COMPARISON AND SELECTION OF POWER PLANTS

The following factors are considered for the selection of power plant

1. Depending on the load requirement

2. Availability of fuel and water

3. Availability of fuel storage facility.

4. Transportation facility.

5. Availabilitv land

6. Environmental conditions

7. Efficiency of the plant

8. Capacity of the plant.

9. Distance from the load center.

10. Life of the plant.

11. Availability of time period for power production.

12. Cost of the fuel used.

13. Nature of losses.

14. Requirement of labours.

15. Depending on the noise of vibration.

Combined MHD-Steam Power Plant

If  the  gas  entering  the  MHD  duct  at  about  3000 ° C  could  be  expanded  to  the ambient   temperature   of   30   ° C,   the   Carnot   efficiency   would   have   reached   90%. Unfortunately,   the  MHD   power  output   is  restricted  because  by  the  time  the  gas temperature  falls  to  2000  ° C  the  electrical conductivity  becomes  very  low  with  the electrons combining with ions to  form  neutral atoms,  and  the generator then ceases  to operate  satisfactorily.  Therefore,  the  MHD  generator  is  used  as  a  topping  unit  and  the MHD exhaust at about 2000 ° C is utilized in raising steam to drive turbine and generate electricity in a conventional steam power

In the closed cycle scheme, helium (or argon) gas seeded with cesium is heated in a nuclear reactor, passed into the MHD duct  and then into the steam generating system (Fig. 3.34). A gas turbine plant can also be used as a bottoming unit (Fig 3.35).

The  material  has  to  stand  up  to  temperatures  above  2200 ° C and  the  corrosive atmospheres of alkali-seeded gases.

The duct  wall will also  need to  be an electrical insulator  at these temperatures.

Materials used are magnesium oxide, strontium zirconate and hafnia. Electrodes in the dc MHD generator perform the same function as brushes in a conventional dc generator. Tungsten or carbon electrodes have been used.

Electrodes  are  often  segmented  to  reduce  energy  losses  due  to  Hall  effect  To reduce the power consumption of  these electromagnets,cryogenic or superconducting coils at liquid helium temperatures have been suggested.

The only fuel which  has  better  characteristics than coal is  char,  which contains almost no hydrogen and, in general, results in a 25% increase in the performance of the generator.

GAS TURBINE-STEAM TURBINE POWER PLANT

The air standard cycle for a gas turbine power plant  is the Brayton cycle which, like Rankine cycle, also  consists of two reversible adiabatics and two reversible

isobars,  but  unlike  Rankine  cycle  the  working  fluid  does  not  undergo  phase change.

A gas turbine plant can be either open or closed. Simple, open gas turbine plant is shown in Fig. 3.6.

Since the product of combustion is the working  fluid which produces power by doing  work on the blades of the gas turbine,  it  is an  internal  combustion plant. However, unlike the reciprocating internal combustion engine, the gas turbine is a steady  flow  device  and  the  blades  are  always  subjected  to  the  highest  gas temperature.

To  limit  the  maximum  gas  temperature to  about  1200  K  at  inlet  to  the  turbine consistent with the materialized, a high air-fuel ratio is used.

The  disadvantages  of  a  gas  turbine  power  plant  in  a  utility  system  are  the
following:

1.  Large  compressor  work  input,  since  the  power  required  to  drive  the  compressor  is considerably  higher  than  that  required  by  a  pump  for  the  same  pressure  rise.  The compressor thus consumes a large part of the work produced by the turbine.

2. Large exhaust loss, since the exhaust gas temperature is quite high and also the mass
flow rate of gas is large due to high air —fuel ratio used.

3. Machine  inefficiencies, since with the decrease  in compressor  efficiency (i the work
input to the compressor increases and with the decrease in turbine efficiency ( the work output  from  the  turbine  decreases.  At  certain  values  of  i  and  17  a  situation  may  arise when  the  compressor  consumes  more  power  than  what  the  turbine  develops.  So,  the machine efficiencies of the compressor and the turbine have to be high enough to yield justifiable net work output.

