The above image represents steady$-$state conduction through a plane wall with

energy generation. You know that the thermal conductivity of the wall is k$=86$

$($W$)/($m$-$K$)$ and the value of g$^()$ is $425000($W$)/($m$^(3)).$ The spacing between the nodes

is $0\mathrm{.}030$ m and the heat transfer equation governing the internal nodes is

$($d$^(2)$T$)/($dx$^(2))+(($g$^()))/($k$)=0$

If you are given that T$1=824$K and T$2=793$K$,$ determine the temperature at node

$7($in K$)$ using finite difference methods. Be sure to carry plenty of decimals as your

answer must fall within a $0\mathrm{.}5\%$ tolerance.