +39,12 @@ $`\left\lbrace \begin{array}{lllll} |
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\over \partial \theta})]
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\over \partial \theta})]
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\end{array} \right. `$
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\end{array} \right. `$
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We can now compute the viscous heating (see Eq. 27.30 from Mihalas and Mihalas 1984)
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We can now compute the viscous heating (see Eq. 27.30 from Mihalas and Mihalas 1984):
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We do not include here the heating from the central star.
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$`Q^+ = 2\rho \nu (\tau _{RR}^2+\tau _{\varphi \varphi}^2+\tau_{\theta \theta}^2
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+{1\over 2}(\tau _{R\varphi}^2+\tau _{\theta\varphi}^2+\tau _{R\theta}^2-{1/over 3}(\nabla \cdot \vec v)^2)`$
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We will consider in the following the heating from the central star.
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## How we derive the equation for the internal energy
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## How we derive the equation for the internal energy
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