A Pressurized Water Reactor fuel rod is $12ft$ long and $0\mathrm{.}374$ inches in diameter $($outer$)$ on a $0\mathrm{.}496$ inch square pitch. The fuel pellet diameter is $0\mathrm{.}3225$ inches. The fuel rod gap is constant with a width of $0\mathrm{.}0065$ inches. The system pressure is $2250$ psia and can be assumed to be constant. The coolant at the inlet is at $557F$ with an injection mass flow rate of $2475lb\frac{m}{h}r.$ The average linear heat rate is $8\mathrm{.}5k\frac{W}{f}t.$ The peak to average power ratio is given as $1\mathrm{.}37$ for a sine power shape. Assume no extrapolation distance, a constant gap heat transfer coefficient of $1000BT\frac{U}{h}{r}_r-f{t}^2-F,$ and a constant convective heat transfer coefficient of $7000BT\frac{U}{h}{r}_{-}f{t}^2-F.$ Also assume constant fluid properties given as:

$=46\mathrm{.}39\frac{lbm}{f{t}^3},c_p=1\mathrm{.}261\frac{\text{B}\text{T}\text{U}}{lbm-F},k=0\mathrm{.}334\frac{\text{B}\text{T}\text{U}}{hr-ft-F},=0\mathrm{.}222\frac{lbm}{ft-hr}$

The fuel thermal conductivity is constant at $1\mathrm{.}2BT\frac{U}{h}r-ft-F$ and the cladding thermal conductivity is $10\mathrm{.}5$ BTU$/$hr$-$ft$-$F$.$

Calculate and plot the axial distributions for the coolant, outer cladding, inner cladding, pellet surface, and pellet centerline temperatures.$(5$ points$)$