$5.(15)$ Let's consider a brick wall again, this time in transient mode. The wall is initially at $10$ C $.$ At $\backslash (\backslash$mathrm$\{$t$\}=0\backslash )$ the sun comes up and strikes the wall giving it a constant heat flux of $750\backslash (\backslash$mathrm$\{$W$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash )$ into the wall. The wall is $20$ cm thick. Ignore convection for this problem, and also ignore radiation leaving the wall. This is an approximation we make to simplify the problem.

At what time is the Fo $\backslash (=0\mathrm{.}1\backslash )?$ For times shorter than that we can use the semi$-$infinite approximation.

Plot the wall temperature profile at that time $($T$($x$)$ vs$.$ x$\backslash ()\backslash ).$

What is the surface temperature of the wall at that time? $($note that this calculation ignores the heat losses from the wall, which would lower the temperature$)$