unit3 ht phase change

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



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.



3.3



3.4



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



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.



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



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.



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.



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.



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.



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.



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



3.14

v Logmean temperature differences

1 2

12



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



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



3.17



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.



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



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.



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

unit3 ht phase change

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