4.  Low  cycle  efficiency,  due  to  the  large  exhaust  loss,  large  compressor  work  and
machine inefficiencies.

5. Costly fuel, since the cost of kerosene and other fuels used is much higher than that of
coal. Its availability is also not always guaranteed.

Due to the above factors, the cost of power generated by a stationary gas turbine plant for
a utility system is high. However, a gas turbine plant offers certain advantages also, as given below:

1. Less installation cost

2. Less installation time

3. Quick starting and stopping

4. Fast response to load changes

So, a gas turbine plant is often used as a peaking unit for certain hours of the day when the  energy  demand  is  high.  A  large  steam  plant  designed  to  meet  peak  loads  would operate at an uneconomical load factor during most of the year.

Thermodynamics of Brayton-Rankine Combined Cycle Plant

Let  us  consider  two  cyclic  power  plants  coupled  in  series,  the  topping  plant operating  on  Brayton  cycle  and  the  bottoming  one  operating  on  Rankine  cycle
(Fig. 3.7).

Helium  gas  may  be  the  working  fluid  in  the  topping  plant  and  water  in  the bottoming   plant.   As  shown   in   Section  3.4.1,   the  overall  efficiency  of  the combined plant is given by Eq. (3.6)

neglecting the pump work.As  inlet  temperatures  to  gas  turbine  keep  increasing  (due  to  the  use  of  better material  and  blade  cooling),  the  importance  of  supplementary  firing  diminishes further. However, supplementary firing may provide increased operating and fuel flexibilities in CC plants, which may fall into the following two categories.

1. Combined cycle plants with limited supplementary firing Supplementary  firing  raises  the  temperature  of  the  exhaust  gas  to  800  to  900  ° C.

Relatively  high  flue  gas  temperature  raises  the  condition  of  steam  (84  bar,  525  ° C), thereby  improving  the  efficiency  of  the  steam  cycle.

COMBINED CYCLE PLANTS

The  maximum  steam  temperature  in  a  power  cycle  does  not  exceed  600  ° C, although the temperature in a dry bottom pulverized coal furnace  is about  1300
°C.

By  superposing  a  high  temperature  power  plant  as  a  topping  unit  to  the  steam plant,  a  higher  energy  conversion  efficiency  from  fuel  to  electricity  can  be achieved, since the combined plant operates through a higher temperature range.

Combined plants may be of the following types:
(i) Gas turbine —steam turbine plant

(ii) MHD —steam plant

(iii) Thermionic —steam plant

(iv) Thermoelectric —steam plant

MHD (Magneto Hydro Dynamic) -STEAM POWER PLANT

The  maximum  steam  temperature  and  pressure  being  fixed  by  metallurgical considerations, the minimum temperature by the ambient conditions, and with the optimum  degree  of  regeneration  and  number  of  reheats,  the  ceiling  for  the conversion efficiency of a conventional thermal power station is somewhere near
45%.

There  is  a  great  deal  of  world-wide  interest  to  achieve  a  higher  conversion efficiency and  hence,  fuel economy,  by converting “heat”  directly to  electricity eliminating the link process of producing mechanical energy via steam.

The  magneto  hydrodynamic  (MHD)  power  generation  seems  to  be  the  most promising for a utility system.

The  maximum  limiting  temperature  for  turbine  blades  being  750 —800  ° C,  the
MHD  generator  is  capable  of  tapping  the  vast  potential  offered  by  modern furnaces, which can reach temperatures of more than 2500 K, and up to 3000 K with preheating of air.

Principle of MHD Power Generation

Faraday’ s law  of electromagnetic  induction  states  that  when  a  conductor  and  a magnetic  field  move relative to  each other,  an electric  voltage  is induced  in the conductor.

The conductor may be a solid, liquid or gas. In an MHD generator, the hot ionized gas replaces the copper windings of an alternator.

When a gas  is  heated to  high temperatures, the valence electrons of the excited atoms move on to higher quantized orbits and ultimately, at certain energy levels they fly off and become free electrons.

For  a  gas  to  be  conducting,  a  certain  number  of  free  electrons  must  be  present along with an equal number of ions and the main body of neutral atoms.

