Thermal Energy Equation
Thermal Energy Equation#
\(\mathrm{f}_1\mathrm{f}_4\boldsymbol{v}\cdot\boldsymbol{\nabla}\Theta\) |
1401 |
rhotv_grad_s |
\(\mathrm{f}_1\mathrm{f}_4\boldsymbol{v'}\cdot\boldsymbol{\nabla}\Theta'\) |
1402 |
rhotvp_grad_sp |
\(\mathrm{f}_1\mathrm{f}_4\boldsymbol{v'}\cdot\boldsymbol{\nabla}\overline{\Theta}\) |
1403 |
rhotvp_grad_sm |
\(\mathrm{f}_1\mathrm{f}_4\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\overline{\Theta}\) |
1404 |
rhotvm_grad_sm |
\(\mathrm{f}_1\mathrm{f}_4\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\Theta'\) |
1405 |
rhotvm_grad_sp |
\(\mathrm{f}_1\mathrm{f}_4v_r\frac{\partial \Theta}{\partial r}\) |
1406 |
rhotvr_grad_s |
\(\mathrm{f}_1\mathrm{f}_4v_r'\frac{\partial \Theta'}{\partial r}\) |
1407 |
rhotvpr_grad_sp |
\(\mathrm{f}_1\mathrm{f}_4v_r'\frac{\partial \overline{\Theta}}{\partial r}\) |
1408 |
rhotvpr_grad_sm |
\(\mathrm{f}_1\mathrm{f}_4\overline{v_r}\frac{\partial \overline{\Theta}}{\partial r}\) |
1409 |
rhotvmr_grad_sm |
\(\mathrm{f}_1\mathrm{f}_4\overline{v_r}\frac{\partial \Theta'}{\partial r}\) |
1410 |
rhotvmr_grad_sp |
\(\mathrm{f}_1\mathrm{f}_4\frac{v_\theta}{r}\frac{\partial \Theta}{\partial \theta}\) |
1411 |
rhotvt_grad_s |
\(\mathrm{f}_1\mathrm{f}_4\frac{v_\theta'}{r}\frac{\partial \Theta'}{\partial \theta}\) |
1412 |
rhotvpt_grad_sp |
\(\mathrm{f}_1\mathrm{f}_4\frac{v_\theta'}{r}\frac{\partial \overline{\Theta}}{\partial \theta}\) |
1413 |
rhotvpt_grad_sm |
\(\mathrm{f}_1\mathrm{f}_4\frac{\overline{v_\theta}}{r}\frac{\partial \overline{\Theta}}{\partial \theta}\) |
1414 |
rhotvmt_grad_sm |
\(\mathrm{f}_1\mathrm{f}_4\frac{\overline{v_\theta}}{r}\frac{\partial \Theta'}{\partial \theta}\) |
1415 |
rhotvmt_grad_sp |
\(\mathrm{f}_1\mathrm{f}_4\frac{v_\phi}{r \mathrm{sin}\theta}\frac{\partial \Theta}{\partial \phi}\) |
1416 |
rhotvp_grad_s |
\(\mathrm{f}_1\mathrm{f}_4\frac{v_\phi'}{r \mathrm{sin}\theta}\frac{\partial \Theta'}{\partial \phi}\) |
1417 |
rhotvpp_grad_sp |
\(\mathrm{f}_1\mathrm{f}_4\frac{v_\phi'}{r \mathrm{sin}\theta}\frac{\partial \overline{\Theta}}{\partial \phi}\) |
1418 |
rhotvpp_grad_sm |
\(\mathrm{f}_1\mathrm{f}_4\frac{\overline{v_\phi}}{r \mathrm{sin}\theta}\frac{\partial \overline{\Theta}}{\partial \phi}\) |
1419 |
rhotvmp_grad_sm |
\(\mathrm{f}_1\mathrm{f}_4\frac{\overline{v_\phi}}{r \mathrm{sin}\theta}\frac{\partial \Theta'}{\partial \phi}\) |
1420 |
rhotvmp_grad_sp |
\(-c_6\boldsymbol{\nabla}\cdot\boldsymbol{F}_{cond}\) |
1421 |
s_diff |
\(-c_6\boldsymbol{\nabla}\cdot\boldsymbol{F'}_{cond}\) |
1422 |
sp_diff |
\(-c_6\boldsymbol{\nabla}\cdot\boldsymbol{\overline{F}}_{cond}\) |
1423 |
sm_diff |
\(c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\left(\frac{\partial^2 \Theta}{\partial r^2}+\frac{\partial \Theta}{\partial r}\left[\frac{2}{r}+\frac{\mathrm{d}}{\mathrm{dr}}\mathrm{ln}\left\{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\right\} \right]\right)\) |
1424 |
s_diff_r |
