You have a $1-$D $($Cartesian coordinates, i$.$e$.$ a $1-$D wall$)$

steady$-$state conduction problem, constant thermal

properties, with energy generation $(q^{}).$ The material is

$4\mathrm{.}0$ cm thick $($i$.$e$.L=0\mathrm{.}040m),$ and has a constant

thermal conductivity of $k=65\mathrm{.}0(\frac{W}{m-K}).$ The temperature

distribution within the object is:

$T(x)=a+b{x}^2$

With: $a=100\mathrm{.}0C$

$b=-1000\mathrm{.}0(\frac{C}{m^2})$

Starting with the Heat Diffusion Equation $($Equation $2\mathrm{.}21$

from our textbook$),$ and using the data given above,

determine the following:

Determine the heat generation rate$(q^{})$ within the

wall.

Determine the heat flux $(q)$ at $x=0$ and at $x=L.$