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.
Given answers to be: i) 14.65 kN; 6.16 kN; 8.46 kN ii) 8.63 kN; 9.88 kN iii) Bearing 6315 for B1 & B2, or Bearing 6215 for B1
(b)
A steel 'hot rolled structural hollow section' column of length 5.75 m, has
the cross-section shown in Figure Q.5(b) and supports a load of 750 kN.
During service, it is subjected to axial compression loading where one end
of the column is effectively restrained in position and direction (fixed) and
the other is effectively held in position but not in direction (pinned).
i)
Given that the steel has a design strength of 275 MN/m², determine
the load factor for the structural member based upon the BS5950
design approach using Datasheet Q.5(b).
[11]
ii)
Determine the axial load that can be supported by the column
using the Rankine-Gordon formula, given that the yield strength of
the material is 280 MN/m² and the constant *a* is 1/30000.
[6]
300
600
2-300 mm
wide x 5 mm
thick plates.
Figure Q.5(b)
L=5.75m
Pinned
Fixed
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