b) A steel cylinder of 150 mm in length and 60 mm in diameter is placed horizontally inside
a room that maintains its temperature and pressure of 30 °C and 1 atm respectively. If
the surface temperature of the steel cylinder is 70 °C, estimate the heat transfer rate from
the steel cylinder due to natural convection. Neglect the heat transfer from the ends of
the cylinder.
[CO2/PO2/WP1/WP3/WP4/WK3/WK4] (12 marks)
Nusselt number for horizontal cylinder in free convection:
$$Nu = \left\{0.60 + \frac{0.387 Ra^{1/6}}{\left[1+ \left(\frac{0.559}{Pr}\right)^{9/16}\right]^{8/27}}\right\}^2$$
Table Q3: Properties of Air at 1 atm
| Temperature [°C] | Density $\rho$ [kg/m³] | Thermal conductivity $w$/(m.°c)] | Dynamic viscosity $\mu$ [kg/(m.s)] | Kinematic viscosity $\nu$ [m²/s] | Prandtl number Pr |
|---|---|---|---|---|---|
| 30 | 1.164 | 0.02630 | 1.850×10⁻⁵ | 1.589×10⁻⁵ | 0.7070 |
| 50 | 1.092 | 0.02735 | 1.963×10⁻⁵ | 1.798×10⁻⁵ | 0.7228 |
| 70 | 1.028 | 0.02881 | 2.052×10⁻⁵ | 1.995×10⁻⁵ | 0.7177 |