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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_infinity=325+0.1875*t K and h=20 W/m^2*K. Assuming the properties of the steel to be k=40 W/m*K, rho=7800 kg/m^3, and c=600 J/kg*K,
(a) Sketch the ball termperature verses time for 0<t<1 hour. Also show the ambient temperature, T_infinity, in your graph. Explain the special features of the ball temperature behavior
(b) Find an expression for the ball temperature as a function of time,T(t), for 0<t<1 hour. Was your sketch in (a) correct?
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