$(2).$ A plate which generates heat at a volumetric rate $q^{}{?}^{\text{'}\text{'}\text{'}}$ is placed

inside a tube and cooled by convection. The width of the plate is $w$ and its

thickness is $.$ The heat transfer coefficient is $h$ and coolant temperature

is $T_{}.$ The temperature at the interface between the tube and the plate is

$T_w.$ Because of concern that the temperature at the center may exceed

design limit$,$ you are asked to estimate the steady state center

temperature of the plate by using simplified fin approach. The following

data are given: $h=62,\frac{W}{m^2}C,W=3cm,=2\mathrm{.}5mm,T_W=110C,T_{}=94$

$C,q^{}{?}^{\text{'}\text{'}\text{'}}=2\mathrm{.}5{10}^7\frac{W}{m^3},K=18\frac{W}{m}C$