1. In a heavy rainy day, water accumulated in the roof of a room, and diffused through the room ceiling that has width "L" and thickness "t". You can consider the diffusion to take place in two dimensions as shown in the figure. Luckily, the bottom side of the wall is painted with a material that continuously and completely absorbs the water and drains it (green line in the figure) so that there is a continuous source and sink for the water in the ceiling. The saturation concentration of water in the ceiling material is cA. The sides of the ceiling are painted with water impermeable paint (red lines in the figure). Consider the water to be 100% pure with no other component diffusing. Based on the discussion above, answer the following questions: a. State at least 5 valid assumptions. b. Develop and simplify the differential equation that represents that concentration distribution of water in the ceiling material. c. State all necessary boundary and initial conditions. d. Sketch the flux lines that you expect (without any mathematical solution, just what you expect based on your understanding)