$Nu_{D}=hD/k$
$Nu_{D}=0.26 \times (6.14 \times 10^{6})^{0.6} \times (7.56)^{0.35}=2152.5$
$T_{c}=800+\frac{2000}{4\pi \times 50 \times 0.5}=806.37K$ $Nu_{D}=hD/k$ $Nu_{D}=0
$h=\frac{Nu_{D}k}{D}=\frac{2152.5 \times 0.597}{2}=643.3W/m^{2}K$
lets first try to focus on
$Re_{D}=\frac{\rho V D}{\mu}=\frac{999.1 \times 3.5 \times 2}{1.138 \times 10^{-3}}=6.14 \times 10^{6}$
$\dot{Q}=\frac{423-293}{\frac{1}{2\pi \times 0.1 \times 5}ln(\frac{0.06}{0.04})}=19.1W$ $Nu_{D}=hD/k$ $Nu_{D}=0
$\dot{Q}=h \pi D L(T_{s}-T