482
FUNDAMENTALS OF HEAT AND MASS TRANSFER
Further increase in the heat addition rate increases the surface temperature and
individual bubbles combine to form a column of vapour also called slugs of vapour rise directly
out of the surface. The columns wil
629
As areas A1 and A3 are equal and
also A2 and A4 are equal.
A3F32 = A1F14
substituting in A,
A1,2 F1,23,4 = A1F13 + A2 F24 + A1F14 + A3F32
= A1F13 + A2F24 + 2 A1F14
.(B)
F1,23,4, F13, F24 can be determined directly from charts as these areas are rectan
179
TWO DIMENSIONAL STEADY HEAT CONDUCTION
Some more boundary conditions are solved in textbooks exclusively on conduction. For
complex boundaries the use of computers softwares will provide the temperature distribution
and heat flow at surfaces at a reas
95
STEADY STATE CONDUCTION
2.11
A part of a sphere of ID D1 and OD D2 and cut as shown in Fig. 2.11 conducts heat along the
direction shown. Derive the general conduction equation and integrate the same for steady conditions without heat generation. Assum
CONVECTION
293
The important methods of analysis used in convection studies are
1. Analytical method which can again be subdivied as
(i) Formulating and solving the differential equation, also known as exact method
(ii) Formulating and solving integral eq
2
Chapter 2
STEADY STATE CONDUCTION
2.0 CONDUCTION
Conduction is the mode of energy transfer as heat due to temperature difference in a solid or
any phase of material where the mass is contiguous and in thermal contact. Microscopically
this mode of energy
584
FUNDAMENTALS OF HEAT AND MASS TRANSFER
13.3 REAL SURFACES
Solids and liquids emit radiation from the surface, with the material involved limited to a
small thickness at the surface. Gases however emit radiation over the whole volume. Real
surfaces rad
CONTENTS
v
Preface to the Third Edition
1
AN OVERVIEW OF HEAT TRANSFER
125
1.0
Introduction 1
1.1
Heat Transfer 1
1.2
Modes of Heat Transfer 2
1.3
Combined Modes of Heat Transfer 8
1.4
Dimensions and Units 10
1.5
Closure 11
Solved Problems 11
Exercise Pro
506
FUNDAMENTALS OF HEAT AND MASS TRANSFER
Solution: Two basic relations are used: Assuming unit width and depth x,
heat transfer as measured by condensate = heat convected
m hfg = h x T
h = m hfg/xT
Where m is the flow rate kg/s and T = (Tg Tw)
The heat
242
FUNDAMENTALS OF HEAT AND MASS TRANSFER
1
dT
d
. d =
=
cV
q hA(T T ) q hA
letting = (T T)
Integrating from 0 to time
FG
H
q hA 2
1
1
=
ln
hA
q
cV
IJ as hA
K
1
=0
LM OP
N Q
L 12 0.04 120 OP = 0.8576
q 12 0.04 (120 30)
= exp M
q
N 0.5 750 Q
q hA 2
hA
,
209
TRANSIENT HEAT CONDUCTION
Example 6.4: A thick concrete wall fairly large in size initially at 30C suddenly has its surface
temperature increased to 600C by an intense fire which lasted for 25 minutes. The material
will disintegrate upto a depth where
CONVECTIVE HEAT TRANSFER-PRACTICAL CORRELATIONS-FLOW OVER SURFACES
347
Example 8.11: Considering the data of Example 8.10, determine the average value of convection
coefficient and Cf values taking into consideration the laminar region. Compare with probl
398
FUNDAMENTALS OF HEAT AND MASS TRANSFER
Using energy balance,
DL q = mc Tm
L=
L=
mc Tm
Dq
0.01 4178 (60 20)
0.02 15 10 3
= 1.773 m.
Example 9.8: A solar concentrator causes a heat flux of 2000 W/m2 on tube of 60 mm ID.
Pressurised water flows throu
266
FUNDAMENTALS OF HEAT AND MASS TRANSFER
For point 3, 4 surface temperature ratio is also required: This ratio from location chart
for x/L = 1 is 0.803.
For point 3, mid plane of one and surface of the second.
