Radioactive wastes are packed in a thin-walled spherical container. The wastes generate thermal energy nonuniformly recording to the relation q . = q . o [ 1 − ( r / r o ) 2 ] where is the local rate of energy generation per unit volume, q . is a constant, and r o is the radius of the container. Steady-state conditions are maintained by submerging the container in a liquid that is at T ∞ and provides a uniform convection coefficient h. Determine the temperature distribution, T ( r ) , in the container. Express your result in terms of q . o , r o , T ∞ , h , and the thermal conductivity k of the radioactive wastes.
Radioactive wastes are packed in a thin-walled spherical container. The wastes generate thermal energy nonuniformly recording to the relation q . = q . o [ 1 − ( r / r o ) 2 ] where is the local rate of energy generation per unit volume, q . is a constant, and r o is the radius of the container. Steady-state conditions are maintained by submerging the container in a liquid that is at T ∞ and provides a uniform convection coefficient h. Determine the temperature distribution, T ( r ) , in the container. Express your result in terms of q . o , r o , T ∞ , h , and the thermal conductivity k of the radioactive wastes.
Solution Summary: The author explains the radial temperature distribution in the container, which is given by T(r)=T_infty +
Radioactive wastes are packed in a thin-walled spherical container. The wastes generate thermal energy nonuniformly recording to the relation
q
.
=
q
.
o
[
1
−
(
r
/
r
o
)
2
]
where is the local rate of energy generation per unit volume,
q
.
is a constant, and
r
o
is the radius of the container. Steady-state conditions are maintained by submerging the container in a liquid that is at
T
∞
and provides a uniform convection coefficient h.
Determine the temperature distribution,
T
(
r
)
,
in the container. Express your result in terms of
q
.
o
,
r
o
,
T
∞
,
h
,
and the thermal conductivity k of the radioactive wastes.
Radioactive wastes are packed in a thin-walled spherical container. The wastes generate thermal
energy nonuniformly according to the relation ġ = ġ, 1–(r/r.)* | where ġ is the local rate of
energy generation per unit volume, ġ, is a constant, and r, is the radius of the container. Steady-
state conditions are maintained by submerging the container in a liquid that is at T, and provides
a uniform convection coefficient h.
Coolant
T, h
- ġ = 4, [1– (rlr,²]
11
The initial temperature distribution of a 5 cm long stick is given by the
following function. The circumference of the rod in question is completely
insulated, but both ends are kept at a temperature of 0 °C. Obtain the heat
conduction along the rod as a function of time and position ? (x =
1.752 cm²/s for the bar in question)
100
A) T(x1) = 1 Sin ().e(-1,752 (³¹)+(sin().e (-1,752 (²) ₁ +
1
3π
TC3
.....)
100
t + ··· .......
13) T(x,t) = 200 Sin ().e(-1,752 (²t) + (sin (3). e (-1,752 (7) ²) t
B)
3/3
t + …............)
C) T(x.t) = 200 Sin ().e(-1,752 (²t) (sin().e(-1,752 (7) ²) t
–
D) T(x,t) = 200 Sin ().e(-1,752 (²)-(sin().e (-1,752 (²7) ²) t
E) T(x.t)=(Sin().e(-1,752 (²t)-(sin().e(-1,752 (²) t+
t + ··· .........)
t +....
t + ··· .........)
…..)
Heat Transfer question
In order to cool down a hot steel sphere (its diameter is 5 cm), CO2 gas is blown over it through a pipe with a diameter of 10 cm. The CO2 gas is kept at atmospheric pressure while moving through a smooth pipe at a speed of 6 m/sec. The gas temperature entering the pipe is 300K and exiting the pipe is 340 K. The pipe temperature at the entrance is 350K and at the exit is 550K. The sphere is located just about the pipe exit.
Find the convective heat transfer coefficient of the gas moving in the pipe, the heat transfer rate at the pipe and the pipe length. What is the surface temperature of the sphere if the heat transfer rate between the sphere and the gas is 7W and its surface temperature is higher than the gas?
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