A rectangular rod $(3$ cm by $5$ cm $)$ is exposed to hot combustion gases on its top and bottom

surfaces. On the left and right sides $($including the corners$),$ it is clamped by constant

temperature blocks at $T_{\text{u}\text{n}\text{i}\text{f}\text{o}\text{r}\text{m}}=200C.$ The combustion gases are very hot at $T_{,o}=1400C$ and

produce a convection coefficient, $h_{\text{g}\text{a}\text{s}}$ of $400\frac{W}{m^2}-K.$ The rod is made of a stainless steel alloy

with $k=15\frac{W}{m}-K.$ To avoid potential degradation of the rod material, a $1-$ cm square channel

runs through the center of the rod. Air at $T_{,i}=50C$ and $h_{\text{a}\text{i}\text{r}}=100\frac{W}{m^2}-K$ flows through this

channel in an attempt to cool the rod.

a$)$ Using the finite difference method with $1$ cm node spacing and MATLAB's backslash operator,

solve for the temperature distribution throughout the rod.

b$)$ Plot the temperature distribution using MATLAB's mesh function.

Note: You can complete this whole problem in MATLAB and print it using the Publish feature.