(Solved): Consider a rectangular aluminium slab subjected to boundary conditions such that heat diffuses in x ...

Consider a rectangular aluminium slab subjected to boundary conditions such that heat diffuses in $x?y$ plane surface, as shown below. Answer the following; (a) Write the steady-state governing equation for heat conduction (diffusion) and list the assumptions involved. (b) Write the equivalent finite-difference equation and determine the temperatures at the internal nodal (grid) points. (c) Determine the average heat flux across each surface. Take, thermal conductivity of aluminium as $190\mathrm{W}/{\mathrm{m}}^2?\mathrm{K}$. Consider the unsteady heat conduction behavior of the above problem, and answer the following; (a) Write the governing differential equation. (b) Use appropriate CFL criterion and compute the time-step size for explicit finitedifference calculations. (c) Use MacCormack technique and determine the temperatures at internal grids for the first 2 time-steps. (Note: all the steps must be written in the calculations)