A long. highly polished aluminum rod of diameter D = 35 mm is hung horizontally in a large room. The initial rod temperature is T i = 90 ° C, and the room air is T ∞ = 20 ° C . At time t 1 = 1250 s, the rod temperature is T 1 = 65 ° C, and, at time t 2 = 6700 s, the rod temperature is T 2 = 30 ° C . Determine the values of the constants C and n that appear in Equation 5.26. Plot the rod temperature versus time for 0 ≤ t ≤ 10 , 000 s . On the same graph, plot the rod temperature versus time for a constant value of the convection heat transfer coefficient, evaluated at a rod temperature of T ¯ = ( T i + T ∞ ) / 2. For all cases, evaluate properties at T ¯ = ( T i + T ∞ ) / 2.
A long. highly polished aluminum rod of diameter D = 35 mm is hung horizontally in a large room. The initial rod temperature is T i = 90 ° C, and the room air is T ∞ = 20 ° C . At time t 1 = 1250 s, the rod temperature is T 1 = 65 ° C, and, at time t 2 = 6700 s, the rod temperature is T 2 = 30 ° C . Determine the values of the constants C and n that appear in Equation 5.26. Plot the rod temperature versus time for 0 ≤ t ≤ 10 , 000 s . On the same graph, plot the rod temperature versus time for a constant value of the convection heat transfer coefficient, evaluated at a rod temperature of T ¯ = ( T i + T ∞ ) / 2. For all cases, evaluate properties at T ¯ = ( T i + T ∞ ) / 2.
Solution Summary: The author plots the temperature versus time graph for the rod temperature between the time period of 0s to 10,000 s and corresponding to the constant heat transfer coefficient.
A long. highly polished aluminum rod of diameter
D
=
35
mm
is hung horizontally in a large room. The initial rod temperature is
T
i
=
90
°
C,
and the room air is
T
∞
=
20
°
C
.
At time
t
1
=
1250
s,
the rod temperature is
T
1
=
65
°
C,
and, at time
t
2
=
6700
s,
the rod temperature is
T
2
=
30
°
C
.
Determine the values of the constants C and n that appear in Equation 5.26. Plot the rod temperature versus time for
0
≤
t
≤
10
,
000
s
.
On the same graph, plot the rod temperature versus time for a constant value of the convection heat transfer coefficient, evaluated at a rod temperature of
T
¯
=
(
T
i
+
T
∞
)
/
2.
For all cases, evaluate properties at
T
¯
=
(
T
i
+
T
∞
)
/
2.
Q1: Determine the length, angle of contact, and width of a 9.75 mm thick
leather belt required to transmit 15 kW from a motor running at 900 r.p.m. The
diameter of the driving pulley of the motor is 300 mm. The driven pulley runs at
300 r.p.m. and the distance between the centers of two pulleys is 3 meters. The
density of the leather is 1000 kg/m³. The maximum allowable stress in the
leather is 2.5 MPa. The coefficient of friction between the leather and pulley is
0.3. Assume open belt drive.
5. A 15 kW and 1200 r.p.m. motor drives a compressor at 300 r.p.m. through a pair of spur gears having
20° stub teeth. The centre to centre distance between the shafts is 400 mm. The motor pinion is made
of forged steel having an allowable static stress as 210 MPa, while the gear is made of cast steel
having allowable static stress as 140 MPa. Assuming that the drive operates 8 to 10 hours per day
under light shock conditions, find from the standpoint of strength,
1. Module; 2. Face width and 3. Number of teeth and pitch circle diameter of each gear.
Check the gears thus designed from the consideration of wear. The surface endurance limit may be
taken as 700 MPa. [Ans. m = 6 mm; b= 60 mm; Tp=24; T=96; Dp = 144mm; DG = 576 mm]
4.
G
A micarta pinion rotating at 1200 r.p.m. is to transmit 1 kW to a cast iron gear at a speed of 192 r.p.m.
Assuming a starting overload of 20% and using 20° full depth involute teeth, determine the module,
number of teeth on the pinion and gear and face width. Take allowable static strength for micarta as 40
MPa and for cast iron as 53 MPa. Check the pair in wear.
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