Problem 2 Unsteady state heat conduction in a cube (35 points) Consider unsteady state heat conduction in a cube (dimensions: 2L 2L * 2L) with L = 0.1 m, p = 1000 kg/m', Cp = 3000 J/kg-K, and k = 50 W/mK initially at Ti = 400C is subjected to cooling by air at T = 25C with the convection coefficient of h = 200 W/mK. We are interested to find temperatures T(x, y, z) in the cube and the total amount of heat Q transferred to the surrounding air at time 1. a) Estimate the temperatures at the center To = T(0,0,0), half way from all surfaces T1 = T(0.5L, 0.5L, 0.5L), and the corner of the cube T2 = T(L, L, L) at time 1 = 10 minutes using Heisler charts. (20 points) b) Use the lumped capacitance method to estimate the average temperature (Tave) in the cube at = 10 minutes and the total amount of heat Q transferred from the cube to the surrounding air in the first 10 minutes. (10 points) c) Discuss if the estimated Q in part b is accurate or not. If not, why and how can you better estimate it? (5 points)