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The rate of heat transfer from the entire plate is 710.8 kW
The properties of mercury at the film temperature of (75+25)/2= 50°C
k = 8.83632 W/m °C
v = 1.056 × [tex]10^-^7[/tex] m²/s
Pr = 0.0223
The local Nusselt number relation for liquid metals is given by
[tex]N_u =\frac{h_sx}{k} = 0.565 9Re_x Pr)^\frac{1}{2}[/tex]
The average heat transfer coefficient for the entire surface can be determined from
[tex]h = \frac{1}{L} \int\limits^1_0 {h_x} \, dx[/tex]
Substituting the local Nusselt number relation into the above equation and performing the integration we obtain
[tex]N_u = 1.13 (Re_s Pr)^\frac{1}{2}[/tex]
The Reynolds number is
[tex]Re_L = \frac{VL}{v} = \frac{(0.01)(3m)}{1.056 * 10^-^7 m^2/s} = 0.028 * 10^7[/tex]
Using the relation for the Nusselt number, the average heat transfer coefficient and the heat transfer rate are determined to be
Q = 710.8 kW
Therefore, the rate of heat transfer from the entire plate is 710.8 kW
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