Before ironing, an iron needs to be
warmed up to a certain temperature. The iron temperature is different
for different fabric. The resistance wires are used to generate the energy
needed to
warm the iron up.

Known:

The power of the iron is =
100 W and 85% of the heat generated in the resistance wires is
transferred to the iron base plate

The materials of the base plate is aluminum alloy
2024-76 (ρ = 2770 kg/m^{3} and
c_{p}=
875 J/(kg-^{o}C)) and the base plate thickness δ =
0.5 cm, and the area is A = 0.02 m^{2}

Initially the iron is in equilibrium with the ambient air at
T_{initial} = 20 ^{o}C

The convection heat transfer coefficient h = 35 W/(m^{2}-^{o}C)

The emissivity of the base plate to the ambient ε = 0.6

Questions

Determine the minimum time needed for the base plate
temperature to reach T_{final} = 140^{ o}C.

After the temperature reaches
140^{ o}C,
how much energy is needed to keep the base at 140^{ o}C?

Approach

Energy Balance Diagram

The heat needed to increase the base plate's temperature
from T_{inital} to T_{final} is:

Q = c_{p} m (T_{final} - T_{initial})

where
m = mass of the base
c_{p} = specific heat

The energy balance of the base plate (Energy balance
will be introduced in the following section):

Energy in: 85% of the heat generated by the wires.

Energy out: convection, radiation heat loss to the ambient air.

Energy storage: the energy in the base to increase the base's temperature.