A 1 .0 m × 1 .5 m double-pane window consists of two 4-mm-thick layers of glass ( k = 0 .78 W/m .K) and that are separated by a 5-mm air gap ( k a i r = 0 .025 W/m .K) . and The heat flow through the air gap is assumed to be by conduction. The inside and outside air temperatures are 20°C and -20°C, respectively, and the inside and outside heat transfer coefficients are 40 and 20 W/m 2 ⋅K. Determine (a) the daily rate of heat loss through the window in steady operation and (b) the temperature difference across the largest thermal resistance.
A 1 .0 m × 1 .5 m double-pane window consists of two 4-mm-thick layers of glass ( k = 0 .78 W/m .K) and that are separated by a 5-mm air gap ( k a i r = 0 .025 W/m .K) . and The heat flow through the air gap is assumed to be by conduction. The inside and outside air temperatures are 20°C and -20°C, respectively, and the inside and outside heat transfer coefficients are 40 and 20 W/m 2 ⋅K. Determine (a) the daily rate of heat loss through the window in steady operation and (b) the temperature difference across the largest thermal resistance.
Solution Summary: The author explains the rate of heat loss per day through the window. The conductive thermal resistance of the glass 1 is determined as R_1=
A 1
.0 m
×
1
.5 m
double-pane window consists of two 4-mm-thick layers of glass
(
k
= 0
.78 W/m
.K)
and that are separated by a 5-mm air gap
(
k
a
i
r
= 0
.025 W/m
.K)
.
and The heat flow through the air gap is assumed to be by conduction. The inside and outside air temperatures are 20°C and -20°C, respectively, and the inside and outside heat transfer coefficients are
40 and 20 W/m2 ⋅K. Determine (a) the daily rate of heat loss through the window in steady operation and (b) the temperature difference across the largest thermal resistance.
20.
[Ans. 9; 71.8 mm]
A semi-elliptical laminated spring is made of 50 mm wide and 3 mm thick plates. The length between
the supports is 650 mm and the width of the band is 60 mm. The spring has two full length leaves and
five graduated leaves. If the spring carries a central load of 1600 N, find:
1. Maximum stress in full length and graduated leaves for an initial condition of no stress in the
leaves.
2. The maximum stress if the initial stress is provided to cause equal stress when loaded.
[Ans. 590 MPa ; 390 MPa ; 450 MPa ; 54 mm]
3. The deflection in parts (1) and (2).
Q6/ A helical square section spring is set inside another, the outer spring having a free
length of 35 mm greater than the inner spring. The dimensions of each spring are as
follows:
Mean diameter (mm)
Side of square section (mm)
Active turns
Outer
Inner
Spring
Spring
120
70
8
7
20
15
Determine the (1) Maximum deflection of the two springs and (2) Equivalent spring
rate of the two springs after sufficient load has been applied to deflect the outer
spring 60 mm. Use G = 83 GN/m².
Q2/ The bumper springs of a railway carriage are to be made of rectangular section wire.
The ratio of the longer side of the wire to its shorter side is 1.5, and the ratio of mean
diameter of spring to the longer side of wire is nearly equal to 6. Three such springs
are required to bring to rest a carriage weighing 25 kN moving with a velocity of
75 m/min with a maximum deflection of 200 mm. Determine the sides of the
rectangular section of the wire and the mean diameter of coils when the shorter side is
parallel to the axis of the spring. The allowable shear stress is not to exceed 300 MPa
and G = 84 kN/mm².
Q6/ A belical
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