A metal rod, originally at $350\backslash$deg C and measuring $8$ mm in diameter and $1$ m in length, is suddenly immersed in oil at $100\backslash$deg C$.$ The convective heat transfer coefficient between the rod and oil is $225$ W$/$m$\text{'}$K$.$ Verify the applicability of the lumped capacity analysis. If the lumped capacity analysis is applicable:Determine the time required, using this method, for the rod to cool to $200\backslash$deg C$.$If the lumped capacity analysis is not applicable: Specify the alternative method you would employ.Take the properties of the metal rod as : Density $($p$)$: $8000$ kg$/$m$\text{'},$ Specific heat capacity $($Cp$)$: $460$ J$/$kgK$,$ Thermal conductivity $($k$)$: $70$ W$/$mK