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Energy conservation

The assumptions in the energy conservation equations are of minor importance at least in our case. It is, however, for general application of the conservation equations vital to indicate the simplifications.

Analogously to the momentum equations we have neglected the correlation effects of the distribution of enthalpy^6.4 across the cross section in the energy equations such that the correlation coefficient of, say, the liquid phase, $C_{h\ell}$, defined by

$$C_{h\ell} \;\hbox{$=$\kern-0.68em\raise1.1ex \hbox{$\scrip... ...ell \mbox{$<\!{u_\ell}\!>$}_\ell (1-\mbox{$<\!{\alpha}\!>$})}$$ (6.30)

is assumed approximately unity. The same applies to the energy equation of the vapor phase.

According to Ishii and Mishima [17] this assumption is very good except for highly transient cases.

Secondly, the conduction of heat, both turbulent and non-turbulent, in the axial direction is neglected. This simplification is good since the driving temperature differential is small especially in the saturated region. Put differently we have a large $\mbox{\bf Pe}$^6.5 in the reactor core.

Finally the viscous dissipation is neglected, ie the irreversible conversion of mechanical energy into internal energy by viscous forces. In our case dealing with a low-viscosity fluid moving with low velocity (the Brinkmann number^6.6 is small, $\mbox{\bf Br} \ll 1$) this assumption is validated especially when this irreversible heat source is compared to a typical heat input in a fuel element of 2 MW.

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