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Lectut MIN 210 PDF 02 Steam Generators 5f7Vpu5

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RAVI KUMAR Boilers
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Page 1: Lectut MIN 210 PDF 02 Steam Generators 5f7Vpu5

RAVI KUMAR

Boilers

Page 2: Lectut MIN 210 PDF 02 Steam Generators 5f7Vpu5

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� A BOILER is an enclosed pressure vessel where heat

generated through the combustion of fuel is used for

converting water into steam.

� The volume of water increases 1600 times when

converted into steam.

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 2

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…boilers

� Boiler is an gadget to produce steam

� Thermal energy released through combustion of fuel is

used to generate steam at the desired temperature and

pressure.

� The steam is expanded in steam engine or steam turbine

to produce mechanical work.

� Process Industries

� HVAC applications

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 3

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…boilers

� IBR Steam Boiler

� Any closed vessel exceeding 5 gallons of volume i.e. 22.75 liters

and used for steam generation under pressure (Section 28&29

IBR act.).

� IBR Steam Pipe

� Any pipe through which steam passes from a boiler to a prime

mover or other user or both, if pressure at which steam passes

through such pipes exceeds 3.5 kg/cm2 gauge or such pipe

exceeds 254 mm in diameter.

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 4

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Boiler Systems

� Water Treatment system

� Feed Water system

� Steam System

� Blow down System

� Fuel Supply system

� Air Supply system

� Flue Gas system

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 5

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Type of Boilers

� Fire Tube Boiler

� Water Tube Boiler

� Packaged Boiler

� Fluidized Bed Combustion Boiler

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 6

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Fire Tube Boilers

Fire tube boilers, typically have a lower initial cost, are more fuel

efficient (82%) and easier to operate, but they are limited generally

to capacities of 25 tons/hr and pressures of 17.5 kg/cm2. The

steam variation is less.

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Water Tube Boilers

� Used in Power Plants

� Steam Capacity 4.5-120 T/hr

� High Capital Cost

� Used for high pressure high

capacity steam boiler

� Demands more control

� Calls for very stringent water

quality

� More efficient than fire tube

boiler.

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 8

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Merits of water tube boiler over fire tube boiler

� Steam generation is quick as the saturation temperature in

attained in short time.

� Large evaporative capacity and the steam pressure can go

up to -20 MPa.

� Heat exchange is effective as the flue gases travel at right

angles to the direction of water flow.

� High combustion efficiency due to complete combustion of

fuel in the larger space of shell.

� Uniform temperature due to quick circulation of water

keeps the thermal stresses low.

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 9

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…merits of water tube boiler over fire tube boiler

� Easy to transport and erect.

� Damage due to the bursting of water tube is less

serious. Therefore, water tube boilers are sometimes

called safety boilers.

� All parts of the water tube boilers are easily accessible

for cleaning, inspecting and repairing.

� The water tube boiler's furnace area can be easily

altered to meet the fuel requirements.

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 10

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eeDemerits

� It is less suitable for impure and sedimentary water, as a small

deposit of scale may cause the overheating and bursting of

tube. Therefore, use of pure feed water is essential.

� They require careful attention. The maintenance costs are

higher.

� Failure in feed water supply even for short period is liable to

make the boiler over-heated.

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 11

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Advantages of Fire Tube Boiler

� Low cost

� Fluctuations of steam demand can be met easily

� It is compact in size.

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 12

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Classification of water tube boilers

� Horizontal straight tube boilers

� Longitudinal drum

� Cross-drum.

� Bent tube boilers

� Two drum

� Three drum

� Low head three drum

� Four drum.

� Cyclone fired boilers

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 13

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…classification of water tube boilers

� According to position of furnace.

� i) Internally fired

� (ii) Externally fired

� In internally fired boilers the grate combustion chamber are

enclosed within the boiler shell, whereas, in case of extremely

fired boilers and furnace and grate are separated from the

boiler shell.

