Answer:3.879 kJ
Explanation:
Given
Cross-section of duct [tex]A=40\times 200=8000 mm^2[/tex]
i.e. characteristic diameter[tex]=\frac{4A}{P}=\frac{4\times 8000}{2(200+40)}=66.66 mm[/tex]
[tex]k=0.035 W/m-K[/tex]
Temperature of Hot gases [tex]T_{\infty }=120^{\circ}C[/tex]
Length of Duct [tex]L=4 m[/tex]
Surface Temperature of duct [tex]T_s=20^{\circ}C[/tex]
Nusselt Number [tex]Nu=89[/tex]
[tex]Nu=89=\frac{hD}{k}[/tex]
[tex]89=\frac{h\times 66.66\times 10^{-3}}{0.035}[/tex]
[tex]h=46.77 W/m^2-K[/tex]
[tex]Q=hA\Delta T[/tex]
[tex]Q=46.77\times \pi d\cdot L\cdot \Delta T[/tex]
[tex]Q=46.77\times \pi \times 0.066\times 4\times (120-20) [/tex]
[tex]Q=3.879 kJ[/tex]
