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Output

The output from the thermal design computation is written to a MATLAB mat-file with the name
<input_filename>.mt3 and the file is retrieved by issuing the MATLAB command load <input filename>.mt3 -mat in the MATLAB command window. Having retrieved the contents of the mat-file the workspace holds the following variables:

l

Vector of z-coordinates (relative to the core bottom) for the thermal calculations [m].

l

Vector of bulk liquid temperatures at the z-coordinates in z_t [ ${}^\circ\mbox{C}$].

l

Vector which holds the linear heat generation rate for one rod, $q_{\mbox{\protect\scriptsize rod}}'$ [W/m], at the z-coordinates in z_t.

l

Vector which holds the maximum (center line) fuel temperature at the z-coordinates in z_t.

l

Vector of temperatures at the fuel surface, T(R_f) [ ${}^\circ\mbox{C}$], at the z-coordinates in z_t.

l

Vector of temperatures at the inner surface of the cladding, $T(R_f+d_{\mbox{\protect\scriptsize gap}})$ [ ${}^\circ\mbox{C}$], at the z-coordinates in z_t.

l

Vector of wall temperatures (ie at the outer surface of the cladding), T_w [ ${}^\circ\mbox{C}$], at the z-coordinates in z_t.

l

Vector of average fuel temperatures, $\overline{T}{}_f$ [ ${}^\circ\mbox{C}$], at the z-coordinates in z_t. The average $\overline{T}{}_f$ is to be used in the neutronics calculation--the method of calculation is described below.

l

Simple variable which holds the gap conductance, H_g [W/( ${\mbox{m}}^2\cdot$K)].

As shown above we calculate an average fuel temperature, $\overline{T}{}_f$. The mathematical definition of $\overline{T}{}_f$ [ ${}^\circ\mbox{C}$] is given by

$$\overline{T}{}_f \;\hbox{$=$\kern-0.68em\raise1.1ex \hbox{... ...riptstyle\triangle$}}\;\frac{1}{A_f} \int\limits_{A_f} T(r) dA$$ (12.1)

where A_f is the cross-sectional area of fuel in a fuel rod [${\mbox{m}}^2$]. If we use the geometry depicted in Figure 11.1 the above equation can be written

$$\overline{T}{}_f = \frac{1}{\pi R_f^2} \int\limits_{0}^{R_f... ... \pi r dr = \frac{2}{R_f^2} \int\limits_{0}^{R_f} T_f(r) r dr$$ (12.2)

In practice, we calculate the integral numerically by means of the Simpson formula with 6 concentric rings.

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