The following expression represents the heat generation rate within a cylindrical fuel element for a gas-cooled nuclear reactor: q(r) = qo[1 - (r/R)^2](w/m^3).
Where qo denotes a constant term and R shows the radius of the fuel element. Considering the outer surface of the cylindrical element to be a uniform temperature Ts,
1) Construct a mathematical formulation for the thermal conductive process inside the element.
2) Write down the boundary conditions in this situation for solving the governing equation.