Air at 27°C and 1 atm flows over a flat plate at velocity of 2 m/s. Assume that the plate is heated over its entire lenght to a temperature of 60°C. Calculate the heat transferred in (a) the first 20 cm of the plate and (b) the first 40 cm of the plate.
Using the properties of air 48.5 °C
(a) Assuming unit Width in Z direction
\[Re_{x}=\frac{u_{\infty}x}{v}=\frac{3\times0.25}{17.36\times10^{-6}} = 43200\]
\[Nu_{x} = 0.332\left ( Re_{x} \right )^{0.5}\left ( Pr \right )^{1/3}=0.332\left ( 43200 \right )^{0.5}\left ( 0.7 \right )^{1/3}=61.4\]
\[h_{x}=\frac{Nu_{x}\, k}{x} = \frac{61.4\times0.02749}{0.25}=6.75\,W/m^{2}K\]
\[\bar{h} = 2h_{x}=2\times6.75=13.5\,W/m^{2}K\]
\[z = 1\,m, Q_{25\,cm} = \bar{h}A\left ( T_{w} – T_{\infty} \right )=13.5\left ( 0.25\times 1 \right )\left ( 70-27 \right )=145.1\,W\]
(b) Assuming unit width in z direction
\[Re_{x}=\frac{u_{\infty}x}{v}=\frac{3\times0.45}{17.36\times10^{-6}} = 77765\]
\[Nu_{x} = 0.332\left ( Re_{x} \right )^{0.5}\left ( Pr \right )^{1/3}=0.332\left ( 77765 \right )^{0.5}\left ( 0.7 \right )^{1/3}=82.4\]
\[h_{x}=\frac{Nu_{x}\, k}{x} = \frac{82.4\times0.02749}{0.45}=5.034\,W/m^{2}K\]
\[\bar{h} = 2h_{x}=2\times 5.034 = 10.07 \,W/m^{2}K\]
\[z = 1\,m, Q_{45\,cm} = \bar{h}A\left ( T_{w} – T_{\infty} \right )=10.07\left ( 0.45\times 1 \right )\left ( 70-27 \right )=194.85\,W\]
