Question

Hollow spherical iron container with outer diameter 20 cm and thickness 0.4 cm is filled with iced water at 0C. If the outer surface temperature is 5"C, determine the approxi- mate rate of heat loss from the sphere, in kW, and the rate at which ice melts in the container. The heat from fusion of water is 333.7 kJ/kg

Answer 1

The answer is below

Step-by-step explanation:

Outer diameter = Do = 20 cm = 0.2 m

Thickness = L = 0.4 cm = 0.004 m

Diameter = D =outer diameter - thickness = 0.2 - 0.004 = 0.196 m

Area = πD² = π × (0.196)² = 0.1207 m²

The thermal conductivity of iron (k) is given as 80.2 W/m.K

The heat transfer rate is given as:

ΔT = 5°C - 0°C = 5°C

h = 333.7 kJ/kg = 333.7 * 10³ J/kg

`\dot{Q}=kA(\Delta T)/(L)=80.2*0.1207*(5)/(0.004) =12100=12.1\ kW`

The rate at which the ice melts is given as:

`\dot{m}_(melt)=\frac{\dot{Q}}{h} =(12100)/(333.7*10^3)=0.036\ kg/s`