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# Consider the steel balls of Problem 56 except now the air temperature increases with time as

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?

Problem 5.6

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.

Jun 27 2020 View more View Less