A metal spherical tank is filled with chemicals undergoing an exothermic reaction. The reaction provides a uniform heat flux on the inner surface of the tank. The tank has an inner diameter of 5 m, and its wall thickness is 10 mm. The tank vall has a variable thermal conductivity given as ( k ( T ) = k 0 (1+ β T), where k 0 = 9.1 W/m .K, β = 0.0018 K − 1 , and T is in K. The area surrounding the tank has an ambient temperature of 15 °C, the tank’s outer surface experiences convection heat transfer with a coefficient of 80 W/m 2 ⋅K. Determine the heat flux on the tank’s inner surface if the inner surface temperature is 120°C.
A metal spherical tank is filled with chemicals undergoing an exothermic reaction. The reaction provides a uniform heat flux on the inner surface of the tank. The tank has an inner diameter of 5 m, and its wall thickness is 10 mm. The tank vall has a variable thermal conductivity given as ( k ( T ) = k 0 (1+ β T), where k 0 = 9.1 W/m .K, β = 0.0018 K − 1 , and T is in K. The area surrounding the tank has an ambient temperature of 15 °C, the tank’s outer surface experiences convection heat transfer with a coefficient of 80 W/m 2 ⋅K. Determine the heat flux on the tank’s inner surface if the inner surface temperature is 120°C.
Solution Summary: The author explains the rate of heat transfer at the tank’s outer surface.
A metal spherical tank is filled with chemicals undergoing an exothermic reaction. The reaction provides a uniform heat flux on the inner surface of the tank. The tank has an inner diameter of 5 m, and its wall thickness is 10 mm. The tank vall has a variable thermal conductivity given as
(
k
(
T
)
=
k
0
(1+
β
T), where
k
0
=
9.1
W/m
.K,
β
=
0.0018
K
−
1
,
and T is in K. The area surrounding the tank has an ambient temperature of 15 °C, the tank’s outer surface experiences convection heat transfer with a coefficient of 80 W/m2 ⋅K. Determine the heat flux on the tank’s inner surface if the inner surface temperature is 120°C.
7. A distributed load
w(x) = 4x1/3
acts on the beam AB shown in Figure 7, where x is measured in meters and w is in kN/m. The
length of the beam is L = 4 m. Find the moment of the resultant force about the point B.
w(x) per unit length
L
Figure 7
B
4. The press in Figure 4 is used to crush a small rock at E. The press comprises three links ABC,
CDE and BG, pinned to each other at B and C, and to the ground at D and G. Sketch free-body
diagrams of each component and hence determine the force exerted on the rock when a vertical
force F = 400 N is applied at A.
210
80
80
C
F
200
B
80
E
60%
-O-D
G
All dimensions in mm.
Figure 4
2. Figure 2 shows a device for lifting bricks and concrete blocks. It comprises two compo-
nents ABC and BD, with a frictionless pin at B. Determine the minimum coefficient of friction
required at A and D if the device is to work satisfactorily.
W
all dimensions in inches
Figure 2
D
Chapter 2 Solutions
Heat and Mass Transfer: Fundamentals and Applications
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