1
GATE ME 2016 Set 2
Numerical
+2
-0
Two cylindrical shafts $$A$$ and $$B$$ at the same initial temperature are simultaneously placed in a furnace. The surfaces of the shafts remain at the furnace gas temperature at all times after they are introduced into the furnace. The temperature variation in the axial direction of the shafts can be assumed to be negligible. The data related to shafts $$A$$ and $$B$$ is given in the following Table.

The temperature at the center-line of the shaft $$A$$ reaches $${400^ \circ }C$$ after two hours. The time required (in hours) for the center-line of the shaft $$B$$ to attain the temperature of $${400^ \circ }C$$ is ____________

2
GATE ME 2016 Set 1
Numerical
+2
-0
A steel ball of $$10$$ $$mm$$ diameter at $$1000$$ $$K$$ is required to be cooled to $$350$$ $$K$$ by immersing it in a water environment at $$300$$ $$K.$$ The convective heat transfer coefficient is $$1000\,\,W/{m^2}$$-$$K.$$ Thermal conductivity of steel is $$40$$ $$W/m$$-$$K.$$ The time constant for the cooling process $$\tau$$ is $$16s.$$ The time required (in $$s$$) to reach the final temperature is __________________.
3
GATE ME 2013
+2
-0.6
A steel ball of diameter $$60$$ $$mm$$ is initially in thermal equilibrium at $${1030^ \circ }C$$ in a furnace. It is suddenly removed from the furnace and cooled in ambient air at $${30^ \circ }C$$ with convective heat transfer coefficient $$h = 20\,W/{m^2}K.$$ The thermo-physical properties of steel are: density $$\rho = 7800\,\,kg/{m^3},$$ , 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 $${1030^ \circ }C$$ to $${430^ \circ }C$$ is
A
$$519$$
B
$$931$$
C
$$1195$$
D
$$2144$$
4
GATE ME 2011
+2
-0.6
A spherical steel ball of $$12mm$$ diameter is initially at $$100K.$$ It is slowly cooled in a surrounding of $$300K.$$ The heat transfer coefficient between the steel ball and the surrounding is $$5W/{m^2}K.$$ The thermal conductivity of steel is $$20$$ $$W/mK.$$ The temperature difference between the centre and the surface of steel ball is
A
large because conduction resistance is far high than the convective resistance.
B
large because conduction resistance is far less than the convective resistance.
C
small because conduction resistance is far high than the convective resistance.
D
small because conduction resistance is far less than the convective resistance.
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