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===Example A=== One physically reasonable pair of sources/sinks of entropy in the fluid arise in the context of what [<b>[[Appendix/References#LL75|<font color="red">LL75</font>]]</b>] identify as the ''general equation of heat transfer'', namely, <div align="center"> <table border="0" cellpadding="5" align="center"> <tr> <td align="right"> <math>\rho T \frac{ds_\mathrm{fluid}}{dt}</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> - \nabla\cdot \vec{F}_\mathrm{cond} + \Psi \, . </math> </td> </tr> </table> [<b>[[Appendix/References#LL75|<font color="red">LL75</font>]]</b>], §49, p. 185, Eq. (49.4)<br /> [<b>[[Appendix/References#Shu92|<font color="red">Shu92</font>]]</b>], Vol. II, §3, p. 30, Eq. (3.26)<br /> [<b>[[Appendix/References#P00|<font color="red">P00</font>]]</b>], Vol. I, §8.4, p. 369, Eq. (8.35) </div> In this expression, <div align="center"> <table border="0" cellpadding="5" align="center"> <tr> <td align="right"> <math>\vec{F}_\mathrm{cond}</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math>-\mathcal{K}_\mathrm{cond} \nabla T \, ,</math> </td> </tr> </table> [<b>[[Appendix/References#Shu92|<font color="red">Shu92</font>]]</b>], Vol. II, §3, p. 28, Eq. (3.19) </div> where, <span title="Coefficient of thermal conductivity"><math>\mathcal{K}_\mathrm{cond}</math></span> is the coefficient of ''thermal'' conductivity; and the ''rate of viscous dissipation'', <div align="center"> <table border="0" cellpadding="5" align="center"> <tr> <td align="right"> <math>\Psi</math> </td> <td align="center"> <math>\equiv</math> </td> <td align="left"> <math> \pi_{ik} \frac{\partial v_i}{\partial x_k} \, , </math> </td> </tr> </table> [<b>[[Appendix/References#Shu92|<font color="red">Shu92</font>]]</b>], Vol. II, §3, p. 29, following Eq. (3.25) </div> where <span title="Viscous stress tensor"><math>\pi_{ik}</math></span> is the "viscous stress tensor," as defined, for example: by equation (15.3) on p. 48 of [<b>[[Appendix/References#LL75|<font color="red">LL75</font>]]</b>]; by equation (44) on p. 52 of [<b>[[Appendix/References#T78|<font color="red">T78</font>]]</b>]; and by equation (8.34) on p. 369 of [<b>[[Appendix/References#P00|<font color="red">P00</font>]]</b>]. Note that when [<b>[[Appendix/References#Shu92|<font color="red">Shu92</font>]]</b>] defines <span title="Viscous stress tensor"><math>\pi_{ik}</math></span> — see his equations (3.19) and (3.20) on p. 28 — he implicitly zeroes out the coefficient of bulk viscosity component, keeping only the shear viscosity component because it is the piece that is usually of interest in astrophysical discussions. [<b>[[Appendix/References#Shu92|<font color="red">Shu92</font>]]</b>] goes on to explain — see on p. 23 immediately following his equation (2.36) — together, the pair of terms on the right-hand-side express the "<font color="#007700">time rate of adding heat (through heat conduction and the viscous conversion of ordered energy in differential fluid motions to disordered energy in random particle motions).</font>"
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