Question

# 1. Heat is flowing steadily in a metal plate whose shape is an infinite rectangle occupying the-a 0 of the (r, y) plane. The temperature at the point

(z,y) is denoted by u(x, y). The sides z = ta are insulated, the temperature approaches zero as yoo, while the side y = 0 is maintained at a fixed temperature -T for a 0). Coefficients A, B, C and D (D is a trigonometric expression) have to be calculated and highlighted in your assignment. Full marks are awarded for a complete step by step proof. iii. Take 7 the temperature from part a) to be equal to the last two figures of your student Monash ID number (if ID XXXXXX31, take T-31; ID XXXXXX09, take T-9; ID XXXXX1100, take T=10). And take a = 1. In MATLAB, on the same graph plot the partial sum up to the 50th harmonic of u(x,y) for 10 relevant values y = 0,0.01, 0.02, and continuing with any y of your own choice. Label and ADD a legend to the graph and publish the graph of your solution, and attach it to the assignment. iii. For what value y does the temperature drop to 10% of the initial temperature for 0 <