It is given that :
Let the mean bulk temperature [tex]$=\frac{50+100}{2}$[/tex]
[tex]$=75^\circ C$[/tex]
From the property table at 1 bar and [tex]$75^\circ C$[/tex],
[tex]$K=0.02917 \ W/\mu K, \ Pr = 0.71055 $[/tex]
Flow is laminar as Re = 4000 for laminar.
Flow Nusselt Number is given by :
[tex]$\overline{Nu} = 0.664 (Re)^{0.5} Pr^{1/3} = \frac{hd}{K}$[/tex]
[tex]$\theta = 4 \times 0.2 \times 0.1 \times (100-50)$[/tex]
[tex]$=17.32$[/tex]
At 10 bar and [tex]$75^\circ C$[/tex],
[tex]$\rho = 9.999 \ kg/m^3 , \ \mu =20.91 \times 10^{-6}$[/tex]
[tex]$K=30.05 \times 10^{-7} \ W/\mu K, \ Pr = 0.7092, \ C_p=1.019 \ kJ/kg K$[/tex]
[tex]$Re_2 = \frac{9.999 \times 2 \times V}{1 \times 20.9 \times 10^{-6}}$[/tex]
Initial, [tex]$Re_i = \frac{1 \times V}{1 \times 20.82 \times 10^{-6}}$[/tex]
[tex]$=40000$[/tex]
[tex]$V=40000 \times 0.2 \times 20.82 \times 10^{-6}$[/tex]
[tex]$Re_2 = \frac{9.999 \times 2 \times 40000}{1 \times 20.9 \times 10^{-6}}$[/tex]
[tex]$Re_2=796477.01$[/tex]
Flow is turbulent.
This Nusselt number is given by :
[tex]$Nu=(0.037)(Re)^{0.8}- 8\pi Pr^{1/3}=958.75$[/tex]
[tex]$h=\frac{958.75 \times k}{0.2}$[/tex]
[tex]$=144.05 \ W /\mu^2C$[/tex]
[tex]$\theta =144.05 \times 0.2 \times 0.1 \times (100.5)$[/tex]
[tex]$=144.05 \ \omega$[/tex]
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