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PROBLEM \# 4[ 20pts] Consider a 4cm diameter spherical steel ball (k=50W/(mK)) which is cooling by convection in air at 25C with h=5000W/(m2K). The initial temperature is 800K. The thermal diffusivity of the ball is =18106m2/s (a) Using a lumped capacitance analysis, calculate the temperature at the centre of the ball after 1 second. (b) Using a lumped capacitance analysis, calculate the fraction of the energy removed after 50 seconds. (Note: Relative to 25C reference.) (c) Is the lumped capacitance method valid? Justify your answer. (d) Repeat part a) using the first term spatial solution