[cig-commits] commit 2403 by bangerth to /var/svn/dealii/aspect

[dealii.demon at gmail.com]

Revision 2403

Rewrite a formula one more time.

U   trunk/aspect/doc/manual/manual.tex
U   trunk/aspect/doc/manual.pdf


http://www.dealii.org/websvn/revision.php?repname=Aspect+Repository&path=%2F&rev=2403&peg=2403

Diff:
Modified: trunk/aspect/doc/manual/manual.tex
===================================================================
--- trunk/aspect/doc/manual/manual.tex	2014-04-02 20:55:40 UTC (rev 2402)
+++ trunk/aspect/doc/manual/manual.tex	2014-04-03 12:57:22 UTC (rev 2403)
@@ -545,6 +545,9 @@
   transport through convection is several orders of magnitude more important
   than through thermal conduction.
 
+  The thermal conductivity $k$ is often expressed in terms of the
+  	extit{thermal diffusivity} $\kappa$ using the relation $k = 
ho C_p \kappa$.
+
 \item 	extit{The intrinsic specific heat production $H=H(\mathbf x)$:} Units
   $rac{	extrm{W}}{	extrm{kg}}=rac{	extrm{m}^2}{	extrm{s}^3}$.
 
@@ -6073,12 +6076,15 @@
 steady-state one-dimensional downward flow with vertical velocity $v_y$, it
 simplifies to the following:
 egin{gather*}
+
ho C_p
 v_y
 rac{\partial T}{\partial y} = 
-T rac{\Delta S}{C_p} v_y rac{\partial X}{\partial y} 
-+ \kappa
+
ho T \Delta S v_y rac{\partial X}{\partial y} 
++ 
ho C_p \kappa
 rac{\partial^2 T}{\partial y^2}.
 \end{gather*}
+Here, $
ho C_p \kappa = k$ with $k$ the thermal conductivity and $\kappa$ the
+thermal diffusivity.
 The first term on the right-hand side of the equation describes the latent heat
 produced at the phase transition: It is proportional to the temperature T, the
 entropy change $\Delta S$ across the phase transition divided by the specific

Modified: trunk/aspect/doc/manual.pdf
===================================================================
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