$$ Nu = \left{ 0.6 + \frac{0.387 Ra_D^{1/6}}{[1 + (0.559/Pr)^{9/16}]^{8/27}} \right}^2 $$ 2012 Hollywood Movie Tamil Dubbed Download Isaimini Full Today
The characteristic length $L$ for a vertical plate is its height ($L = 0.2 , \text{m}$). P1flyingringesp Here
Substituting values: $$ Ra_L = \frac{(9.81)(0.003096)(80 - 20)(0.2)^3}{(1.798 \times 10^{-5})^2} (0.7228) $$ $$ Ra_L = \frac{9.81 \times 0.003096 \times 60 \times 0.008}{3.233 \times 10^{-10}} (0.7228) $$ $$ Ra_L \approx 3.27 \times 10^7 $$
$$ Ra_D = \frac{g \beta (T_s - T_\infty) D^3}{\nu^2} Pr $$ $$ Ra_D = \frac{(9.81)(0.00279)(150 - 20)(0.5)^3}{(2.14 \times 10^{-5})^2} (0.705) $$ $$ Ra_D \approx 1.55 \times 10^9 $$
For air, $Pr \approx 0.72$, so the denominator term $[1 + (0.492/Pr)^{9/16}]^{4/9} \approx 1.06$. Simplifying for air (or solving strictly):
Now, solve for $h$: $$ h = \frac{Nu \cdot k}{L} = \frac{48.31 \times 0.02735}{0.2} $$ $$ h \approx 6.61 , \text{W/m}^2 \cdot \text{K} $$
The rate of heat transfer is approximately 39.7 W . Problem 9-2: Horizontal Cylinder Analysis (Sample Problem) Problem Statement: A 2-m-long, 0.5-m-diameter horizontal steam pipe passes through a large room. The surface temperature of the pipe is $150^\circ C$, and the room air temperature is $20^\circ C$. Determine the rate of heat loss from the pipe by natural convection.
Solve for $h$: $$ h = \frac{Nu \cdot k}{D} = \frac{47.75 \times 0.0305}{0.5} $$ $$ h \approx 2.91 , \text{W/m}^2 \cdot \text{K} $$