(Solved): onsider the heat equation in ab vertical rectangle plate (you may assume that the left edge o ...

onsider the heat equation in $$a\times b$$ vertical rectangle plate (you may assume that the left edge of the atangle is the line $$x=0$$ and the bottom edge is the line $$y=0$$.) (a) Assume that the four edges of the plate are in contact with ice $$\left(0^{?}\mathrm{C}\right)$$, and the initial temperature at each point $$(x,y)$$ of the plate is a function of $$x$$ and $$y$$ (say, $$f(x,y)$$ ). Derive the initial and boundary conditions. (6 Marks) (b) Write down the initial-boundary value problem described above. (6 Marks) (c) Solve the initial-boundary value problem found in part (b). (18 Marks) [30 Marks]