W m. Consider a small ball bearing (d = 3mm) of Inconel which is held and heated with a flame to a a uniform temperature T; = 1300K. Simultaneously at t = 0s, the flame is removed and the ball bearing is released, so that if falls experiencing an average heat transfer coefficient of h = 10 in air at Too = 298K. Assume that the average heat transfer coefficient can be used for any time after t = 0s, assume that it cools before it encounters any surface. Evaluate material properties at the nearest multiple of 200K Properties at Various Temperatures (K) k (W/mKle, dkg ) Properties at 300K Melting Point (k) Composition 100 200 400 600 800 1000 1200 1500 2000 2500 (k/m) (3/k-K) ( WK) (m 439 1665 8510 11.7 3.1 8.7 17.0 27.6 Inconel X-750 (739 Ni, 150 6.7 Fe) 10.3 372 135 473 20.5 546 24.0 626 33.0 510 a) The instantaneous rate of heat transfer [W] from the ball bearing will be greatest at t = 0 when the ball bearing temperature is highest. What is the magnitude of this rate of this heat transfer [W]? Consider both radiation and convection from the surface. (assume e = 1 and Tsur = T) b) Calculate the time, tcool, it takes for the ball bear to be cool enough to touch safely. Assume it is safe to touch if (tcool) = 325 K. Ignore the impact of radiation, assume large Fourier number i. Calculate the Biot number (at least two significant figures) ii. Is LCM justified? iii. Calculate tcool (s) (use lumped capacitance model)