� According to the position of principle axis

� i) Vertical (ii) Horizontal (iii) Inclined

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 14

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…classification of water tube boilers

� According to application

� i) Stationary (ii) Mobile, (Marine, Locomotive)

� According to the circulating water

� i) Natural circulation (ii) Forced circulation

� According to steam pressure

� i) Low pressure (ii) Medium pressure (iii) Higher pressure

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 15

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Packaged Boiler

� Generally shell type with fire

tube design

� High heat release rate in small

combustion space

� More number of passes

� Large number of small diameter

tubes leading to good

convective heat transfer

� Higher thermal efficiency

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 16

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…packaged boiler

� Small combustion space and high heat release rate

resulting in faster evaporation.

� Large number of small diameter tubes leading to good

convective heat transfer.

� Forced or induced draft systems resulting in good

combustion efficiency.

� Number of passes resulting in better overall heat

transfer.

� Higher thermal efficiency levels compared with other

boilers.February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 17

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Fluidized Bed Boiler

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 18

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eeBoilers

� Lancashire Boiler

� Cochran Boiler

� Locomotive boiler

� Babcock Wilcox Boiler

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Lankashire Boiler

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Lankashire Boiler

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 21

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Lankashire Boiler

� It is a stationary, fire tube, internally fired boiler. The size isapproximately from 7-9 meters in length and 2-3 meters indiameter.

� It is stationary fire tube, internally fired, horizontal, naturalcirculation boiler.

� This is a widely used boiler because of its good steaming qualityand its ability to burn coal of inferior quality.

� It has two large internal flue tubes having diameter between 80cm to 100 cm in which the grate is situated.

� This boiler is set in brickwork forming external flue so that theexternal part of the shell forms part of the heating surface.

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 23

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Construction of Lancashire Boiler

� Cylindrical shell

� Furnace tubes, bottom flue and side flues

� Grate

� Fire bridge

� Dampers

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 24

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Features of Lankashire Boiler

� The feed pipe projecting into the boiler is perforated to ensure

uniform water distribution.

� Heating surface area per unit volume is considerably large.

� Maintenance is easy.

� Suitable where a large reserve of hot water is needed.

� This boiler due to the large reserve capacity can easily meet

load fluctuations.

� Super-heater and economizer can be easily incorporated into

the system, therefore; overall efficiency of the boiler can be

considerably increased(80-85%).

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 25

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Mountings

� Pressure gauge and water level indicator provided at the front.

� Safety valve, steam stop valve, low water and high steam safety

valve and man-hole are provided on the top of the shell.

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…mountings

High steam low water safety valve

It is a combination of two valves. One is lever safety valve, which

blows-off steam when the working pressure of steam exceeds.

The second valve operates by blowing-off the steam when the

water level falls below the normal level.

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 27

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…mountings

Blow-off clock

It is situated beneath the front portion of the shell for theremoval of mud and sediments. It is also used to empty the waterin the boiler during inspection.

Fusible plug

It is provided on the top of the main flues just above the grate. Itprevents the overheating of the boiler tubes by extinguishing thefire when the water level falls below a particular level. A lowwater level alarm is mounted in the boiler to give a warning whenthe water level falls below the preset value.

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 28

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Cornish Boiler

� One large flue tube.

� Shell length 4- 7 m

� Shell diameter 1.25-1.75 m

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Chochran Boiler

� It is very compact and requires

minimum floor area.

� Any type of fuel can be used with

this boiler

� Well suited for small capacity

requirements.

� It gives about 70% thermal

efficiency with coal firing and about

75% with oil firing

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 30

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…Chochran Boiler

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Babcock and Wilcox boiler

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 32

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Babcock and Wilcox Boiler

� The evaporative capacity of this boilers is high compared with

other boilers (20 to 40 T/hr). The operating pressure lies

between 11.5 to 17.5 bar.

� The draught loss is minimum compared with other boilers.

� The defective tubes can be replaced easily.

� The entire boiler rests over an iron structure, independent of

brick work, so that the boiler may expand or contract freely.

The brick walls which form the surroundings of the boiler are

only to enclose the furnace and the hot gases.

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 34

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Locomotive Boiler

� Locomotive boiler is a horizontal fire tube type mobile boiler.

