Thermal Energy Equation ==================================================================== =================================================================================================================================================================================================================================================================================== ====== ===================== :math:`\mathrm{f}_1\mathrm{f}_4\boldsymbol{v}\cdot\boldsymbol{\nabla}\Theta` 1401 rhotv\_grad\_s :math:`\mathrm{f}_1\mathrm{f}_4\boldsymbol{v'}\cdot\boldsymbol{\nabla}\Theta'` 1402 rhotvp\_grad\_sp :math:`\mathrm{f}_1\mathrm{f}_4\boldsymbol{v'}\cdot\boldsymbol{\nabla}\overline{\Theta}` 1403 rhotvp\_grad\_sm :math:`\mathrm{f}_1\mathrm{f}_4\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\overline{\Theta}` 1404 rhotvm\_grad\_sm :math:`\mathrm{f}_1\mathrm{f}_4\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\Theta'` 1405 rhotvm\_grad\_sp :math:`\mathrm{f}_1\mathrm{f}_4v_r\frac{\partial \Theta}{\partial r}` 1406 rhotvr\_grad\_s :math:`\mathrm{f}_1\mathrm{f}_4v_r'\frac{\partial \Theta'}{\partial r}` 1407 rhotvpr\_grad\_sp :math:`\mathrm{f}_1\mathrm{f}_4v_r'\frac{\partial \overline{\Theta}}{\partial r}` 1408 rhotvpr\_grad\_sm :math:`\mathrm{f}_1\mathrm{f}_4\overline{v_r}\frac{\partial \overline{\Theta}}{\partial r}` 1409 rhotvmr\_grad\_sm :math:`\mathrm{f}_1\mathrm{f}_4\overline{v_r}\frac{\partial \Theta'}{\partial r}` 1410 rhotvmr\_grad\_sp :math:`\mathrm{f}_1\mathrm{f}_4\frac{v_\theta}{r}\frac{\partial \Theta}{\partial \theta}` 1411 rhotvt\_grad\_s :math:`\mathrm{f}_1\mathrm{f}_4\frac{v_\theta'}{r}\frac{\partial \Theta'}{\partial \theta}` 1412 rhotvpt\_grad\_sp :math:`\mathrm{f}_1\mathrm{f}_4\frac{v_\theta'}{r}\frac{\partial \overline{\Theta}}{\partial \theta}` 1413 rhotvpt\_grad\_sm :math:`\mathrm{f}_1\mathrm{f}_4\frac{\overline{v_\theta}}{r}\frac{\partial \overline{\Theta}}{\partial \theta}` 1414 rhotvmt\_grad\_sm :math:`\mathrm{f}_1\mathrm{f}_4\frac{\overline{v_\theta}}{r}\frac{\partial \Theta'}{\partial \theta}` 1415 rhotvmt\_grad\_sp :math:`\mathrm{f}_1\mathrm{f}_4\frac{v_\phi}{r \mathrm{sin}\theta}\frac{\partial \Theta}{\partial \phi}` 1416 rhotvp\_grad\_s :math:`\mathrm{f}_1\mathrm{f}_4\frac{v_\phi'}{r \mathrm{sin}\theta}\frac{\partial \Theta'}{\partial \phi}` 1417 rhotvpp\_grad\_sp :math:`\mathrm{f}_1\mathrm{f}_4\frac{v_\phi'}{r \mathrm{sin}\theta}\frac{\partial \overline{\Theta}}{\partial \phi}` 1418 rhotvpp\_grad\_sm :math:`\mathrm{f}_1\mathrm{f}_4\frac{\overline{v_\phi}}{r \mathrm{sin}\theta}\frac{\partial \overline{\Theta}}{\partial \phi}` 1419 rhotvmp\_grad\_sm :math:`\mathrm{f}_1\mathrm{f}_4\frac{\overline{v_\phi}}{r \mathrm{sin}\theta}\frac{\partial \Theta'}{\partial \phi}` 1420 rhotvmp\_grad\_sp :math:`-c_6\boldsymbol{\nabla}\cdot\boldsymbol{F}_{cond}` 1421 s\_diff :math:`-c_6\boldsymbol{\nabla}\cdot\boldsymbol{F'}_{cond}` 1422 sp\_diff :math:`-c_6\boldsymbol{\nabla}\cdot\boldsymbol{\overline{F}}_{cond}` 1423 sm\_diff :math:`c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\left(\frac{\partial^2 \Theta}{\partial r^2}+\frac{\partial \Theta}{\partial