From Figure 2.5 it is evident that, over a wide temperaturerange, the temperature dependence of the thermalconductivity of many solids may be approximated by alinear expression of the form k = k o + a T , where k o isa positive constant and a is a coefficient that may bepositive or negative. Obtain an expression for the heatflux across a plane wall whose inner and outer surfacesare maintained at T 0 and T 1 , respectively. Sketch theforms of the temperature distribution corresponding to a > 0 , a = 0 , and a < 0.
From Figure 2.5 it is evident that, over a wide temperaturerange, the temperature dependence of the thermalconductivity of many solids may be approximated by alinear expression of the form k = k o + a T , where k o isa positive constant and a is a coefficient that may bepositive or negative. Obtain an expression for the heatflux across a plane wall whose inner and outer surfacesare maintained at T 0 and T 1 , respectively. Sketch theforms of the temperature distribution corresponding to a > 0 , a = 0 , and a < 0.
Solution Summary: The author explains the expression of heat flux and temperature distribution for different values of a.
From Figure 2.5 it is evident that, over a wide temperaturerange, the temperature dependence of the thermalconductivity of many solids may be approximated by alinear expression of the form
k
=
k
o
+
a
T
,
where
k
o
isa positive constant and a is a coefficient that may bepositive or negative. Obtain an expression for the heatflux across a plane wall whose inner and outer surfacesare maintained at
T
0
and
T
1
,
respectively. Sketch theforms of the temperature distribution corresponding to
a
>
0
,
a
=
0
,
and
a
<
0.
PROBLEM 3.23
3.23 Under normal operating condi-
tions a motor exerts a torque of
magnitude TF at F. The shafts
are made of a steel for which
the allowable shearing stress is
82 MPa and have diameters of
dCDE=24 mm and dFGH = 20
mm. Knowing that rp = 165
mm and rg114 mm, deter-
mine the largest torque TF
which may be exerted at F.
TF
F
rG-
rp
B
CH
TE
E
1. (16%) (a) If a ductile material fails under pure torsion, please explain the failure
mode and describe the observed plane of failure.
(b) Suppose a prismatic beam is subjected to equal and opposite couples as shown
in Fig. 1. Please sketch the deformation and the stress distribution of the cross
section.
M
M
Fig. 1
(c) Describe the definition of the neutral axis.
(d) Describe the definition of the modular ratio.
using the theorem of three moments, find all the moments, I only need concise calculations with minimal explanations. The correct answers are provided at the bottom
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