6.
Ozisik, M.N., Heat Transfer, McGraw Hill Book Co., 1994.
UNIT I
BASIC CONCEPTS IN HEAT TRANSFER
1.1
Heat Energy and Heat Transfer
Heat is a form of energy in transition and it flows from one system to another, without
transfer of mass, whenever there i
Fig. 2.7 a differential control volume within the boundary layer for laminar flow over a
plane wall
udy xdx udy
or,
u / x v y 0,
u
v
dxdy vdx .dxdy
x
x
the equation of continuity.
(2.20)
Concept of Critical Thickness of Insulation
The addition of insulat
LESSON NOTES
U6MEA31 HEAT AND MASS TRANSFER
VELTECH Dr.RR & Dr.SR TECHNICAL UNIVERSITY
U6MEA31 HEAT AND MASS TRANSFER
LT PC
3 1 0 4
OBJECTIVES
To familiarize the students with
Conduction, convection and radiation heat transfer
Applications of heat transfe
Fig. 3.1 (a) Rotating matrix regenerator
Fig. 3.1 (b) Stationary matrix regenerator
In a recuperator, hot and cold fluids flow continuously following he same path. The heat
transfer process consists of convection between the fluid and the separating wall,
above 50C
0.002
Treated feed water
0.0002
Industrial air
0.0004
Fuel oil
0.0009
Steam, nonoilbearing 0.00009
Quenching oil
0.0007
Alcohol vapours
0.00009
However, fouling factors must be obtained experimentally by determining the values of
U for both cl
2.2. Methods for Determining Heat Transfer Coefficient
The convective heat transfer coefficient in forced flow can be evaluated by:
(a)
Dimensional Analysis combined with experiments;
(b) Reynolds Analogy an analogy between heat and momentum transfer;
(c)
2.9 Heat and Mass Transfer
Example 2.5 Hot gases at 175C flow through a metal pipe (outer diameter 8 cm). The
convective heat transfer coefficient at the outside surface of the insulation (k = 0.18 W mK) IS
2.6 W m1K and the ambient temperature IS 25C. Ca
per hour is
0.918 (53.4 18) (12 20) 3600 = 28077.58 kJ/hr
Assuming the latent heat of vaporization of water as 2430 kJ/kg, the quantity of water to
be sprinkled over the surface such that it evaporates and consumes 28077.58 kJ/hr, is
&
M
w
= 28077.58/2430
where
R 1/ h1 L1 / k1 L2 / k 2 L3 / k 3 1/ h 2
R 1/ 30 0.3 /1.5 0.2 / 3.5 0.1/ 0.256 1/10 0.75
and
&/ A 1170 / 0.78 1500 W / m 2
Q
The overall heat transfer coefficient,
U 1/ R 1/ 0.78 1.282 W / m 2 K
Since the gas temperature is very high, we should cons
or,
d
H
H
dT
0 uCTdy CT dx 0 udy dx k dy
=
d
H
H
dx
y0
0 uCTdy dx 0 uTCdy dx
or
(2.3)
d
k dT
u T T dy
dx 0
C dy
y 0
dT
dy
y0
The boundary conditions are:
or,
(2.3)
Velocity profile
Temperature profile
u = 0 at y = 0
T = Tw at y = 0
u = 0 at y =
T = T at
Example 1.15 A steam pipe (inner diameter 16 cm, outer diameter 20 cm, k = 50 W/mK) is
covered with a 4 cm thick insulating material (k = 0.09 W/mK). In order to
reduce the heat loss, the thickness of the insulation is Increased to 8mm.