r}\left[\frac{2}{r}+\frac{\mathrm{d}}{\mathrm{dr}}\mathrm{ln}\left\{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\right\} \right]\right)` 1424 s\_diff\_r :math:`c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\left(\frac{\partial^2 \Theta'}{\partial r^2}+\frac{\partial \Theta'}{\partial r}\left[\frac{2}{r}+\frac{\mathrm{d}}{\mathrm{dr}}\mathrm{ln}\left\{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\right\} \right]\right)` 1425 sp\_diff\_r :math:`c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\left(\frac{\partial^2 \overline{\Theta}}{\partial r^2}+\frac{\partial \overline{\Theta}}{\partial r}\left[\frac{2}{r}+\frac{\mathrm{d}}{\mathrm{dr}}\mathrm{ln}\left\{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\right\} \right]\right)` 1426 sm\_diff\_r :math:`c_6\frac{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5}{r^2}\left(\frac{\partial^2 \Theta}{\partial \theta^2}+\mathrm{cot}\theta\frac{\partial s}{\partial\theta}\right)` 1427 s\_diff\_theta :math:`c_6\frac{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5}{r^2}\left(\frac{\partial^2 \Theta'}{\partial \theta^2}+\mathrm{cot}\theta\frac{\partial \Theta'}{\partial\theta}\right)` 1428 sp\_diff\_theta :math:`c_6\frac{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5}{r^2}\left(\frac{\partial^2 \overline{\Theta}}{\partial \theta^2}+\mathrm{cot}\theta\frac{\partial \overline{\Theta}}{\partial\theta}\right)` 1429 sm\_diff\_theta :math:`c_6\frac{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5}{r^2\mathrm{sin^2}\theta}\frac{\partial^2 \Theta}{\partial \phi^2}` 1430 s\_diff\_phi :math:`c_6\frac{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5}{r^2\mathrm{sin^2}\theta}\frac{\partial^2 \Theta'}{\partial \phi^2}` 1431 sp\_diff\_phi :math:`c_6\frac{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5}{r^2\mathrm{sin^2}\theta}\frac{\partial^2 \overline{\Theta}}{\partial \phi^2}` 1432 sm\_diff\_phi :math:`F_Q(r)` 1433 vol\_heat\_flux :math:`\mathrm{f}_6(r)` 1434 vol\_heating :math:`c_5\Phi(r,\theta,\phi)` 1435 visc\_heating :math:`\mathrm{f}_7c_4\left( {\boldsymbol{\mathcal{J}}}\cdot{\boldsymbol{\mathcal{J}}} \right)` 1436 ohmic\_heat :math:`\mathrm{f}_7c_4\left( {\boldsymbol{\mathcal{J}'}}\cdot{\boldsymbol{\mathcal{J}'}} \right)` 1437 ohmic\_heat\_pp :math:`\mathrm{f}_7c_4\left( \overline{\boldsymbol{\mathcal{J}}}\cdot\overline{\boldsymbol{\mathcal{J}}} \right)` 1438 ohmic\_heat\_pm :math:`\mathrm{f}_7c_4\left( \overline{\boldsymbol{\mathcal{J}}}\cdot{\boldsymbol{\mathcal{J}'}} \right)` 1439 ohmic\_heat\_mm :math:`\mathrm{f}_1\mathrm{f}_4v_r\Theta` 1440 rhot\_vr\_s :math:`\mathrm{f}_1\mathrm{f}_4v_r'\Theta'` 1441 rhot\_vrp\_sp :math:`\mathrm{f}_1\mathrm{f}_4v_r'\overline{\Theta}` 1442 rhot\_vrp\_sm :math:`\mathrm{f}_1\mathrm{f}_4\,\overline{v_r}\Theta'` 1443 rhot\_vrm\_sp :math:`\mathrm{f}_1\mathrm{f}_4\,\overline{v_r}\,\overline{\Theta}` 1444 rhot\_vrm\_sm :math:`\mathrm{f}_1\mathrm{f}_4v_\theta \Theta` 1445 rhot\_vt\_s :math:`\mathrm{f}_1\mathrm{f}_4v_\theta'\Theta'` 1446 rhot\_vtp\_sp :math:`\mathrm{f}_1\mathrm{f}_4v_\theta'\overline{\Theta}` 1447 rhot\_vtp\_sm :math:`\mathrm{f}_1\mathrm{f}_4\,\overline{v_\theta}\Theta'` 1448 rhot\_vtm\_sp :math:`\mathrm{f}_1\mathrm{f}_4\,\overline{v_\theta}\,\overline{\Theta}` 