Download - Unit3 HT Phase Change
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.1
UNITIII
v Heat transfer by change of phase includes
a) Condensation
b) Boiling
c) Melting (or) Solidification
d) Sublimation
v Heat transfer occurs, in which respective latent heat is released. Phase change
occurs in constant temperature & Heat transfer coefficient is high.
v Buckingham Pi Theorem will be used to find the appropriate dimensionless
parameters.
For condensation or boiling the convection coefficient depends on the
difference between surface and saturation temperature (T=Tw - Tsat )
According to Buckingham theorem any physical equation may be defined
by
(Q1, Q2, Q3, Qm) = 0
Which is a function of m common quantities Q1, Q2,Q3..Qm.
If n fundamental dimensions M, L, t, T etc are chosen, then the equation may
be transformed into a new equation containing (m-n) dimensionless terms
represented by as
(1, 2, 3,.., 3-n),where each terms consists of quantities of
Qs.
Jakob number Ja = CpT = Max sensible energy
hfg latentheat
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.2
Bond number Bo = Gravitational body force = g(e1 ev)L2
Surface tension
v Condensation: When a saturated vapour comes in contact with a surface the
temperature of which is maintained below the saturation temperature at the
vapour pressure, the vapour condenses in to liquid releasing the latent heat of
condensation.
v Modes of condensation:
a) Drop arise condensation & b) Film wise condensation
Film wise Condensation: The condensate wets the surface and forms a liquid
film on the surface that slides down under the influence of gravity.
The thickness of the liquid film increases in the flow direction as more vapour
condenses on the film.
Drop wise condensation: The condensed vapour forms droplets on the
surface instead of a continuous film and the surface is covered by countless
droplets of varying diameters.
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.3
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.4
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.5
v Nusslets Theory: Exception of liquid metals, this theory is still widely used
to better understand heat transfer during condensation.
Assumptions made for Nusselt Theory
Heat transfer occurs the condensate layer is pure conduction and the liquid
temperature profile is linear.
The liquid temperature at the interface is that of saturated vapour.
Heat transfer is at steady state.
Condensate flow is under the action of gravity and is laminar
The plate is maintained at a uniform temperature of the vapour Tf . The vapour
is pure, dry and saturated.
Local film thickness ( as x )
Local heat transfer coefficient hx as x
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.6
v Pool boiling: If the heating surface is submerged in the liquid and if there is
no bulk motion of fluid, then the boiling process is known as pool boiling.
v Nucleate boiling: It involves two separate processes, the formation of bubbles
(nucleation) and the subsequent growth and motion of these bubbles.
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.7
Two conditions for nucleate boiling:
1. The liquid at the heating surface must be superheated.
2. There must be dissolved gasses present to form the nuclei of bubbles.
v Partial film boiling & Film boiling:
The heat flux rate is very high in nucleate boiling because of the agitation motion
of bubbles. The increasing number of bubbles forms an unstable film, the thermal
conductivity of which is very low. The portion of the surface covered by vapour
bubbles at any instant is effectively insulated. The heat flux rate decreases with
increase in temperature, which happens in partial film, transition or unstable film
boiling. Film boiling: When the surface is completely covered by vapour blanket,
heat transfer from the surface to the liquid occurs by conduction through a stable
vapour film.
Farber-scorah boiling curve
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.8
If the temperature exceeds 1000C radiation an effect gradually predominates the
heat flux rapidly increases.
Since the Twe temperature exceeds the melting point of the solid, destruction or
failure of the system may occur.
For this reason point C is often called the burn out point or the boiling crisis
indicating onset of departure from nucleate boiling. (DNB)
v Forced convection Boiling / Flow Boiling
In Pool boiling, fluid flow is mainly due to the buoyancy driven motion of
bubbles originating from the heated surface.
In forced convection boiling, flow is due to direct motion of fluid as well as due
to buoyancy effects. Conditions strongly depend on geometry, which may involve
external flow or internal flow over heated plates, cylinders or spheres.
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.9
Heat Exchanges
Heat is transferred from one fluid to another. The hot fluid gets cooled and the fluid
is heated.
Types of heat exchanges
1. Transfer type heat Exchanges or recuperators,
2. Storage type heat Exchanges or recuperators,
3. Direct contact type heat exchangers or mixers.
In transfer type or recuperator, the two fluids are kept separate and they do not mix.
Heat is transferred through the separating walls.
In storage type heat exchanger or a regenerator, hot and cold fluid flow alternately
through a solid matrix of high heat capacity.
Single matrix storage type heat exchanger
During heating period, hot fluid flows through the matrix, values A and B are kept
open, C and D are closed.
