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 :

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

2. ℎ = 100 Wm^-2K ^-1 , k = 100 Wm^-1K ^-1 , 𝑑 = 1 mm, T_P = 325 K

3. ℎ = 100 Wm^-2K ^-1 , k = 1000 Wm^-1K ^-1 , 𝑑 = 1 mm, T_P = 325 K

4. ℎ = 1000 Wm^-2K ^-1 , k = 1 Wm^-1K ^-1 , 𝑑 = 1 m, T_P = 350 K