Problem $2(5$ points$)$: A solid cylinder of unit length, radius $r_0=100mm,k_s=20\frac{W}{m}-K$ is surrounded by an insulating shell of unit length, radius

$r_{\text{I}}=200mm,k_{\text{I}}=5\frac{W}{m}-K.$ The solid cylinder has $q_g^{}=+{10}^4\frac{W}{m^3}.$ Ambient air around the insulating shell is at $T_{}=25C,h=1000\frac{W}{m^2}-K.$

Draw a schematic of the problem, label all the radii and parameters. The insulating shell has $q_g^{}=0.$

For the solid cylinder, with $T(r)=\frac{-q_g^{}{r}^2}{4k}+c_{1}logr+c_2,$ determine the value of $c_1$ as well as heat transfer rate $q(r_0)$ at $r=r_0$

Using thermal resistance networks, determine temperature at $r=r_0$ and $r=r_0,$ respectively. Then, determine $c_2$ from part $(2)$

Sketch the temperature and heat flux profiles as a function of radius $r.$ Obtain$/$show proper concavity, label nature of curvesProblem $2(5$ points$)$: A solid cylinder of unit length, radius $0=100$ mm$,=20$ W$/$m$-$K is surrounded by an insulating shell of unit length, radius

$=200$ mm$,=5$ W$/$m$-$K$.$ The solid cylinder has $$

$=+104$ W$/$m$3.$ Ambient air around the insulating shell is at $\backslash$infty $=25$ oC$,=1000$ W$/$m$2-$K$.$

$1.$ Draw a schematic of the problem, label all the radii and parameters. The insulating shell has $$

$=0.$

$2.$ For the solid cylinder, with $()=$

$2$

$4+1$ log $+2,$ determine the value of $1$ as well as heat transfer rate $(0)$ at $=0$

$3.$ Using thermal resistance networks, determine temperature at $=0$ and $=0,$ respectively. Then, determine $2$ from part $(2)$

$4.$ Sketch the temperature and heat flux profiles as a function of radius $.$ Obtain$/$show proper concavity, label nature of curves