Consider the steel balls of Problem 5.6, except now the air temperature increases with time as T∞(t) 325 K at, where a 0.1875 K/s.
(a) Sketch the ball temperature versus time for 0 ≤ t ≤ 1 h. Also show the ambient temperature, T∞, in your graph. Explain special features of the ball temperature behavior.
(b) Find an expression for the ball temperature as a function of time T(t), and plot the ball temperature for 0 ≤ t ≤ 1 h. Was your sketch correct?
Steel balls 12 mm in diameter are annealed by heating to 1150 K and then slowly cooling to 400 K in an air environment for which T∞ = 325 K and h = 20 W/m2 ∙ K. Assuming the properties of the steel to be k = 40 W/m∙ K, 7800 kg/m3, and c = 600 J/kg ∙ K, estimate the time required for the cooling process.
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