Since  a  very  high  temperature  is  required  to  ionize  a  gas  (thermal  ionization) which cannot be endured by the materials available, the hot gas is seeded with an alkali  metal,  such  as  cesium  or  potassium  (K or  KOH)  having  a  low  ionization potential (energy needed to ionize one g mol of atoms) before the gas enters the MHD duct.

An adequate electrical conductivity of the order of 10 mho/m can thus be realized at somewhat lower temperatures in the range 2200—2 700 ° C.

A simple view of the MHD generator is shown inFig The duct through which the electrically conducting ionized gas flows has two sides supporting a strong transverse magnetic field of 4  —5 tesla (1 tesla = iü gauss) at right angles to the flow and the other sides forming the faces of electrodes which are joined through an electrical circuit.

As the  hot  ionized gas or plasma  enters the MHD duct, due to the effect  of the strong magnetic field and the consequent Lorentz force, there is a decrease in the kinetic  energy  of  the  plasma,  and  the  electrons  and  ions  get  deposited  on  the opposite electrodes.

The power generated per unit length is approximately proportional to cru B where c-is the electrical conductivity, u is the velocity of the gas, B is the magnetic field strength and p is the density.

The power produced being dc, the conversion to ac is done by an inverter. Figure
3.31  shows  the  principal  components  of  a  typical  MHD  plant  and  its  cycle  of operations on T —s diagram.

HYDRO POWER PLANT

In a hydro power plant, the potential energy of water stored in a dam is made use
of in running a water turbine coupled to an electrical generator.

It is esti mated that bout 23 per cent of the total electric power in the world comes from hydro power.

In Tamil Nadu. the total generation of power from hydroelectric plants amounts to
1950 MW and in all India level, it amounts to about 18000 MW.

Layout of a Hydro Power Plant

The layout of a hydro power plant is given in Fig. 17.7.

The  water  from  the  dam  is  brought  to  the  water  turbine  by  a  large  diameter penstock pipe. The penstock pipe is made of steel or reinforced concrete.

It is desirable to eliminate sharp bends in the penstock pipe to avoid the  loss of head and special anchoring.

Depending upon the load on the turbine, the amount of water needed is controlled automatically by a valve operated by a centrifugal governor.

In  case  the  amount  of  water  is  suddenly  reduced  or  stopped  by  the  governor mechanism.  water  coming  down  with  a  high  velocity  will  produce  turbulence
resulting in a water hammer in the pipe.

The penstock pipe may be damaged due to the water hammer. To prevent this, a surge tank is provided. From the turbine, water is allowed to pass through a draft tube to the tail race.

The tail race is the water path leading the discharge water from the turbine to the river or canal.

DIESEL POWER PLANT

• The layout of a diesel power plant is given in Fig. 17.6.

• Multicylinder 2-stroke turbocharged Diesel engines are used in power plants. In turbocharged engine,

• The atmospheric air is compressed by a compressor run by an exhaust driven gas turbine and the compressed air is taken inside the cylinder.Due to this, mass of air intake  and  amount  of  fuel  burnt  will  be  considerably  increased  giving  rise  to increased output power and higher thermal efficiency.

• Due to turbo charging, the operating temperature of the engine  is  increased.  So the lubricating oil coming out of the engine should be cooled in an oil cooler.

• The  cooling  water  from  the  engines  is  normally  cooled  in  a  spray  tank  and recirculated. Due to high capacity, the engine is started by using com pressed air.

GAS TURBINES

• Gas turbines are used mainly for electric power generation and also in jet engines of aircrafts and in turbochargers of internal combustion (IC) engines.

• It  has  limited  application  in  marine  engines.  Gas  turbines  have  the  unique advantage of using any type of fuel, i.e. solid, liquid or gas.

• Gas turbines operate either on an open cycle or in a closed cycle.

Working of an Open Cycle Single Stage Gas Turbine

• A simple open cycle gas turbine is represented in Fig. 17.3(a).

• It consists of a compressor, a combustion chamber and a turbine.

• The compressor and turbine co by a common shaft with a suitable flange.

