Consider a rectangular plate with two-dimensional heat conduction, i.e. T(x,y). Three sides of the plate are maintained at the constant temperature T1, and the upper side has a temperature distribution, in the form of sine-wave, impressed upon it. The differential equation representing the two-dimensional heat transfer in the plate at steadystate is given as dx2d2T+dy2d2T=0 (a) Write the appropriate boundary conditions. Assume that the thermal properties of the plate are constant and same in both directions. (b) Solve the differential equation by using separation of variables method to obtain the steadystate two-dimensional temperature profile on the plate, T(x,y)