A long post of circular cross section having a total lengthof $=2$ and diameter d$=10$ mm is placed outside at night as shown in the schematic. Aportion of the post $(0$ x Lgen$)$ is perfectly insulated and experiences uniform heat generation,$=30/3.$ The post loses heat by convection and radiation, as shown. The post has anemissivity $=0\mathrm{.}5.$ The convective heat transfer coefficient is $=10/2$ and it is $300$ Koutside $($i$.$e$.,==300).$HW$1\mathrm{.}3($a$)$: Calculate the flux of heat moving along the axis of the post $($from bottom to top$)$ aty$=$Lgen by calculating in units of $/2.$HW$1\mathrm{.}3($b$)$: The temperature of the post can be approximated to be a constant of $=305.$Using this approximation, calculate the ratio of heat dissipated by the rod from radiation versusthat by convection.HW$1\mathrm{.}3($c$)$: Do you think the approximation of a constant post temperature in part $($b$)$ to bereasonable? Justify your answer in $1-3$ sentences.