Axial Variation of Fuel, Clad, and Coolant Temperatures

Axial Variation of Fuel, Clad, and Coolant Temperatures 

In deriving the equations for the heat flow out of fuel elements, we have so far assumed that the rate of heat generation per unit volume is constant in the axial direction. In practice, of course, this is not the case for the unreflected reactor with uniform coolant density the flux, and hence the 

We consider a core of height H, made up of vertical rod-type elements. The coolant is assumed to flow upwards through the core, parallel to the fuel elements. Each fuel element is considered as having a certain fraction of the total coolant flow associated with it. The core cross section may be divided as shown in Fig. 6.8 in order to define the flow area for each element. The mass flow rate per element is given the s5mibol m. 

For simplicity we consider the fuel rod which lies along the axis of the core. If the extrapolation distance is small enough to be ignored in comparison with H, the flux variation along the length of the element is of cosine form and, if the fuel distribution is uniform, the variation of heat generation rate per unit volume is then 

Consider a small section of the element, of length dz, at distance z above the central plane. The heat generation rate in this segment is q A dz, where As is the cross-sectional area of the fuel. In equilibrium, the heat generation rate will be equal to the rate at which heat is taken up by the coolant, which is given by mCpdTf, where Cp is the specific heat at constant pressure for the fluid and dTf is the rise in bulk coolant temperature over the length dz (it is 

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