• Air from the atmosphere is taken and compressed to a pressure ratio ranging from 2-8 before assing to the combustion chamber where the fuel is injected.

• The fuel burns and the temperature is raised at constant pressure. Then, it passes to the turbine where it expands to its original pressure before being exhausted to atmosphere. Fig. 17.3 (b).

Advantages of Gas Turbines

1. Possibility to use any type of fuel.

2. Compact size, less weight and low space requirement.

3. Simple foundation and low installation cost.

4. Less requirement of lubrication oil, water, etc.

5. Vibration is less.

Disadvantages of Gas Turbines

1. High operating temperature in the combustion chamber and in the turbine. So we need special high temperature alloys.

2.  Thermal  efficiency  is  very  low  in  the  case  of  simple  gas  turbine  due  to  high temperature of about 450° C in the waste exhaust gases.
and also for cooling.

Methods to Improve the Thermal Efficiency of a Single Stage Gas Turbine

1.By using a regenerator to heat the compressed air before entering the
combustion chamber as in Fig. 17.4 thereby making use of the heat in the exhaust gases before
leaving to the atmosphere.

2.   By   using   a   multistage   compressor   with   intercooling   to   reduce   the   work   of compression.

3.  By  using  a  multistage  turbine  to  reduce  the  temperature  of  exhaust  gases  before leaving the turbine.

Closed Cycle Gas Turbine

The closed cycle plant can use some stable gas with a higher specific heat as the working medium.

Instead   of   burning   the   fuel  directly   in   the   air   steam,   an   externally   fired combustion  chamber  or  furnace  is  used  and  heat  is  transferred  to  the  working medium through a heat exchanger.

Intercooler is also provided to improve the overall efficiency of compressions.

As  a  multistage  turbine  is  used,  the  temperature  of  exhaust  gases  leaving  the turbine is considerably reduced resulting in a higher thermal efficiency.

The regenerator preheats the gas before entering the furnace. By these provisions, the thermal efficiency is further increased to about 30 per cent.

The closed cycle has the following advantages:

1. Flexibility as to the type of fuel.

2. Uncontaminated working medium, and hence maintenance is easier.

3. Possibility of using a gas having better thermal properties as the working medium. By using an inert gas with high specific heat, the unit will become compact.

NUCLEAR POWER PLANT

A nuclear power plant is very similar to a conventional steam power plant except  for  the  furnace.  The  nuclear  reactor  becomes  the  furnace  in  this case.

It  has been estimated that  complete  fission of 1  kg of uranium produces heat energy equivalent to 4500 tons of coal or 1700 tons of oil.

Some of the important commercial reactors commonly used for power generation are given below:

1. Boiling water reactor (BWR)

2. Pressurized water reactor (PWR)

3. Gas cooled reactor (GCR)

Boiling Water Reactor

• A simple boiling water reactor is shown in Fig. 17.2.

• Due  to  nuclear  fission  of  the  fuel  uranium,  large  amount  of  heat  is produced.

• The   nuclear   reaction   and   thereby   the   temperature   is   controlled   by moderators.

• The  coolant  used  here  is  water  which  absorbs  the  heat  produced  in  the reactor. Water evaporates and steam is generated in the reactor itself.

• In this type of power plant. there is no need for a separate boiler.

• The steam produced in the reactor is used to run the turbine coupled with a generator from which we get the electrical power.

• The steam after expansion i the turbine is condensed in the condenser. The condensate  after  getting  heated  in  several  feed  water  heaters  is  pumped again into the reactor by means of feed pump.

• In  the  reactor,  the  thermal  shielding  reduces  the  heat  loss  and  th  thick concrete shielding prevents external radiation.

• In the primary loop, the pressuriser maintains a high pressure in the water in the range of 150 bar. Due to the high pressure of water in the reactor, the water does not boil.

• The coolant  gets heated  in the reactor and the  hot water goes to the boiler and transfers the heat to the feed water in the boiler in the secondary loop.

• The  feed  water  evaporates  and  becomes  steam and  runs a  turbo  generator  from which power is obtained. Functions of various parts of the reactor are the same as those of a boiling water reactor.

