$(15$ points$)$ The steady state temperature distribution across a wall, where $L=1\mathrm{.}0m,is$

$T(x)=a{x}^3+b{x}^2+cx.$ The origin $of$ the $x$ coordinate $isat$ the left side $of$ the image shown below.

Calculate the following:

$a.$ The rate $of$ heat transfer entering the wall $atx=0m,q_{in}$

$b.$ The rate $of$ heat transfer exiting the wall $atx=1m,q_{\text{o}\text{u}\text{t}}$

$c.$ There $isno$ generation $in$ the wall, calculate the stored energy, hat$(E_{ST})$

$(15$ points$)$ The steady state temperature distribution across a wall, where $L=1\mathrm{.}0m,$ is

$T(x)=a{x}^3+b{x}^2+cx.$ The origin of the $x$ coordinate is at the left side of the image shown below.

Calculate the following:

a$.$ The rate of heat transfer entering the wall at $x=0m,q_{in}$

b$.$ The rate of heat transfer exiting the wall at $x=1m,q_{\text{o}\text{u}\text{t}}$

c$.$ There is no generation in the wall, calculate the stored energy, $E_{ST}^{}$

$-55$

$-10$

No cen

$2+2bx+c$