HEAT TRANSFER 849

dharm

\M-therm\Th15-4.pm5

Rate of evaporation of liquid air :
The heat flow from the inner sphere surface to outer sphere
surface is given by,

Q

AT T

F

A

A

12 11

4

2

4

1

112

2

2

1

2

111

=

−

F −

HG

I

KJ

++−

F

HG

I

− KJ

σ

ε

ε

ε

ε

()

=

4

1 1 1

1

2

1

4

2

4

1

1

2

2

12

22

πσ

ε

ε

ε

ε

rT T

r

r

()−

F −

HG

I

KJ

++−

F

HG

I

KJ

=

40 120

100

300

100

1003

003

1 1003

003

0

0

2

44

2

π× × FHG IKJ −FHG IKJ

L

N

M

M

O

Q

P

P

F −

HG

I

KJ++

F −

HG

I

KJ×

F

HG

I

KJ

()

.

.

.

.

.105 5.67

.105

.15

=

0.7855 (2.07 81)

32.33 1 15.84

61.99

49.17

−

++

=− = – 1.26 W

• ve sign indicates that heat is gained by the surface 1, means, heat is flowing from outside
  surface to inside surface.

∴ The rate of evaporation =

1.26 3600

209.35 1000

×
× = 0.0217 kg/h. (Ans.)
Example 15.31. Liquid oxygen (boiling temperature = – 182°C) is to be stored in spherical
container of 30 cm diameter. The system is insulated by an evacuated space between inner sphere and
surrounding 45 cm inner diameter concentric sphere. For both spheres ε = 0.03 and temperature of the
outer sphere is 30°C. Estimate the rate of heat flow by radiation to the oxygen in the container.
Solution. Given : T 1 = – 182 + 273 = 91 K, T 2 = 30 + 273 = 303 K, ε 1 = ε 2 = 0.03
d 1 = 30 cm = 0.3 m, d 2 = 45 cm = 0.45 m.
Rate of heat flow, Q 12 :
The heat flow between the two concentric
spheres by radiation is given by

Q 12 =

AT T

F

A

A

114 24

1

112

2

2

1

2

111

σ

ε

ε

ε

ε

()−

− + F −

HG

I

− KJ

For concentric spheres

F 12 − = 1

and A
A

d

d

1

2

1

2

(^22)

F
HG
I
KJ
=F
HG
I
KJ
0.3
0.45
= 0.4444
A 1 = 4π (^) r 12 = 4π ×
03
2
F.^2
HG
I
KJ = 0.283 m
2
Fig. 15.55
Oxygen
1
2
30 Cº
Evacuated
space
–182 Cº
ε= 0.03
Fig. 15.56
T 1
r 1
r 2
T 2