Gas Cooled Reactor

• The schematic diagram of a gas cooled reactor is shown in Fig. 17.2(b).

• In this, gas CO is employed as coolant and the heat carried by the gas from the reactor is either used for steam generation in the secondary circuit like pressurized water  reactor  or  is  directly  used  as  the  working  fluid  in  a  gas  turbine  plant. Usually the gas used is CO and graphite is the moderator.

• C  O gas gets heated in the reactor and loses its heat to the superheater, evaporator and economiser tubes in the secondary loop.

• The cooled gas is recirculated again in the primary loop by means of a gas blower. The superheat ed steam is expanded in the turbine to run the generator to produce electrical power.

Advantages of a Nuclear Power Plant

1. Very large amount of heat is liberated by a very small quantity of fuel

2. Suitable for large power generation

3. Cost of fuel transportation and storage is less.

Disadvantages

1.Installation cost is very high.

2. Availability of nuclear fuel is scarce and cost is high.

3. Large number of trained and qualified personnel are required to oper ate the plant.

4. Maintenance cost is higher.

5.  We  have  the  problems  involved  in  waste  disposal  and  also  the  risk  of  radiation
hazards.

STEAM POWER PLANT

The layout of a steam power plant is given in Fig

• Steam from the boiler is taken to the turbine through the steam pipe fitted with an expansion joint.

• The joint provides a flexible connection to prevent any crack in the steam pipe which   is  subjected  to   expansion  and  contraction  due  to  the  variation  of temperature.

• From the turbine, the steam enters a condenser, details of which are shown in Fig.   In the condenser, the exhaust steam from the turbine is condensed due to which a high vacuum is produced.

• Due to the vacuum, the power output and the thermal efficiency of the turbine are considerably in creased.

• In the condenser, cooling water is circulated by a pump through the water tubes to condense the exhaust steam.

• The cooling water at the outlet becomes hot and it is taken to a cooling pond or a cooling tower to cool and to recalculate the same water if the power plant is not located on the bank of a river or a lake.

The condensate from the condenser before entering the boiler is subjected to the
following treatments.

1. Removal of air and oxygen

2. Preheating the feed water in different stages using low pressure heater (LPH) deaerator
and high pressure heater (HPH).

Air and oxygen are removed at the air ejector and the deaerator. In case, air and oxygen
are not removed from the feed water, the vacuum cannot he main tained in the condenser, resulting in loss of power and thermal efficiency.

Factors to be Considered in the Selection of a- Site for a Steam Power Plant

1.  The  location  of  the  plant  should  be  at  a  minimum  distance  from  the  load  centre
(consumer) to avoid transmission losses.

2. Availability of water is a desirable factor.

3. The water should be preferably free from salt to reduce the cost for water treatment.

4. The soil should be satisfactory for a strong foundation.

5.  The  site  should  be  away  from  the  thickly  populated  area  to  reduce  the  effect  of pollution.

INTRODUCTION TO POWER PLANTS

Power plants are used for the generation of electric power.   
In  1950.  the  total  installed  capacity  in  Tamil  Nadu  was  only  156    MW
which has    been increased to about 5473 MW in 1990.

On all India basis, the figures in the same period were 2301 MW and 6393
MWrespectively.

In  India,  the  per  capita  consumption  of  electricity  was  only 12  kWh  in
1950    which has increased to about 280 kWh in 1990 while in Japan, it
has gone as high as 5633 kWh.

CLASSIFICATION OF POWER PLANTS

Power plants can be mainly classified as follows:

1. Steam power plant

2. Nuclear power plant

3. Gas turbine power plant

4. Diesel power plant

5. Hydro power plant

6. Power from alternate sources of energy

HEAT EXCHANGERS

INTRODUCTION

• The devices that are used to facilitate heat transfer between two or more fluids at different temperatures are known as heat exchangers.

• Different types and sizes of heat exchangers are used in steam power plants, chemical processing units, building heating and air conditioning, house hold refrigerators, car radiators, radiators for space vehicles etc.

