Question

Calculate the heat transfer coefficient for a rate of free convection heat loss from a 30 cm diameter sphere maintained at 100°C and exposed to atmospheric air at 20°C.
The following properties are given:
$\rho =1.06kg/m^3,C_p=1008J/kgK$
$k=\mathrm{0.028.5}W/mK;\mu =20.03\times {10}^{-6}kg/m.s$
$v=18.97\times {10}^{-6}{m}^2/sec;\beta =\frac{1}{333}{K}^{-1}$
Use the following correlation if required: $Nu=0.53(Gr.Pr{)}^{1/4}$

• A. $3.33\frac{W}{m^{2}K}$
• B. $53.2\frac{W}{m^{2}K}$
• C. $2.1\frac{W}{m^{2}K}$
• D. $5.32\frac{W}{m^{2}K}$

Answer 1

The correct option is D $5.32\frac{W}{m^{2}K}$

$Nu=\frac{h.D}{k}=0.53{(\frac{g\beta \Delta T{D}^3}{v^2}\times \frac{\mu C_p}{k})}^{\frac{1}{4}}$

$\frac{h\times 0.3}{0.0285}=0.53{(\frac{9.81\times \frac{1}{333}\times 80\times (0.3{)}^2}{(18.97\times {10}^{-6}{)}^2}\times \frac{20.03\times {10}^{-6}\times 1008}{0.0285})}^{\frac{1}{4}}$

$h=5.32W/m^{2}K$