2. A solid steel ball 5cm in diameter is at a uniform temperature of 450C. It is quenched in a controlled environment whose temperature is initially 90C but which increases linearly with time at the rate of 10 C per minute. Given: Surface heat transfer coefficient =58W/m2K Density of steel =8000kg/m3 Specific heat of steel =0.42kJ/kgK Neglect internal temperature gradients and find the variation of temperature of the ball with time. Find the value of the minimum temperature to which the ball cools and the time taken to attain this temperature. Show that the assumption made to neglect internal temperature gradients is valid