Question $2$

The temperature distribution inside a slab $($with $2m$ length$)$ exposed to an ambient environment

can be represented as:

$k\frac{d^{2}T}{d{z}^2}+Q-\frac{UL}{A}(T-25)=0$

where $k$ is the slab thermal conductivity, $T$ is the slab temperature, $z$ is the axial position, $Q$ is the

heat generated inside the slab, $U$ is the overall heat transfer coefficient, $L$ is the slab length, and $A$

is the slab surface area. For this coursework, assume that $U\frac{L}{A}$ is $0\mathrm{.}3\frac{W}{m^3}K.$ The measurements

show that $T(0)=40C$ and $T(2)=80C.$

The slab thermal conductivity, $k,$ is $0\mathrm{.}1$

a$)$ If the heat generated inside the slab is constant at $Q=30\frac{W}{m^3}K,$ provide an algebraic

expression of temperature versus slab length and using MS Excel, plot the temperature

distribution.

b$)$ A researcher proposes that the heat generated inside the slab should be dependent on the

axial position, where $Q=z^2+2z+1.$ For this case, generate an algebraic expression of

temperature versus slab length and, using MS Excel, plot the temperature distribution.