The temperature distribution across a wall $0\mathrm{.}3$ m thick at a certain instant of time is $T(x)=a+bx+c{x}^2,$ where $T$ is in degrees

Celsius and $x$ is in meters, $a=200C,b=-200\frac{C}{m},$ and $c=30\frac{C}{m^2}.$ The wall has a thermal conductivity of $1\frac{W}{m}*K.$

$($a$)$ On a unit surface area basis, determine the rate of heat transfer into and out of the wall and the rate of change of energy stored by

the wall assuming that volumetric heat generation does not occur.

$($b$)$ If the cold surface is exposed to a fluid at $100C,$ what is the convection coefficient?

The rate of heat transfer into wall, in $\frac{W}{m^2}$ :

$q_{in}^{\text{'}\text{'}}=$

$\frac{W}{m^2}$

The rate of heat transfer out of wall, in $\frac{W}{m^2}$ :

$q_{\text{o}\text{u}\text{t}}^{\text{'}\text{'}}=$

$\frac{W}{m^2}$

The rate of change of energy stored by the wall, in $\frac{W}{m^2}$ :

$E^{\text{'}\text{'}st}=$

$\frac{W}{m^2}$

The convection coefficient, in $\frac{W}{m^2}*K$ :

$h=,\frac{W}{m^2}*K$

Physical Properties Mathematical Functions