Q$7.$ A rectangular region of $)xa,0y(b$ is initially at $0$ K $.$ For times $t>0,$ the boundaries at $x=0$ and $y=0$ are kept insulated, and the boundaries at $x=$a and $y=b$ are kept at $0$ K $,$ while heat is generated in this region at a rate of $g(t)$ per unit volume. Obtain an expression for the temperature distribution in this region using Duhamel's theorem.