� The main requirement of this boiler is that it should produce

steam at a very high rate.

� Therefore, this boiler requires a large amount of heating

surface and large grate area to burn coal at a rapid rate.

� In order to provide the large heating surface area, a large

number of fire tubes are setup and heat transfer rate is

increased by creating strong draught by means of steam jet.

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 35

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Advantages

� Large rate of steam generation per square metre of heating

surface. To some extent this is due to the vibration caused by

the motion.

� It is free from brickwork, special foundation and chimney. This

reduces the cost of installation.

� It is very compact. The pressure of the steam is limited to about

20 bar.

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 38

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Boiler Mountings

� Components which are mounted over the body of the boiler

itself for the safety of the boiler and for complete control of the

process of steam genertion. They are integral part of the boiler.

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� As per IBR following mountings should be fitted:

� Two safety valves

� Two water level indicators

� Pressure gauge

� Fusible plug

� Steam stop valve

� Feed check valve

� Blowoff Cock

� Man and mud hole

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 40

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Safety Valve

� Blow off the steam when pressure exceeds the working

pressure.

� Dead weight Safety valve

� Spring loaded safety valve

� Lever safety valve

� High steam low water safety valve

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Dead weigh safety valve

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Lever Safety Valve

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Spring Loaded Safety Valve

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High Steam Low Water Safety Valve

� To blow off steam when pressure is high

� To blow off steam when water level is low

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Water Level Indicator

� v

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Fusible Plug

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Steam Stop Valve/Junction Valve

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Feed Check Valve

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Blow off Cock

� To empty the boiler

when it is required

to be cleaned.

� To reduce the water

level in case it is

high.

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Man Hole

� A opening in boiler through which a man can enter a boiler for

cleaning and inspection purposes.

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Boiler Accessories

� Installed either inside or outside the boiler to increase

efficiency of the boiler and to assist in the proper working of

the boiler.

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Various boiler accessories

� Air Pre heater

� Economise

� Super heater

� Feed Pump

� Injector

� Steam Trap

� Steam Separator

� Pressure Reducing Valve

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Air Preheater

� It is a waste heat recovery device which is placed in the path of

the waste flue gases going to the chimney thereby abstracting

heat from the flue gases and transferring it to air before it is

used for combustion.

� It is placed in the chimney above the preheater.

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Economiser

� It recovers a part of heat from the heat carried away in the flue gases up the chimney or stack and to utilize it for heating the feed water supplied to the boiler.

� Function: It is a device in which the waste heat of the flue gases is utilsed for heating the feed water.Advantages :

� The temperature range between various parts of the boiler is reduced which results in reduction of stresses due to unequal expansion.

� If the boiler is fed with cold water it may result in chilling the boiler metal.

� Evaporative capacity of the boiler is increased.

� Overall efficiency of the plant is increased.

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Superheater

� To increase the temperature of the steam above its saturation

point.

� Super heaters are heat exchangers in which heat is transferred

to the saturated steam to increase its temperature.

� Superheated steam has the following advantages :

Steam consumption of the engine or turbine is reduced.

Losses due to condensation in the cylinders and the steam

pipes are reduced.

Erosion of turbine blade is eliminated.

Efficiency of steam plant is increased.

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Steam Trap

� Steam traps are a type of automatic valve that filters out

condensate (i.e. condensed steam) and non-condensable gases

such as air without letting steam escape.

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Steam Separator

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Feed Pump

� To pump feed water to the boiler.

� The reciprocating pumps run by steam from the same boiler to

which water is to be fed.

� Rotary feed pumps are run either by a small steam turbine or

by an electric motor.

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HIGH PRESSURE BOILER

� Low pressure Boiler <20 bar

� Medium Pressire 20<p<75 bar

� High Pressure >75 bar

� Pressure higher than 75 bar goes up to 200 bar.

� Max stem temperature 600 oC.

� Forced circulation of water

� To avoid the resistance to flow parallel set of tube arrangement

is made.

� Small steam separation drum and sometimes free from drum.

