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