During cooling period, values A, B are closed and C, D is open.
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.10
In a rotary regenerator there is a matrix rotating at a rpm, driven by a motor through
reduction gears. This type of heat exchanger is used in steam power plant for pre
heating of air called Ljungstrom air preheater.
Notes:
Heat transfer in a heat exchanger usually involves convection in each fluid and
conduction through the wall separating the fluid.
In the analysis of heat exchangers, it is convenient to work with an overall heat
transfer coefficient.U.
Direct contact: Heat exchanger heat by direct contact. Open feed water
heaters, desuperheaters, cooling towers and jets condensers are examples of
such heat exchangers.
Two types of flow arrangement are possible in a double pipe heat exchanger.
i) Parallel flow both the hot and cold fluids flow in same direction.
ii) Counter flow both the fluids flows in opposite direction.
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.11
Shell and tube heat exchangers contain a large number of tubes packed in a
shell with their axis parallel to that of a shell.
In compact heat exchangers, the two fluids usually move perpendicular to
each other, and such flow configuration is called cross flow. The cross flow is
further classified as unmixed and mixed flow, depending on the flow configuration.
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.12
v The overall heat transfer coefficient:
Heat exchanger typically involves two flowing fluids separated by a solid
wall.
Heat is first transferred from the hot fluid to the wall by convection.
Through the wall by conduction.
From the wall to cold fluid by convection.
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.13
Thermal Resistance Network associated with heat transfer in a double pipe
heat exchanger.
The rate of heat transfer can be expressed as
R = Ri+Rwau+Ro
= 1 + ln(D0/ Di) + 1 hi Ai 2kL ho Ao
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.14
v Logmean temperature differences
1 2
12
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.15
Multipass and cross flow heat exchangers:
For parallel flow and counter flow heat exchangers the log mean temperature
difference Tlm is best suited , but for cross flow and multipass shell and tube heat
exchangers it I convenient to relate the equivalent temperature difference as ,
Tlm = FTlm,cf
F is the correction factor, which depends on the geometry od the heat exchanger
and the inlet and outlet temperatures of the hot and cold fluid systems. Tlm,cf is the
log mean temperature difference for the case of a counter flow.
The correction factor F for a heat exchanger is a measure of deviation of the Tlm
from the corresponding values for the counter flow case.
The correction factor F for common cross flow and shell and tube heat exchanger
versus two temperature ratios P and R defined as
P = t2 t1 1 and 2 represents inlet and outlet T1 t1 T and t represents the shell and tube side temperatures. R = T1 T2 t2 t1
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.16
F < 1 for a cross flow and multipass shell and tube heat exchangers.
F = 1 corresponds to the counter flow heat exchanger.
F1
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.17
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.18
The Effectiveness-NTU method: The log mean temperature difference (LMTD) method discussed is easy to use in heat exchanger analysis when the inlet and outlet temperatures of the hot and cold fluids are known or can be determined from an energy balance. Once Tlm , the mass flow rate and overall heat transfer coefficient are available, the heat transfer surface area of the heat exchanger can be determined from
!"#$ LMTD method is very suitable for determining the size of a heat exchanger.
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.19
If the type and size of heat exchangers are specified then effectiveness NTU method
analysis is preferred.
Heat transfer effectiveness % ,
& ''()*
Actual heat transfer rate Maximum Possible heat transfer rate
Heat Exchanged,
% $+,"1 -1
T1 - hot fluid entry temp
t1 - cold fluid entry temp
The effectiveness relations of the heat exchangers typically involve the dimensionless
group ./0
1(23 , This quantity is called the number of transfer units NTU and is
expressed as
4"5 ./01(23
./0( 16(23
Capacity Ratio c,
7 1(231()*
(86(23
(86()*
Thus, larger the NTU larger the heat
exchanger %
% is a function of
4"59 7 :,7-+;, ./01(23
, 1(231()*
U=overall heat transfer coefficient,
As=heat transfer surface Area,
NTU is proportional to As
NTU is a measure of the heat transfer
surface area. As
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.20
With standard data book the fouling factors can be assumed, in the surface to be
coated with 0.2 mm of limestone as a starting point to account for the effects of
fouling.
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Heat and Mass Transfer Mechanical Engineering
Ajai S | Lecturer/MECH
3.21
Notes:
References
1. Heat Transfer - A Practical Approach by Yugnus A Cengel. 2. Sachdeva R C, Fundamentals of Engineering Heat and Mass Transfer
New Age International, 1995. 3. Nag P.K, Heat Transfer, Tata McGraw-Hill, New Delhi, 2002