A die-cast component has a mass of 1.2 kg and density 7150 kg/m3with surface area of 0.075 m2. The thermal conductivity of the material is 95 W/mK and the specific heat is 385 J/kgK. It comes out of the machine at 345°C and is exposed to air at 20°C with a convective heat transfer coefficient of 56.8 W/m2K.
Determine (i) The temperature of the part after 5 minutes (ii) The time required to reach 50°C (iii) The time constant (iv) The value of convective heat transfer coefficient up-to which the lumped parameter model can be used (v) The volume/area ratio up-to which the lumped parameter model can be used.