A ball of 12 mm in diameter is at a given temperature of 1000 K. It is to be cooled to a final temperature of 300 K in an air environment at 250 K and a convection coefficient of 20 W / m2 -K. The properties of the material of the ball are k= 40 W/ m • K, p= 7800 kg1m3, c= 600 J1kg-K. Assume the radiation effects to be negligible.
1. Calculate the characteristic length of the ball
Answers
Explanation:
A ball of 12 mm in diameter is at a given temperature of 1000 K. It is to be cooled to a final temperature of 300 K in an air environment at 250 K and a convection coefficient of 20 W / m2 -K. The properties of the material of the ball are k= 40 W/ m • K, p= 7800 kg1m3, c= 600 J1kg-K. Assume the radiation effects to be negligible.
1. Calculate the characteristic length of the ball
(a) 2 mm (b) 4 mm (c) 6 mm (d) 3 mm
2. Calculate the thermal time constant of the given problem
(a) 300 s (b) 300 s-1 (c) 468 s (d) 468 s-1
3.Calculate the Biot number of the given problem
(a) 0.001 (b) 0.01 (c) 0.1 (d) 1
4. Based on the Biot number obtained in Question-3, which of the following statements is true
(a) Conduction resistance is large in comparison to surface
convection resistance (b) Conduction resistance is small in comparison to
surface convection resistance (c) Conduction and surface convection
resistances are comparable (d) None of the above
5. Calculate the time taken by the ball to cool to the final temperature of 300 K.
(a) 468.36 s (b) 126736 s (c) 1500 s (d) 792.85 s
6. Calculate the time taken by the ball to cool to the fatal temperature of 250 K.
(a) 468.3 s (b) 1263.6 s (c) 0s (d) infinitely long time
7. What is the steady state temperature of the ball?
(a) 1000 K (b) 250 K (c) 300 K (d) Cannot be determined from the given
information.
8. If the radiation effects are not negligible, and must be considered in the analysis
(a) The lumped parameter approach cannot be applied
(b) The convection heat transfer coefficient must be replaced by an overall heat transfer coefficient taking into account the radiation effects for Biot number calculation
(c) The applicability of lumped parameter approach can no longer be checked by utilizing the Biot number
(d) The convection effects can be neglected
9. The lumped parameter approach is valid when
(a) Biot number is high (b) Conduction resistance is low as compared to surface heat transfer resistance (c) Both (a) and (b) are correct (d) None of the above
10. The time constant in transient heat conduction is indicative of
(a) thermal energy storage (or release) relative to surface convective heat transfer (b) strength of conduction heat transfer relative to surface convection heat transfer (c) strength of conduction heat transfer relative to surface radiation heat transfer (d) None of the above