Quench hardening is a mechanical process in which the ferrous metals or alloys are first heated and then quickly cooled down to improve their physical properties and avoid phase transformation. Consider a 40 cm × 20 cm block of copper alloy (k = 120 W/m · K, α = 3.91 × 10^-6 m²/s) being heated uniformly until it reaches a temperature of 800°C. It is then suddenly immersed into the water bath maintained at 15°C with h = 100 W/m² · K for quenching process. However, the upper surface of the metal is not submerged in the water and is exposed to air at 15°C with a convective heat transfer coefficient of 10 W/m² · K. Using an explicit finite difference formulation, calculate the temperature distribution in the copper alloy block after 10 min have elapsed using Δt = 10 s and a uniform mesh size of Δx = Δy = 10 cm.

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4 hair = 10 W/m.K 2 3 5 8 6 7 Copper alloy immersed in water for quenching 9 T% = 15C hwater = 100 W/m.K T% = 15C