4.6. consider the standard equilibrium heat equation for the temperature of a bar with no source ut = 0 = uxx on x 2 [0; 1]. at x = 0 the flux into the bar fixed f(0) = a, and the x = 1 boundary condition is mixed ktu(l) = kcu0(l). assume kc = 1. show all of your work to calculate the following. (a) solve for the particular solution. (b) using the above, determine the maximum temperature of the bar and describe its relationship to a and kt . (c) determine f(l) a determine dependence on a and kt . (d) explain in physical terms what happens to the boundary flux if limkt! 0+ u(x) =? , and limkt! ¥ u(x) =?