• This chapter deals with classification of heat exchangers, the overall heat transfer coefficient, LMTD, NTU method and Effectiveness of heat exchangers.

CLASSIFICATION OF HEAT EXCHANGERS

Heat exchangers are broadly classified based on the following considerations.

1. Classification based on Transfer Process

Based on heat transfer process heat exchangers are classified as direct contact and indirect contact


a) Direct contact

In direct contact heat exchangers, heat transfer takes place between two immiscible fluids like a gas and a liquid coming into direct contact.

e.g.: Cooling towers, jet condensers for water vapour, and other vapors utilizing water spray.

b) Indirect contact

In indirect - contact type of heat exchangers the hot and cold fluids are separated by an impervious surface. There is no mixing of the two fluids and these heat exchangers are also known as surface heat exchangers.

e.g: Automobile radiators.

2. Classification based on Compactness

The ratio of the heat transfer surface area on one side of the heat exchanger to the volume is used as a measure of compactness. The heat exchanger having a surface area density on anyone side greater than about 700 m2/m3 is known as a compact heat exchanger.

e.g.: Automobile radiators (1100 m2/m3),Gas turbine engines (6600 m2/m3),
Human lungs (20,000 m2/m3)

3. Classification based on type of construction

Based on the type of construction heat exchangers are classified as follows.

a) Tubular heat exchangers

• Tubular heat exchangers are available in many sizes, flow arrangements and types. They can withstand a wide range of operating pressures and temperatures.

• A commonly used design is shell-and-tube heat exchanger which consists of round tubes mounted on cylindrical shells with their axes parallel to that of the shell.

• The combination of fluids may be liquid-to-liquid, liquid-to -gas or gas-to-gas.

b) Plate heat exchangers

• In these types thin plates are used to affect heat transfer. The plates may be either smooth or corrugated.

• These heat exchangers are suitable only for moderate temperature or pressure as the plate geometry restricts the use of high pressure and temperature differentials.

• The compactness factor for plate exchangers ranges from 120 to 230 m2/m3.

c) Plate fin heat exchangers

• These heat exchangers use louvered or corrugated fins separated by flat plates. Fins can be arranged on each side of the plate to get cross-flow, counter-flow or parallel-flow arrangements.

• These heat exchangers are used for gas-to-gas applications at low pressures (10 atm.) and temperatures not exceeding 800°C.

• They also find use in cryogenic applications. The compactness factor for these heat exchangers is upto 6000 m2/m3.

d) Tube-fin heat exchangers

• Such heat exchanges are used when a high operating pressure or an extended surface is needed on one side. The tubes may be either round or flat.

• Tube-fin heat exchangers are used in gas- 252 Heat and Mass Transfer turbine, nuclear, fuel cell, automobile, airplane, heat pump, refrigeration, Cryogenics etc.

• The operating pressure is about 30 atm. and the operating temperature ranges from low cryogenic temperatures to about 870 Dc.

• The maximum compactness ratio is about 330 m2/m3

e) Regenerative heat exchangers

• Regenerative heat exchangers may be either static type or dynamic type.

• The static type has no moving parts and consists of a porous mass like balls, pebbles, powders etc. through which hot and cold fluids pass alternatively.

e.g.: air preheaters used in coke manufacturing and glass melting plants.

• In dynamic type regenerators, the matrix is arranged in the form of a drum which rotates about an axis in such a manner that a given portion of the matrix passes periodically through the hot stream and then through the cold stream.

• The heat absorbed by the matrix from the hot stream is transferred to the cold stream during its run.

4. Classification based on flow Arrangement

Based on flow arrangement heat exchangers are classified into the following principal types.

a) Parallel-flow

In this heat exchanger, the hot and the cold fluids enter at the same end of the heat exchanger and flow through in the same direction and leave together at the other end as shown in Fig 5(a).

b) Counter flow
In this heat exchanger hot and cold fluids enter in the opposite ends of the heat exchanger and flow in opposite directions as shown in Fig 5(b).

c) Cross flow

In this heat exchanger, the two fluids flow at right angles to each other as shown in Fig 5 (c).
In this arrangement the flow may be mixed or unmixed.

