(1) (Welty, Rorrer, Foster, 6th Edition International Student Version 19.4)
Determine the steady state surface temperature of an electric cable, 25 cm in diameter,
which is suspended horizontally in still air in which heat is dissipated by the cable at a
rate of 27 W per meter of length. The air temperature is 30
.
(2) (Welty, Rorrer, Foster, 6th Edition International Student Version 19.24)
An apparatus, used in an operating room to cool, consists of a coiled tube that is
immersed in an ice bath. Using this apparatus, blood, flowing at 0.006 m3/h, is to be
cooled from 40 to 30
. The inside diameter of the tube is 2.5 mm, and the surface
coefficient between the ice bath and outer tube surface is 500 W/m2.K. The thermal
resistance of the tube wall may be neglected.
Determine the required length of tubing to accomplish the desired cooling. Properties
of blood are the following:
(3) (Welty, Rorrer, Foster, 6th Edition International Student Version 19.25)
A system for heating water with an inlet temperature of 25
temperature of 70
to an exiting
involves passing the water through a thick-walled tube with
inner and outer diameters of 25 and 45 mm, respectively. The outer tube surface is
well insulated, and the electrical heating within the tube wall provides for a uniform
generation of
.
a. For a mass flow rate of water,
, how long must the tube be to
achieve desired outlet temperature?
b. If the inner surface of the tube at the outlet is
, what is the local
convective coefficient at this location?
1
(4) ID 7.24
Steel (AISI 1010) plates of thickness
and length L = 1 m on a side are
conveyed from a heat treatment process and are concurrently cooled by
atmospheric air of velocity
and
in parallel flow over
the plates.
For an initial plate temperature of
, what is the rate of heat transfer from
the plate? What is the corresponding rate of change of the plate temperature? The
velocity of the air is much larger than that of the plate.
(5) ID 7.35
One hundred electrical components, each dissipating 25 W, are attached to one surface
of a square (0.2 m x 0.2 m) copper plate, and all the dissipated energy is transferred to
water in a parallel flow over the opposite surface.
A protuberance at the leading edge of the plate acts to trip the boundary layer, and the
plate itself may be assumed to be isothermal. The water velocity and temperature
and
approximated as
, and the water’s thermophysical properties may be
,
and Pr = 5.2.
2
a. What is the temperature of the copper plate?
b. If each component has a plate contact surface area of 1 cm 2 and the
corresponding contact resistance is
, what is the
component temperature? Neglect the temperature variation across the
thickness of the copper plate.
3
4
(1) (Welty, Rorrer, Foster, 6th Edition International Student Version 19.4)
For a horizontal cylinder
1

0.387 Ra D 6

Nu  0.60 
9

1  0.559 / pr  16


Eg.20  10
q  27 w


D
m



8
27


2

10 5  Ra  1012
 hAT 

D
Nu D AT
Nu D D T
27  Nu D T
Trial & error  T  9.8K
Tsurf  39.8c
(2) (Welty, Rorrer, Foster, 6th Edition International Student Version 19.24)
L U
4
T  T
30
D ρvc p
e

 0.75
T0  T
40
0.2877  4
U
L U
D  vc p
1
A0
1
1

hi Ai h0 A0

1
1 1

hi h0

Ai  A0

h0  500W / m 2  K
hi 
K
Nui
D
.
4V
4(0.006) / 3600
ReD 

 1213
 D   0.0025  7 107

Pr 
hi 
 cP
k

1000  (7 107 )(4000)


 5.6
0.5
la min ar
flow

k
D 1 μ
(1.86)( Re Pr ) 3 ( b ) 0.14
D
L
μw
5
(if temperature variation is not large, μb  μ w )
1
0.5
0.0025  3

0.14

(1.86) 1213(5.6)(
)  1
0.0025
L



 956 L
1
3
1
U
1
3
1

1
L

500 956
1
3
0.002  0.001046 L
0.001178 L
0.2877 
1
3
0.002  0.001046 L
By trial & error
L  0.71m
(3) (Welty, Rorrer, Foster, 6th Edition International Student Version 19.25)
Since outside of the tube is insulated, all heat generated goes to water phase:

q  m c p T  (0.12kg / s )(4177 J / kg.K )(70  25) K
 22.56kW

W 

  (0.0452  0.0252 )  L
3
m 4

kW
q  qV  1.5 106
 1.649 L
 L  13.68m
constant flux  22560W
h
  0.025 (13.68)m2
 21000W / m2
21000
 525W / m2  K
110  70
6
(4) PROBLEM 7.24 (ID)
KNOWN: Plate dimensions and initial temperature. Velocity and temperature of air in
parallel flow over plates.
FIND: Initial rate of heat transfer from plate. Rate of change of plate temperature.
SCHEMATIC:
7
(5) PROBLEM 7.35 (ID)
KNOWN: Operating power of electrical components attached to one side of copper plate.
Contact resistance. Velocity and temperature of water flow on opposite side.
FIND: (a) Plate temperature, (b) Component temperature.
SCHEMATIC:
8