1449 rhot\_vtm\_sm :math:`\mathrm{f}_1\mathrm{f}_4v_\phi \Theta` 1450 rhot\_vp\_s :math:`\mathrm{f}_1\mathrm{f}_4v_\phi'\Theta'` 1451 rhot\_vpp\_sp :math:`\mathrm{f}_1\mathrm{f}_4v_\phi'\overline{\Theta}` 1452 rhot\_vpp\_sm :math:`\mathrm{f}_1\mathrm{f}_4\,\overline{v_\phi}\Theta'` 1453 rhot\_vpm\_sp :math:`\mathrm{f}_1\mathrm{f}_4\,\overline{v_\phi}\,\overline{\Theta}` 1454 rhot\_vpm\_sm :math:`c_P \mathrm{f}_1 v_r T` 1455 enth\_flux\_r :math:`c_P \mathrm{f}_1 v_\theta T` 1456 enth\_flux\_theta :math:`c_P \mathrm{f}_1 v_\phi T` 1457 enth\_flux\_phi :math:`c_P \mathrm{f}_1 v_r' T'` 1458 enth\_flux\_rpp :math:`c_P \mathrm{f}_1 v_\theta' T'` 1459 enth\_flux\_thetapp :math:`c_P \mathrm{f}_1 v_\phi' T'` 1460 enth\_flux\_phipp :math:`c_P \mathrm{f}_1 v_r'\, \overline{T}` 1461 enth\_flux\_rpm :math:`c_P \mathrm{f}_1 v_\theta'\, \overline{T}` 1462 enth\_flux\_thetapm :math:`c_P \mathrm{f}_1 v_\phi'\, \overline{T}` 1463 enth\_flux\_phipm :math:`c_P \mathrm{f}_1\, \overline{v_r}\, T'` 1464 enth\_flux\_rmp :math:`c_P \mathrm{f}_1\, \overline{v_\theta}\, T'` 1465 enth\_flux\_thetamp :math:`c_P \mathrm{f}_1\, \overline{v_\phi}\, T'` 1466 enth\_flux\_phimp :math:`c_P \mathrm{f}_1\, \overline{v_r}\, \overline{T}` 1467 enth\_flux\_rmm :math:`c_P \mathrm{f}_1\, \overline{v_\theta}\, \overline{T}` 1468 enth\_flux\_thetamm :math:`c_P \mathrm{f}_1\, \overline{v_\phi}\, \overline{T}` 1469 enth\_flux\_phimm :math:`-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{\partial \Theta}{\partial r}` 1470 cond\_flux\_r :math:`-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{1}{r}\frac{\partial \Theta}{\partial \theta}` 1471 cond\_flux\_theta :math:`-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{1}{r \mathrm{sin}\theta}\frac{\partial \Theta}{\partial \phi}` 1472 cond\_flux\_phi :math:`-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{\partial \Theta'}{\partial r}` 1473 cond\_fluxp\_r :math:`-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{1}{r}\frac{\partial \Theta'}{\partial \theta}` 1474 cond\_fluxp\_theta :math:`-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{1}{r \mathrm{sin}\theta}\frac{\partial \Theta'}{\partial \phi}` 1475 cond\_fluxp\_phi :math:`-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{\partial \overline{\Theta}}{\partial r}` 1476 cond\_fluxm\_r :math:`-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{1}{r}\frac{\partial \overline{\Theta}}{\partial \theta}` 1477 cond\_fluxm\_theta :math:`-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{1}{r \mathrm{sin}\theta}\frac{\partial \overline{\Theta}}{\partial \phi}` 1478 cond\_fluxm\_phi :math:`\mathrm{f}_1\mathrm{f}_4 v_r \mathrm{f}_{14}` 1479 ref\_advec :math:`\mathrm{f}_1\mathrm{f}_4 v_r' \mathrm{f}_{14}` 1480 ref\_advec\_p :math:`\mathrm{f}_1\mathrm{f}_4 \overline{v_r} \mathrm{f}_{14}` 1481 ref\_advec\_m =================================================================================================================================================================================================================================================================================== ====== =====================