Temperature ratio = 0.443 0.443 0.803 = 0.
659
MASS TRANSFER
Na
N
= b and so Dab = Dba
A
A
as
The total pressure is constant all through the mixture. Hence the difference in partial pressures
will be equal. The Ficks equation when integrated for a larger plane volume of thickness L
will give
(Ca1
680
FUNDAMENTALS OF HEAT AND MASS TRANSFER
EXERCISE PROBLEMS
14.01 Two ducts are carrying a mixture of Nitrogen and Ammonia one having ammonia 80% and N2
20% and the other 80% N2 and 20% ammonia at the same pressure and temperature. These are
connected by
149
HEAT TRANSFER WITH EXTENDED SURFACES (FINS)
Problem 4.2: One end of a long rod of 1 cm dia is maintained at 500C by placing it in a
furnace. The rod is exposed to air at 30C with a convection coefficient of 35 W/m2K. The
temperature measured at a dist
449
NATURAL CONVECTION
The value of h will be lower than 7.54. The plate temperature will be around 1400C.
The value of heat flux is not suitable for free convection as it leads to an unusually high plate
temperature. In case of water this flux may lead t
701
51. In stable film boiling as excess temperature increases sustainable heat flux will increase.
(True)
52. In flow boiling mist flow will sustain higher heat flux.
(False)
53. In condensation film, linear temperature profile is generally assumed.
(Tru
320
FUNDAMENTALS OF HEAT AND MASS TRANSFER
This can be checked using equation in problem 7.9.
FG IJ FG L IJ
H K HL K
h2
u 1
=
h1
u 2
1/ 2
1/ 2
1
2
FG 2 IJ FG 1IJ
H 1K H 2 K
1/ 2
=
1/ 2
= 1.
Problem 7.16: Using the method of dimensional analysis, obtain th
422
FUNDAMENTALS OF HEAT AND MASS TRANSFER
Re = 4 G/D =
= 119043
4 500
1
3600
0.05 29.71 10 6
Turbulent
for a first estimate:
Nu = 0.023 Re0.8 Pr0.3 = 234.4,
Using heat balance,
h = 215.34 W/m2K
FG
H
IJ
K
500
400 + Tmo
120
1047 (400 Tmo) = 216.34 0.05
608
FUNDAMENTALS OF HEAT AND MASS TRANSFER
Equation (13.30) is the most general form which covers radiation heat exchange
1
is known as surface
between any two surfaces whether black or gray. The terms
A
resistance and 1/A1F12 as space resistance.
If
1 =
62
FUNDAMENTALS OF HEAT AND MASS TRANSFER
k = 1.4 W/mK
2
h = 250 W/m K
T0
2
h = 10 W/m K
T1
15C
5C
Q
T2
Q2
Heater
Q2
RC2
50 mm
T0
T2
5C
Q1
Q1
T1
R2
R1
15C
RC1
Q
10 mm
(a)
(b)
Fig. P. 2.8. Problem Model.
9.7684 To 143.58 = 2000
Room side
Q1 =
Back side
Q2
527
HEAT EXCHANGERS
total heat flow, either the heat flow should be summed up using elemental areas and the
temperature difference at the location or more conveniently an average value of temperature
difference should be worked out.
The temperature variat
392
FUNDAMENTALS OF HEAT AND MASS TRANSFER
Example 9.2: Water at 30C enters a pipe of 25 mm ID with a mean velocity of 0.06 m/s. The
pipe surface temperature is 50C. Determine the outlettemperature for lengths of (i) 1 m (ii) 4 m
and (iii) 10 m. Assume hy
686
FUNDAMENTALS OF HEAT AND MASS TRANSFER
87. In pipe flow, convection coefficient at entrance region will be _ compared to
the fully developed region.
(higher)
88. In pipe flow under constant wall heat flux conditions the convection coefficient will be
101
CONDUCTION WITH HEAT GENERATION
Sometimes only T and h will be known. In such cases the equation (3.5(a) can be
modified.
qL
At the boundary
AL q = hA (Tw T) Tw = T +
h
Eqn. (3.5(a) can be written as
The temperature at x = 0 is obtained from (3.5(a) a