A heat slab with an initial uniform temperature of $T_0$ is considered. It has a length $(x=L)$ and wide $(y=W)$ which is

instantly limited from left and bottom to a constant heat flux of $q^{\text{'}\text{'}}.$ The top edge is insulated while the right

edge is at constant temperature of $T_r.$

Assume that the slab does not have any heat transfer with the environment. Derive the unsteady$-$state

model of temperature distribution for this slab using the information given starting with the shell

balance

State the initial and boundary conditions correctly

$($Remember that this model would have two spatial and one accumulation term$).$

$($If you make a mistake during modelling, the rest of calculations will not be considered in your evaluation$).$

Consider the steady$-$state,

Derive the equivalent algebraic equation of the model.

If i and $j$ are defined from zero up to $m$ and $n,$ respectively, specify $n$ and $m.$

Use direct method and create the matrix of the equations. Then solve the equations in Excel.

Use Liebermann method with relaxation factor of $$ and continue the iterations up to $5$ times, and

calculate the last values of $\%$ for each node. Report the last temperature values of the nodes.