helpFigure $1$: Cross section of pipe.

The temperature distribution in the wall of a pipe through which a hot liquid is flowing is

given by the ODE,

$\frac{d^{2}T}{d{r}^2}+\frac{1}{r}\frac{dT}{dr}=0$

Figure $1$ shows a cross$-$section of the pipe with $r_i$ is the inner radius, $r_o$ is the outer radius, $r$ is

the radial distance, $T_i$ is the inner temperature, and $T_o$ is the outside temperature;

a$)$ Find the radial temperature distribution in the cylinder using numerical method, with

inner radius of $0\mathrm{.}12m$ and outer radius of $0\mathrm{.}2m,$ when the inner and outer surfaces are

maintained at $100C$ and $27C$ respectively. Use $dr=0\mathrm{.}02m.$

b$)$ If the analytical solution is given as:

$T=C_{1}lnr+C_2$

Where $C_1$ and $C_2$ are constant unknowns. Find the analytical solution for the

temperature distribution.

c$)$ Find the relative error between the analytical and numerical method.