We have applied the laws of heat transfer by con­duction to solids only and they can be used with a reasonable degree of accuracy where the thermal con­ductivity of the material is known and is constant. For instance through a solid uranium or plutonium rod fuel element and its associated metallic sheath. However, the purpose of the fuel element is to gen­erate heat which can then be transferred from the sur­face of the element to a fluid which, in turn, either directly powers the turbine (BWR) or transfers the heat to a secondary circuit of the power system (mag­nox, AGR and PWR).

The fluid used for the magnox and AGR reactor systems is CO2 which has a relatively poor thermal conductivity and must be circulated at high velocity to give the ‘turbulent’ conditions necessary for high rates of heat transfer. Figure 1.21 illustrates that

QT/A = q = (k/x)(ts — tc)

In practice the ratio (k/x) is difficult to measure or calculate and it is replaced by an empirical constant h:

QT/A = q = h(ts — tc) (1.5)

The factor h is known as ‘the surface heat transfer coefficient’; it is not constant and will vary with a large number of design and operating parameters, e. g., geometry, flow velocity, pressure, temperature.

If the flow velocity in the reactor fuel channel is reduced to a value which produces no turbulence, the flow pattern is known as ‘streamline or viscous’, and there will be a continuous temperature gradient across the fluid. Equation (1.5) would still be valid pro­vided the temperature tc is the mean temperature of the fluid.

For fluids with a higher thermal conductivity than the gaseous coolant used in magnox and AGR re­actors, e. g., water and liquid metals, a similar rela­tionship can also be applied, but in these cases the variation in temperature across the fluid will be dif­ferent to that applied to gases.

Equation (1.5) is important to the designer and operator since it illustrates that for a given tempera­ture differential between the sheath and the coolant the rate of heat extraction from the fuel element is a function of:

• The heat transfer surface area (A).

• The surface heat transfer coefficient (h).

‘h’ is a function of many design and operating factors but in particular the degree of turbulence. The latter is most important with gaseous coolants where, in order to obtain an economic level of heat transfer, a high degree of turbulence is essential. Thus the design of the fuel element sheath geometry must provide:

• A high degree of turbulence by presenting the gas flow with a ‘rough’ profile.

• A high effective surface area without increasing the fuel element diameter (if the latter were increased Equation (1.4) shows that the temperature gradient across the fuel would increase thus reducing the surface temperature tf for a given maximum fuel temperature).

These two effects are achieved by the ‘finning’ and ‘ribbing* geometry of the fuel element sheath. Figure 1.22 shows typical finning on the magnox fuel ele­ments and ribbing on the AGR fuel elements.