A pin fin is used as part of a thermal management system for a power electronics system, as shown in the figure. The tip of the fin can be assumed to be adiabatic. The power electronics system operates at steady state and applies a constant heat transfer rate of q = 50 W to the base of the fin. The fin is initially at T_inf. a) Develop a 1-D explicit transient model to analyze the startup and operating behavior of the pin fin. b) Plot the temperature as a function of time for several instances from t =0 to steady state.

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D-3 mm- k 10 W/m-K1 o = 4000 kg/m³ c=400 J/kg-K h=50 W/m²-K T = 20°C L = 3 cm D-3 mm- k 10 W/m-K1 o = 4000 kg/m³ c=400 J/kg-K h=50 W/m²-K T = 20°C L = 3 cm