Calculate the perc
or,
Bi Fo = 1827; Fo = 1.827/ (8. 68 104) 2.1 103
t/ L2 = k/ ( CL2)t = 2100 and t = 568 = 0.158 hour
We can also compute the change in the internal energy of the object as:
1
1
0
0
U 0 U t CVdT CV Ts T hA / CV exp t hAt / CV dt
=
CV Ts T exp hAt / CV 1
All practical problems of importance encountered in our daily life Involve at least two,
and sometimes all the three modes occuring simultaneously When the rate of heat flow is
constant, i.e., does not vary with time, the process is called a steady state
(b) The Grashof Number (Gr)In natural or free convection heat transfer, die motion of
fluid particles is created due to buoyancy effects. The driving force for fluid motion is the body
force arising from the temperature gradient. If a body with a constan
Fig 1.2 Elemental volume in Cartesian coordinates
First we consider heat conduction the Xdirection. Let T denote the temperature at the
point P (x, y, z) located at the geometric centre of the element. The temperature gradient at the
left
hand
face
(x

7.1 . Transient State SystemsDefined
The process of heat transfer by conduction where the temperature varies with time and
with space coordinates, is called 'unsteady or transient'. All transient state systems may be
broadly classified into two categorie
By solving them,
d = 1,a = l, b = l, c = l,
4
VL
Cp ; 5 4 2
k
Cp
VL
Cp
=
k
VL
k
5
is Prandtl number.
Therefore, the functional relationship is expressed as:
Nu = f (Re, Pr); or Nu = C Rem Prn
(5.15)
where the values of c, m and n are determined exper
and molecular force fields exert a strong influence on the energy exchange In the
collision process. The mechanism of heat propagation in liquids can be conceived as transport of
energy by way of unstable elastic oscillations. Since the density of liquids
Abbaspour, K. C., Yang, J., Maximov, I., Siber, R., Bogner, K., Mieleitner, J.,& Srinivasan, R.
(2007). Modeling hydrology and water quality in the prealpine/alpine Thur watershed using
SWAT. Journal of hydrology, 333(2), 413430.
Akotsi, E. F. N. and Ga
steady state conditions we have:
Fig 1.15
R1 1/ h1A1 1/ 2 1 Lh1
R 2 ln r2 / r1 2Lk1
R 3 ln r3 / r2 2 Lk 2
R 4 1/ h 2 A 2 1/ 23h 2 L
And
&/ 2L T T / R
Q
1
0
T1 T0 / 1/ h1r1 ln r2 / r1 / k1 ln r3 r2 / k 2 1/ h 2r3
Example 1.12 A steel pipe. Inside diamete
wall, a surface heated by an electric heater or a wall near a furnace, there is a uniform
heat flux distribution along the surface. The wall surface will not be an isothermal one. Extensive
experiments have been performed by many research workers for free
cannot be strictly considered onedimensional. It has been suggested that for (A2/A1) >
2, the rate of heat flow can be approximated by the above equation by multiplying the geometric
mean
area
Am = (A1 A2) by a correction factor 0.725.]
4.4
Composite Sur
Fig. 2.1 Principle of heat transfer by convection
2.3. Free and Forced Convection
When the mixing motion of the fluid particles is the result of the density difference
caused by a temperature gradient, the process of heat transfer is called natural or fre
2.5 W/moC and k2 = 0.25 W/moC). The convective heat transfer coefficient at the inside and
outside surfaces are expected to be 250 W/m 2oC and 50 W/m2oC respectively. The
temperature of gases and air are 1000 K and 300 K. If the interface temperature is
6
0.8973  0.16 = 0.7373
and the heat flow rate = (1250 25)/0/7373 = 1661.46 W/m2
The temperature at the inner surface of the wall
= 1250 1660.46 0.0222 = 1213.12C
i.e., when the au gap is not there, the heat flow rate increases but the temperature at the
i
The total resistance = 2.15737 and Q = 275/2.15737 = 127.47 W per m length (Thus the
better insulating material be applied first to reduce the heat loss.) The overall heat transfer
coefficient, U, is obtained as U =
&/ A T
Q
The outer surface area = 320 1
angles to each other. Fig. 3.6 illustrates such an arrangement An automobile radiator is a
good example of crossflow exchanger. These exchangers are 'mixed' or 'unmixed' depending
upon the mixing or not mixing of either fluid in the direction transverse
The surface temperature of the conductor when the outermost radius with insulation is
equal to the critical radius, is given by
/L = 4.147 = (T25/
&
1000
Q
1n 9.375/ 0.75
2 3.142 0.15 16 2 3.142 9.375
or
T = 40.83C.
UNIT III
HEAT EXCHANGERS
3.1 Heat E