Test Academy | A very large metal plate of thickness 𝑑 and thermal conductivity 𝑘 is cooled by a stream of air at temperature 𝑇 ∞ = 300 K with a heat transfer coefficient ℎ, as shown in the figure. The centerline temperature of the plate is T P . In which of the following case(s) can the lumped parameter model be used to study the heat transfer in the metal plate? ℎ = 10 Wm-2K -1 , k = 100 Wm-1K -1 , 𝑑 = 1 mm, TP = 350 K, ℎ = 100 Wm-2K -1 , k = 100 Wm-1K -1 , 𝑑 = 1 mm, TP = 325 K, ℎ = 100 Wm-2K -1 , k = 1000 Wm-1K -1 , 𝑑 = 1 mm, TP = 325 K, ℎ = 1000 Wm-2K -1 , k = 1 Wm-1K -1 , 𝑑 = 1 m, TP = 350 K

Question

A very large metal plate of thickness 𝑑 and thermal conductivity 𝑘 is cooled by a stream of air at temperature 𝑇_∞ = 300 K with a heat transfer coefficient ℎ, as shown in the figure. The centerline temperature of the plate is T_P. In which of the following case(s) can the lumped parameter model be used to study the heat transfer in the metal plate?

Options :

ℎ = 10 Wm^-2K ^-1 , k = 100 Wm^-1K ^-1, 𝑑 = 1 mm, T_P = 350 K
ℎ = 100 Wm^-2K ^-1 , k = 100 Wm^-1K ^-1, 𝑑 = 1 mm, T_P = 325 K
ℎ = 100 Wm^-2K ^-1 , k = 1000 Wm^-1K ^-1, 𝑑 = 1 mm, T_P = 325 K
ℎ = 1000 Wm^-2K ^-1 , k = 1 Wm^-1K ^-1, 𝑑 = 1 m, T_P = 350 K

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