Problem 2. (70 points) When a thin hot plate out of an oven is suddenly subjected to the surrounding medium (air), heat loss occurs by convection and radiation. The rate of temperature change for the plate is given by the following governing equation: dT dt As [o sp (T4 T^)+h(T-T.)] PVC, SB where As is the plate's surface area, p=300kg/m2 is its density, V is its volume, Cv=900 J/kgK is its specific heat at constant volume, e=0.9 is its irradiative emissivity, OsA=5.57x10-8W/mK4 is the Stefan-Boltzman constant, h=30 W/mK is the convection coefficient, and To is the ambient air temperature, 220K. Compute the temperature of the plate with respect to time from t=0 to 20 sec with a time step of At = 10 s using the Euler's implicit method with T(0)= 600K, V = 0.003 m?, and As=0.20 m. Please use Newton's method for each time step with one single iteration. Initial guesses for Newton's method are temperatures at current steps. For example, to find T at t=10s, you can use T at 0 sec for the initial guess and to find T at 20 sec, you can use T at 10 sec for the initial guess