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**1. Homework Statement**

The elements of a boiling water nuclear reactor consist of long cylindrical rods of uranium dioxide (U02) of diameter 8mm surrounded by a thin layer of aluminium cladding. In the reactor core the elements are cooled by boiling water at 285°C with a heat transfer coefficient of 35kW/m^2K. If heat is generated uniformly within the rod at a rate of 760 MW/m^3, calculate the temperature of the cladding and the maximum temperature within the rod. The mean thermal conductivity of U=2 is 2.3 W/m K

**2. Homework Equations**

first part: model it as a slab with equation Q= h(T*-285) ?

second part : T-T* = (Q/4k)r^2

**3. The Attempt at a Solution**

first part: I just assumed that one can model the situation at the wall as a slab with very thin walls and using the equation above with the values of

h= 35kW/m^2K

and

Q=760 MW/m^3*2*pi*0.004 = 19.1 MW/m^3

does not give the required solution of 328°C. I don't really see what exactly is wrong with this calculation and would therefore appreciate if anyone could give me a hint.

second part: completely fine

thanks a lot