A two-dimensional rectangular plate is subjected to fixed temperature boundary conditions shown below. y (m) [ 12 = 150C 1 T = 50C -T2 = 50C x (m) 2 T1 = 50C a) Use the results of the exact solution for the heat equation for these boundary conditions to calculate the temperature at the midpoint (1 m, 0.5 m) by considering the first five terms of the infinite series. b) Assess the error from using only the first three terms of the infinite series. c) If the thermal conductivity of the plate is 50 W/m-K, derive an expression for the heat transfer rate per unit thickness to the plate along the upper surface (0