Consider a solid block extending from y = 0 to y = L in the y coordinate, and from x = 0 to x in the x co-ordinate, as shown in the figure 4. The top and bottom faces at y = 0 and y = L are at temperature T0, face at x = 0 is at temperature T1. Obtain the temperature profile of the block at steady state as follows. (a) Which coordinate system would you choose for analysing the problem? Write down the conservation equation for the temperature field at steady state for this system. (b) Transform the temperature to a new coordinate in such a way that satisfies the same governing equations, but there is a homogeneous boundary condition in all directions except one. Figure: Conduction into a semi-infinite slab.

(c) Use separation of variables to solve for the temperature field. Determine the constants in the solution for the temperature.

(d) What is the total heat transfer at the surface at temperature T1?