\(c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\left(\frac{\partial^2 \Theta'}{\partial r^2}+\frac{\partial \Theta'}{\partial r}\left[\frac{2}{r}+\frac{\mathrm{d}}{\mathrm{dr}}\mathrm{ln}\left\{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\right\} \right]\right)\) |
1425 |
sp_diff_r |
\(c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\left(\frac{\partial^2 \overline{\Theta}}{\partial r^2}+\frac{\partial \overline{\Theta}}{\partial r}\left[\frac{2}{r}+\frac{\mathrm{d}}{\mathrm{dr}}\mathrm{ln}\left\{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\right\} \right]\right)\) |
1426 |
sm_diff_r |
\(c_6\frac{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5}{r^2}\left(\frac{\partial^2 \Theta}{\partial \theta^2}+\mathrm{cot}\theta\frac{\partial s}{\partial\theta}\right)\) |
1427 |
s_diff_theta |
\(c_6\frac{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5}{r^2}\left(\frac{\partial^2 \Theta'}{\partial \theta^2}+\mathrm{cot}\theta\frac{\partial \Theta'}{\partial\theta}\right)\) |
1428 |
sp_diff_theta |
\(c_6\frac{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5}{r^2}\left(\frac{\partial^2 \overline{\Theta}}{\partial \theta^2}+\mathrm{cot}\theta\frac{\partial \overline{\Theta}}{\partial\theta}\right)\) |
1429 |
sm_diff_theta |
\(c_6\frac{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5}{r^2\mathrm{sin^2}\theta}\frac{\partial^2 \Theta}{\partial \phi^2}\) |
1430 |
s_diff_phi |
\(c_6\frac{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5}{r^2\mathrm{sin^2}\theta}\frac{\partial^2 \Theta'}{\partial \phi^2}\) |
1431 |
sp_diff_phi |
\(c_6\frac{\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5}{r^2\mathrm{sin^2}\theta}\frac{\partial^2 \overline{\Theta}}{\partial \phi^2}\) |
1432 |
sm_diff_phi |
\(F_Q(r)\) |
1433 |
vol_heat_flux |
\(\mathrm{f}_6(r)\) |
1434 |
vol_heating |
\(c_5\Phi(r,\theta,\phi)\) |
1435 |
visc_heating |
\(\mathrm{f}_7c_4\left( {\boldsymbol{\mathcal{J}}}\cdot{\boldsymbol{\mathcal{J}}} \right)\) |
1436 |
ohmic_heat |
\(\mathrm{f}_7c_4\left( {\boldsymbol{\mathcal{J}'}}\cdot{\boldsymbol{\mathcal{J}'}} \right)\) |
1437 |
ohmic_heat_pp |
\(\mathrm{f}_7c_4\left( \overline{\boldsymbol{\mathcal{J}}}\cdot\overline{\boldsymbol{\mathcal{J}}} \right)\) |
1438 |
ohmic_heat_pm |
\(\mathrm{f}_7c_4\left( \overline{\boldsymbol{\mathcal{J}}}\cdot{\boldsymbol{\mathcal{J}'}} \right)\) |
1439 |
ohmic_heat_mm |
\(\mathrm{f}_1\mathrm{f}_4v_r\Theta\) |
1440 |
rhot_vr_s |
\(\mathrm{f}_1\mathrm{f}_4v_r'\Theta'\) |
1441 |
rhot_vrp_sp |
\(\mathrm{f}_1\mathrm{f}_4v_r'\overline{\Theta}\) |
1442 |
rhot_vrp_sm |
\(\mathrm{f}_1\mathrm{f}_4\,\overline{v_r}\Theta'\) |
1443 |
rhot_vrm_sp |
\(\mathrm{f}_1\mathrm{f}_4\,\overline{v_r}\,\overline{\Theta}\) |
1444 |
rhot_vrm_sm |
\(\mathrm{f}_1\mathrm{f}_4v_\theta \Theta\) |
1445 |
rhot_vt_s |
\(\mathrm{f}_1\mathrm{f}_4v_\theta'\Theta'\) |
1446 |
rhot_vtp_sp |
\(\mathrm{f}_1\mathrm{f}_4v_\theta'\overline{\Theta}\) |
1447 |
rhot_vtp_sm |
