Question $2.($a$)$ Certain lithium ion batteries $18$ mm in diameter and $65$ mm tall while being charged are found to have a surface temperature $25$ degrees higher than the surrounding air. Assuming an average convection coefficient of $\backslash (2\mathrm{.}5\backslash$mathrm$\{$~W$\}\backslash$cdot $\backslash$mathrm$\{$~m$\}^\{-2\}\backslash$cdot $\backslash$mathrm$\{$~K$\}^\{-1\}\backslash )$ and neglecting radiation, estimate the volumetric heat generation rate inside these batteries. $($b$)$ If the two ends of these batteries are nearly insulated, sketch the temperature distribution inside these batteries as a function of radial distance from their center$-$line. On the same graph indicate the surrounding air temperature. Note any special features on the T$-$r graph.