Respuesta :
Answer:
Re=100,000⇒Q=275.25 [tex]\frac{W}{m^2}[/tex]
Re=500,000⇒Q=1,757.77[tex]\frac{W}{m^2}[/tex]
Re=1,000,000⇒Q=3060.36 [tex]\frac{W}{m^2}[/tex]
Explanation:
Given:
For air [tex]T_∞[/tex]=25°C ,V=8 m/s
For surface [tex]T_s[/tex]=179°C
L=2.75 m ,b=3 m
We know that for flat plate
[tex]Re<30\times10^5[/tex]⇒Laminar flow
[tex]Re>30\times10^5[/tex]⇒Turbulent flow
Take Re=100,000:
So this is case of laminar flow
[tex]Nu=0.664Re^{\frac{1}{2}}Pr^{\frac{1}{3}}[/tex]
From standard air property table at 25°C
Pr= is 0.71 ,K=26.24[tex]\times 10^{-3}[/tex]
So [tex]Nu=0.664\times 100,000^{\frac{1}{2}}\times 0.71^{\frac{1}{3}}[/tex]
Nu=187.32 ([tex]\dfrac{hL}{K_{air}}[/tex])
187.32=[tex]\dfrac{h\times2.75}{26.24\times 10^{-3}}[/tex]
⇒h=1.78[tex]\frac{W}{m^2-K}[/tex]
heat transfer rate =h[tex](T_∞-T_s)[/tex]
=275.25 [tex]\frac{W}{m^2}[/tex]
Take Re=500,000:
So this is case of turbulent flow
[tex]Nu=0.037Re^{\frac{4}{5}}Pr^{\frac{1}{3}}[/tex]
[tex]Nu=0.037\times 500,000^{\frac{4}{5}}\times 0.71^{\frac{1}{3}}[/tex]
Nu=1196.18 ⇒h=11.14 [tex]\frac{W}{m^2-K}[/tex]
heat transfer rate =h[tex](T_∞-T_s)[/tex]
=11.14(179-25)
= 1,757.77[tex]\frac{W}{m^2}[/tex]
Take Re=1,000,000:
So this is case of turbulent flow
[tex]Nu=0.037Re^{\frac{4}{5}}Pr^{\frac{1}{3}}[/tex]
[tex]Nu=0.037\times 1,000,000^{\frac{4}{5}}\times 0.71^{\frac{1}{3}}[/tex]
Nu=2082.6 ⇒h=19.87 [tex]\frac{W}{m^2-K}[/tex]
heat transfer rate =h[tex](T_∞-T_s)[/tex]
=19.87(179-25)
= 3060.36 [tex]\frac{W}{m^2}[/tex]
