Answer:
Here is the correct solution:
The surface area of the sphere is:
A = 4 * pi * r^2
= 4 * pi * (0.12 m/2)^2
= 0.04524 m^2
The surface temperature of the sphere is 110°C, and the surrounding temperature is 20°C. Therefore, the temperature difference is:
ΔT = T_s - T_inf
= 110°C - 20°C
= 90°C
The heat transfer rate due to convection is given by Newton's law of cooling:
Q_conv = h * A * ΔT
Substituting the given values, we get:
Q_conv = 15 W/m^2·°C * 0.04524 m^2 * 90°C
= 60.92 W
The heat transfer rate due to radiation is given by the Stefan-Boltzmann law:
Q_rad = ε * σ * A * (T_s^4 - T_inf^4)
Substituting the given values, we get:
Q_rad = 0.6 * 5.67e-8 W/m^2·K^4 * 0.04524 m^2 * ((110 + 273.15) K)^4 - ((20 + 273.15) K)^4)
= 25.35 W
The total heat transfer rate is the sum of the heat transfer rates due to convection and radiation:
Q_total = Q_conv + Q_rad
= 60.92 W + 25.35 W
= 86.27 W
Therefore, the total rate of heat transfer from the sphere is 86.27 W.
Step-by-step explanation:
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