\(\mathrm{f}_1\mathrm{f}_4\,\overline{v_\theta}\Theta'\) |
1448 |
rhot_vtm_sp |
\(\mathrm{f}_1\mathrm{f}_4\,\overline{v_\theta}\,\overline{\Theta}\) |
1449 |
rhot_vtm_sm |
\(\mathrm{f}_1\mathrm{f}_4v_\phi \Theta\) |
1450 |
rhot_vp_s |
\(\mathrm{f}_1\mathrm{f}_4v_\phi'\Theta'\) |
1451 |
rhot_vpp_sp |
\(\mathrm{f}_1\mathrm{f}_4v_\phi'\overline{\Theta}\) |
1452 |
rhot_vpp_sm |
\(\mathrm{f}_1\mathrm{f}_4\,\overline{v_\phi}\Theta'\) |
1453 |
rhot_vpm_sp |
\(\mathrm{f}_1\mathrm{f}_4\,\overline{v_\phi}\,\overline{\Theta}\) |
1454 |
rhot_vpm_sm |
\(c_P \mathrm{f}_1 v_r T\) |
1455 |
enth_flux_r |
\(c_P \mathrm{f}_1 v_\theta T\) |
1456 |
enth_flux_theta |
\(c_P \mathrm{f}_1 v_\phi T\) |
1457 |
enth_flux_phi |
\(c_P \mathrm{f}_1 v_r' T'\) |
1458 |
enth_flux_rpp |
\(c_P \mathrm{f}_1 v_\theta' T'\) |
1459 |
enth_flux_thetapp |
\(c_P \mathrm{f}_1 v_\phi' T'\) |
1460 |
enth_flux_phipp |
\(c_P \mathrm{f}_1 v_r'\, \overline{T}\) |
1461 |
enth_flux_rpm |
\(c_P \mathrm{f}_1 v_\theta'\, \overline{T}\) |
1462 |
enth_flux_thetapm |
\(c_P \mathrm{f}_1 v_\phi'\, \overline{T}\) |
1463 |
enth_flux_phipm |
\(c_P \mathrm{f}_1\, \overline{v_r}\, T'\) |
1464 |
enth_flux_rmp |
\(c_P \mathrm{f}_1\, \overline{v_\theta}\, T'\) |
1465 |
enth_flux_thetamp |
\(c_P \mathrm{f}_1\, \overline{v_\phi}\, T'\) |
1466 |
enth_flux_phimp |
\(c_P \mathrm{f}_1\, \overline{v_r}\, \overline{T}\) |
1467 |
enth_flux_rmm |
\(c_P \mathrm{f}_1\, \overline{v_\theta}\, \overline{T}\) |
1468 |
enth_flux_thetamm |
\(c_P \mathrm{f}_1\, \overline{v_\phi}\, \overline{T}\) |
1469 |
enth_flux_phimm |
\(-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{\partial \Theta}{\partial r}\) |
1470 |
cond_flux_r |
\(-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{1}{r}\frac{\partial \Theta}{\partial \theta}\) |
1471 |
cond_flux_theta |
\(-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{1}{r \mathrm{sin}\theta}\frac{\partial \Theta}{\partial \phi}\) |
1472 |
cond_flux_phi |
\(-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{\partial \Theta'}{\partial r}\) |
1473 |
cond_fluxp_r |
\(-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{1}{r}\frac{\partial \Theta'}{\partial \theta}\) |
1474 |
cond_fluxp_theta |
\(-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{1}{r \mathrm{sin}\theta}\frac{\partial \Theta'}{\partial \phi}\) |
1475 |
cond_fluxp_phi |
\(-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{\partial \overline{\Theta}}{\partial r}\) |
1476 |
cond_fluxm_r |
\(-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{1}{r}\frac{\partial \overline{\Theta}}{\partial \theta}\) |
1477 |
cond_fluxm_theta |
\(-c_6\mathrm{f}_1\mathrm{f}_4\mathrm{f}_5\frac{1}{r \mathrm{sin}\theta}\frac{\partial \overline{\Theta}}{\partial \phi}\) |
1478 |
cond_fluxm_phi |
\(\mathrm{f}_1\mathrm{f}_4 v_r \mathrm{f}_{14}\) |
1479 |
ref_advec |
\(\mathrm{f}_1\mathrm{f}_4 v_r' \mathrm{f}_{14}\) |
1480 |
ref_advec_p |
\(\mathrm{f}_1\mathrm{f}_4 \overline{v_r} \mathrm{f}_{14}\) |
1481 |
ref_advec_m |