= 1. A plane wall has a thickness 2L = 2 cm. The thermal conductivity of...

 

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= 1. A plane wall has a thickness 2L = 2 cm. The thermal conductivity of the wall is k 10 W/m. K, and the thermal diffusivity is a = 1 × 10-³m²/s. Initially, the wall is at a uniform temperature T₁ = 200°C. The two sides of the wall are suddenly exposed to a cold ambient flow To = 50°C with a convection coefficient h = 10 W/m²K. We want to analyze the transient conduction process in the wall. a) (5 points) What is the time constant of the system? b) (10 points) How long does it take for the surface temperature to reach 100°C? c) (15 points) For the same initial condition, if the convection coefficient increases to h = 300 W/m²K, how long does it take for the midplane temperature to reach 100°C? = 1. A plane wall has a thickness 2L = 2 cm. The thermal conductivity of the wall is k 10 W/m. K, and the thermal diffusivity is a = 1 × 10-³m²/s. Initially, the wall is at a uniform temperature T₁ = 200°C. The two sides of the wall are suddenly exposed to a cold ambient flow To = 50°C with a convection coefficient h = 10 W/m²K. We want to analyze the transient conduction process in the wall. a) (5 points) What is the time constant of the system? b) (10 points) How long does it take for the surface temperature to reach 100°C? c) (15 points) For the same initial condition, if the convection coefficient increases to h = 300 W/m²K, how long does it take for the midplane temperature to reach 100°C?