$Nu_{D}=0.26 \times (6.14 \times 10^{6})^{0.6} \times (7.56)^{0.35}=2152.5$
Solution:
The heat transfer due to radiation is given by: $Nu_{D}=0
$\dot{Q}=10 \times \pi \times 0.004 \times 2 \times (80-20)=8.377W$ $Nu_{D}=0
$\dot{Q}_{rad}=1 \times 5.67 \times 10^{-8} \times 1.5 \times (305^{4}-293^{4})=41.9W$ $Nu_{D}=0
$\dot{Q}_{conv}=150-41.9-0=108.1W$