Part II Choose one problem to answer. Problem 1 Unsteady state heat conduction (35 points) Consider unsteady state heat conduction in (a) a plane wall (wall thickness = 2L), (b) a long square bar (dimensions: 2L2L), and (c) a cube (dimensions: 2L* 24 * 2L) initially at T;= 50C is subjected to heating by hot air at 500C. You need to estimate the temperatures at three different locations: center (T.), half way from all surfaces (T), and surface of the wall or corner of the square bar or cube (T2) at time + = 10 minutes if L = 0.1 m, p= 1000 kg/m', C = 3000 J/kg.K, and k = 50 W/m.K. The convection coefficient of the air is h = 100 W/mK. a) Find T. = T(0), 7) = T(0.05) and T2 = T(0.1) for the plane wall using an appropriate method [Note: Use Heisler charts in the attachment to find these temperatures.] (12 points) b) Find T. = T(0,0), TI = T(0.05, 0.05) and T2 - T(0.1, 0.1) for the long square bar using an appropriate method. (10 points) c) Find T. - T(0,0,0), 7) = T(0.05, 0.05, 0.05) and T, - T(0.1, 0.1, 0.1) for the cube using an appropriate method. (6 points) d) Use the following lumped capacitance equation to estimate the average temperature (Towe) in the plain wall, square bar, and cube, and compare them with the ones found in part a, b and c. 6 points) T-TOO = e-BiFo where: Bi = hle at Fo T: - TO k 22