In general, in a cross flow exchanger, three idealized flow arrangements are possible

1.    The fluids are unmixed
2.    One fluid is mixed, and the other is unmixed
3.    Both fluids are mixed.

d) Multipass flow
Since multi passing increases the overall effectiveness over individual effectiveness they are frequently used in heat exchanger design.

Different multipass flow arrangements are "One shell pass, two tube pass" known as "one - two" heat exchanger, "two shell pass, two  tube pass", etc. as shown in Fig 6.

5. Classification based on heat transfer mechanism

Heat exchangers are classified based on the following modes of heat transfer.

1.    Single phase forced or free convection.

2.    Phase change due to boiling and condensation.

3.    Radiation or combined convection and radiation.

RADIATION

INTRODUCTION

• If the radiation energy is emitted by bodies because of their temperature it is known as thermal radiation.

• The mechanism of radiation is not a simple phenomenon and several theories are proposed to explain the propagation of radiation.

• According to Maxwell's theory, “Radiation is considered as electromagnetic waves, whereas Max Planck's concept treats radiation as photons or quanta of energy. However, both accepts are used to predict the emission and propagation of radiation”.

CONVECTION

INTRODUCTION

• Convection is the mode of heat transfer which involves the motion of the medium that is involved.

• Convection heat transfer requires an energy balance along with the analysis of the fluCid dynamics of the problems considered.

• For basic understanding of convection heat transfer, some basic relations of fluid dynamics and boundary layer analysis are necessary. This chapter deals the concept of convection heat transfer in detail.

FLOW OVER A BODY

• The heat transfer by convection is strongly influenced by the velocity and temperature distribution of the immediate neighborhood of the surface of a body over which a fluid is flowing.

• For simple analysis of heat transfer involving convection, the velocity and temperature distribution at the boundary surface can be known by introducing the boundary - layer concept.

• Two different types of boundary layers are considered for this purpose viz., velocity boundary layer and thermal boundary layer.

VELOCITY BOUNDARY LAYER

• Consider a fluid flowing over a flat plate as shown in Figure 1. Let u∞ be the velocity of the fluid parallel to the plate surface at the leading edge of the plate at x =0.

• When there is no slip at the wall surface, the fluid moving, along the x direction that is in contact with the plate has no velocity. Thus the components of velocity   u(x, y) ≡ u retards along the x direction.

• Hence at the plate surface at y = 0 velocity u becomes zero. This retardation effect reduces considerably on the fluid moving at a sufficiently higher level (y - direction) and at one point the retardation effect is completely negligible.

• The velocity of the fluid at distance y = δ(x) from the surface of the plate where the axial velocity component u is 99 percent of the free stream velocity u∞.

• The locus of such points where u =0.99 u∞ is known as velocity boundary layer δ(x).

• The flow over the plate results in separation of flow field into two distinct regions.

Boundary layer region:


In this region the velocity gradients and shear stress are large due to the rapid variation of the axial velocity component u(x, y) with the distance y from the plate.
Potential flow region:

In this region the velocity gradient and shear stress are negligible. This region is the region outside the boundary layer.

•     This value is dependent on the surface roughness and the turbulence level of the free stream. In the turbulent boundary layer next to the wall, there is a very thin layer called viscous sub-layer in which the viscous flow character is retained by the flow.

•     The region adjacent to the viscous sub-layer is known as buffer layer. In this layer exists fine-grained turbulence and the mean axial velocity increases rapidly with the distance from the wall. The buffer layer is followed by turbulent layer with large scale turbulence.

•     The change in relative velocity with the distance from the wall is very little in this layer. Curved body Consider a curved body on the surface of which the fluid flows.

•     For a curved body the x co-ordinate is measured along the curved surface of the body starting from the stagnation point as shown in Fig. 2. The y co-ordinate is normal to the surface of the body.

•     In the above case, the free stream velocity is not constant but varies with distance along the curved surface. The thickness of boundary layer θ(x) increases with distance x along the surface. After some distance x, the velocity profile u(x, y) exhibits a point of inflection in which a y =0 at the wall surface.

