4). Consider the rectangular slab (semi-infinite in the x-direction) depicted below. The surface at x=0 and y=b are maintained at a temperature T. There is a source of energy/volume S in the slab that heats things up. a. Write down the differential equation and boundary conditions that govern this problem and render them dimensionless. b. We are only interested in the asymptotic solution at long times here, so you can throw out the transient term! Solve for this steady state solution when you are far from the end x=0 (e.g., it will just be a function of y, and should be very familiar!). c. Now for the harder part. Subtracting off the solution you obtained in part b, solve for the temperature distribution as a function of x and y using the same sort of separation of variables solution you did in the last homework (there will be different constants, though, which you will need to obtain - Wolfram alpha works well there!). Don't forget to add the large x solution back in! d. Plot up the depth ( y-direction) average temperature as a function of x