Iron and Iron Board

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/m³ and c_p= 875 J/(kg-^oC)) and the base plate thickness δ = 0.5 cm, and the area is A = 0.02 m²
• Initially the iron is in equilibrium with the ambient air at T_initial = 20^oC
• The convection heat transfer coefficient h = 35 W/(m²-^oC)
• The emissivity of the base plate to the ambient ε = 0.6

1. Determine the minimum time needed for the base plate temperature to reach T_final = 140^o C.
2. After the temperature reaches 140^o C, how much energy is needed to keep the base at 140^o C?
   

1. 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

2. 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.
  
  E_in - E_out = E_storage