14.1 – Energy flux vectors

After evaluating fluxes at the faces of the elemental volumes it is possible to evaluate the vector flux by area unit, q”, in the center of each volume, using an average of fluxes at the interfaces:
 




(14.5)
 
(14.6)


Here e are fluxes in the center of the elemental volumes, perpendicular to lines h and x respectively.


From these average fluxes we can obtain the Cartesian components of the energy flux vector in the center of the elemental volumes using the following expressions:

 


(14.7)

  (14.8)

Here q”x and q”y are, respectively, the Cartesian components of the energy flux vector by unit area in directions x and y in the center of the elemental volumes.
 
We should remark that the metrics on equations (13.7) and (13.8) are evaluated in the center of the elemental volumes and not at the faces. This calculation is discussed in chapter (11).
 
We should also remark that the flux uses the following sign convention:
 
  • Positive (+): When it is oriented on directions West to East or South to North;
  • Negative (-): When it is oriented on directions East to West or North to South.
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