•     This behavior is attributed purely to the curvature of the surface. Beyond this point flow reversal takes place and the boundary layer is detached from the surface. Beyond this point of flow reversal, boundary layer analysis is not applicable and flow patterns become very complicated.

DRAG COEFFICIENT

• Consider a boundary layer having a velocity profile u(x, y). The viscous shear stress 1"x acting on the wall at any given position x is given by,

HEAT CONDUCTION

INTRODUCTION

•  The term heat conduction is applied to the mechanism of internal energy exchange from one Body to another, or from one part of the body to another part, by the exchange of kinetic energy of motion of the molecules by direct communication or by the drift of free electrons in the case of I heat conduction in metals.

• This energy transfer takes place from the higher energy molecules to the lower energy molecules. Conduction usually takes place within the boundaries of a body, or across the boundary of a body into another body placed in contact with the first without any appreciable displacement of the matter comprising the body.

ONE AND THREE DIMENSIONAL HEAT CONDUCTION EQUATIONS

•     Consider a one dimensional system as shown in Fig 1.

•     In the steady state system, the Temperature doesn't change with time.

•     If the temperature changes with time the system is known as unsteady state system.

•     This is the general case where the temperature is not constant.

Velocity Diagrams For Simple and Multistage Turbines

The simple impulse (DE LAVAL) turbine:

• The first commercial steam turbine is the De Laval impulse turbine, which in its elementary form consists of one ring of moving blades, mounted around the periphery of a wheel. The velocity of steam is increased by passing the steam through a group of nozzle placed partially around the periphery of the wheel where expansion takes place from boiler pressure down to exhaust pressure.

•  The high velocity steam when allowed to impinge on the moving blades exerts a force on the blades and produces shaft work. Since the primary force on the blades is due to the high velocity steam jet, this type of turbine is classified as an impulse turbine. The pressure and velocity variation of steam during its flow through the nozzle and the turbine are also indicated in the figure.

Velocity diagram

• The adiabatic flow of fluid through the blades of a turbine is governed by the bladesof a turbine is governed by the continuity, energy and momentum equations.  Theyare , respectively ,    

       

• The momentum equation is particularly important in determining the net force on the moving blades due to a change in fluid velocity. It is to be noted that since velocity is a vector quantity having magnitude as well as direction, the change in fluid velocity must be determined vectorally. 

• For the construction of vector diagrams the following notations are followed in this text

V= Absolute velocity of fluid

Vr= Relative velocity of fluid

Vw= Whirl velocity

Va= Axial velocity of flow

u = Velocity of the moving blades.

• The suffix ‘1’ or ‘2’ denotes the corresponding quantity at inlet or outlet as the case may be. The velocity diagrams are constructed by setting off absolute vectors from a selected origin. The velocity diagrams at inlet and exit of the moving blades are shown in figure. 

• The jet of steam strikes the moving blade with an absolute velocity of V1 at an angle of a1 to the tangent, a1 being termed as the nozzle angle, the tangential component Vw1 at inlet does work on the moving blades as it is the same direction of motion. 

• The axial component Va1 is perpendicular to the direction of motion and hence, does no work on the blades. But the velocity of flow causes steam to flow through the turbine axially and due to this component there will be axial thrust on the rotor. 

• Since the blade is moving with a velocity of u, the stream jet reaches the blade with a relative velocity of Vr1 and is obtained by vectorial subtraction, as shown. The angle between the relative velocity and the tangent is b1, the entrance angle of moving blade required for shockless flow of steam.

   

• The jet leaves the moving blades with a relative velocity of Vr2 whose direction for

            shockless exit, is at an angle b2 to the tangent. The absolute velocity V2 of the stream

            jet leaving the moving blade is obtained by adding vectorially the blade velocity u

            with the relative velocity Vr2. a2 is the angle between the absolute velocity V2 and

            the tangent.

• The tangential component of V2 is Vw2, which is the whirl velocity at exit of the moving blade. Since the blade velocity u is common for both, it is usual to combine the entrance and exit velocity triangles on this common base and figure shows this.