A metal sphere of diameter D, which is at a

Chapter 5, Problem 5.34

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A metal sphere of diameter D, which is at a uniformtemperature Ti, is suddenly removed from a furnace andsuspended from a fine wire in a large room with air at auniform temperature T?and the surrounding walls ata temperature Tsur.(a) Neglecting heat transfer by radiation, obtain anexpression for the time required to cool the sphereto some temperature T.(b) Neglecting heat transfer by convection, obtain anexpression for the time required to cool the sphereto the temperature T.(c) How would you go about determining the timerequired for the sphere to cool to the temperature Tif both convection and radiation are of the sameorder of magnitude?(d) Consider an anodized aluminum sphere (?? 0.75)50 mm in diameter, which is at an initial tempera-ture of Ti?800 K. Both the air and surroundingsare at 300 K, and the convection coefficient is10 W/m2?K. For the conditions of parts (a), (b),and (c), determine the time required for the sphereto cool to 400 K. Plot the corresponding tempera-ture histories. Repeat the calculations for a polishedaluminum sphere (??0.1).

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