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A steel ball of diameter 60 mm is initially in thermal equilibrium at 1030°C in a furnace. It is suddenly removed from the furnace and cooled in ambient air at 30°C, with convective heat transfer coefficient h = 20 W/m²K. The thermophysical properties of steel are: density ρ = 7800 kg/m², conductivity k = 40 W/mK and specific heat c - 600 J/kgK. The time required in seconds to cool the steel ball in air from 1030°C to 430°C is
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- 519
- 931
- 1195
- 2144
Correct Option: D
Diameter of steel ball,
d = 0.06 m
Initial temperature,
Ti = 1030°C
Ambient temperature
T0 = 30°C
Convective heat transfer coefficient
| h = 20 | ||
| m²K |
| ρ = 7800 | ||
| m³ |
| k = 40 | ||
| mK |
| C = 600 | ||
| kg |
Final temperature of steel ball, T = 430°c
Time: t =?
| = e-ht/ρCl.......(i) | |
| Ti - T0 |
| l = | = | = | = | = 0.1 m | ||||
| A | 6 × πd² | 6 | 6 |
From (i)
| = e-20×t/7800×600×0.1 | |
| 1030 - 30 |
t = 2144.16 seconds
