Applying Fouriers law of heat conduction to the fuel

Fourier s law states that the heat flow, t (W), is proportional to the area of flow, A (m ), and the temperature gradient, dT/dx (K/m). In one dimension, this may be written  

It may be shown (Rogers and Mayhew, 1992) that applying Fourier s law to heat conduction in a three-dimensional solid subject to a distributed internal heat source produces the following equation characterizing the steady state  

Its cylindrical nature means that cylindrical coordinates are the most convenient for analysing heat conduction in the fuel pin. A formal statement of equation (A8.4) 

Integrating equation (A8.6) with respect to radial distance, r, gives  

Physically, we know that the maximum temperature will occur at the centre of the pin, i.e. at r = 0, implying (dr,/dr)(0) = 0. Substituting these conditions into equation (A8.7) shows that the constant of integration must be zero. Hence 

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