Consider a spherical shell of inner radius r 1 and outer radius r 2 whose thermal conductivity varies linearly in a specified temperature range as k ( T ) = k 0 ( 1 + β T ) , where k 0 and β are two specified constants. The inner surface of the shell is maintained at a constant temperature of T 1 , while the outer surface is maintained at T 2 . Assuming steady one-dimensional heat transfer, obtain a relation for (a) the heat transfer rate through the shell and (b) the temperature distribution T(r) in the shell.
Consider a spherical shell of inner radius r 1 and outer radius r 2 whose thermal conductivity varies linearly in a specified temperature range as k ( T ) = k 0 ( 1 + β T ) , where k 0 and β are two specified constants. The inner surface of the shell is maintained at a constant temperature of T 1 , while the outer surface is maintained at T 2 . Assuming steady one-dimensional heat transfer, obtain a relation for (a) the heat transfer rate through the shell and (b) the temperature distribution T(r) in the shell.
Solution Summary: The author explains the heat transfer rate through the shell, the thermal conductivity, and the coefficient of the temperature distribution.
Consider a spherical shell of inner radius r1 and outer radius r2 whose thermal conductivity varies linearly in a specified temperature range as
k
(
T
)
=
k
0
(
1
+
β
T
)
,
where k
0
and
β
are two specified constants. The inner surface of the shell is maintained at a constant temperature of T1, while the outer surface is maintained at T2. Assuming steady one-dimensional heat transfer, obtain a relation for (a) the heat transfer rate through the shell and (b) the temperature distribution T(r) in the shell.
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1. A 40 lb. force is applied at point E. There are pins at
A, B, C, D, and F and a roller at A.
a. Draw a FBD of member EFC showing all the known and
unknown forces acting on it.
b. Draw a FBD of member ABF showing all the known and
unknown forces acting on it.
c. Draw a FBD of member BCD showing all the known and
unknown forces acting on it.
d. Draw a FBD of the entire assembly ADE showing all the
known and unknown forces acting on it.
e. Determine the reactions at A and D.
f. Determine the magnitude of the pin reaction at C.
40 lbs.
B
A
6 in.
4 in.
D
F
-5 in.4 in 4.
A crude oil of specific gravity0.85 flows upward at a volumetric rate of flow of 70litres per
second through
a vertical
venturimeter,with an inlet diameter of 250 mm and a throat
diameter of 150mm. The coefficient
of discharge of venturimeter is 0.96. The vertical
differences betwecen the pressure toppings is
350mm.
i)
Draw a well labeled diagram to represent the above in formation
i)
If the two pressure gauges are connected at the tapings such that they are
positioned at the levels of their corresponding tapping points,
determine the
difference of readings in N/CM² of the two pressure gauges
ii)
If a mercury differential
manometer
is connected in place of pressure gauges,
to the tappings such that the connecting tube up to mercury are filled with oil
determine the difference in the level of mercury column.
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