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THERMODYNAMICS - CASE STUDY

    Introduction



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 cp= 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 Tinitial = 20 oC
  • The convection heat transfer coefficient h = 35 W/(m2-oC)
  • The emissivity of the base plate to the ambient ε = 0.6
     
    Questions



 
  1. Determine the minimum time needed for the base plate temperature to reach Tfinal = 140 oC.
  2. After the temperature reaches 140 oC, how much energy is needed to keep the base at 140 oC?
    Approach


Energy Balance Diagram

 
  1. The heat needed to increase the base plate's temperature from Tinital to Tfinal is:

    Q = cp m (Tfinal - Tinitial)

    where
    m = mass of the base
    cp = 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.

    Ein - Eout = Estorage