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…high pressure boilers

� The efficiency and the capacity of the plant can be increased asreduced quantity of steam is required for the same powergeneration if high pressure steam is used.

� The forced circulation of water through boiler tubes providesfreedom in the arrangement of furnace, in addition to the reductionin the heat exchange area.

� The tendency of scale formation is reduced due to high velocity ofwater.

� The danger of overheating is reduced as all the parts are uniformlyheated.

� The differential expansion is reduced due to uniform temperatureand this reduces the possibility of gas and air leakages

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La-Mont Boiler

� First introduced by La-Mont

in the year 1925.

� The capacity of La-Mont

boiler is about 50 T/hr of

superheated steam at a

pressure of 170 bar and at a

temperature of 500 oC.

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…La-Mont boiler

� Small diameter tubes are used, so that high heat transfer rate is maintained.

� The multiple tubes circuit gives flexibility for suitable location of heat transfer equipment.

� A high evaporation rate is achieved in this boiler due to forced circulation of water.

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Benson Boiler� Capacity 150 T/hr at a pressure of 200

bar and at a temperature of 650 oC.

� This boiler has a unique characteristicof absence of steam separating drum.

� The entire process of heating, steamgeneration and superheating is done ina single continuous tube.

Economiser

� The feed water by means of the feedpump is circulated through theeconomiser tubes.

� Hot flue gases pass over the economisertubes and the feed water is preheated

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…Benson boiler

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…Benson boiler

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…Benson boiler

Salient features of Benson Boiler

� As there are no drums, the total weight of benson bolier is 20%

less than other boilers. This also reduces the cost of the boilers.

� As no drums are required, the transfer of the Benson parts is

easy. Majority of the parts may be carried to the site without

pre-assembly.

� Since no drum is used, this is an once-through boiler and the

feed water entering at one end is discharged as superheated

steam at the other end.

� 4Circulating pump and down comers are dispensed with.

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Loeffler Boiler

� Capacity 100 T/hr Pressure 140 bar. T= 500 oC

� Water is heated solely by the superheated steam

� Furnace heat is supplied to economizer and super heater only.

� This boiler can carry higher salt concentration.

� More compact than any indirectly heated boilers having natural circulation.

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…Loeffler boiler

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Velox Boiler

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Boiler Performance

� Evaporative capacity can be expressed in terms of:

� kg of steam/hr

� kg of hour/hr/m of heating surfacecs

� kg of steam/kg of fuel fired

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Boiler Efficiency

Combustion Efficiency

� indicates a burners ability to burn fuel measured by unburned

fuel and excess air in the exhaust.

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…boiler efficiency

Thermal Efficiency

indicates the heat exchangers effectiveness to transfer heat from

the combustion process to the water or steam in the boiler,

exclusive radiation and convection losses

Fuel to Fluid Efficiency

indicates the overall efficiency of the boiler inclusive thermal

efficiency of the heat exchanger, radiation and convection losses -

output divided by input.

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Heat Provided by Fuel

Gross Calorific Value

This is the theoretical total of the energy in the fuel. The gross

calorific value of the fuel includes the energy used for

evaporating the water in the combustion process. The flue gases

from boilers are in general not condensed. The actual amount of

heat available to the boiler plant is therefore reduced.

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Net calorific value

This is the calorific value of the fuel, excluding the energy in the

water vapour discharged to the stack in the combustion process.

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Calorific value of Fuel�

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 76

Bituminous coal 17- 23

Butane 49

Carbon 34

Charcoal 29

Coal (Lignite - Anthrasite) 15- 27

Coke 28- 31

Diesel 42

Ethanol 30

Kerosone 35

Lignite 16

Methane 55

Petrol 44

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Green Boiler Technology

� 98% thermal efficiency

� Environmentally Friendly, Ultra-Low NOx

� Less than 20ppm NOx (standard)

� Less than 10ppm NOx (optional)

� Thoughtful Design Reflects Lessons Learned in the Field

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 77

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eeExcess air

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 78

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Energy Performance Assessment of Boilers

� Evaporation rate

� Quantity of water evaporated in steam per hour expressed in

� kg of steam/hour

� kg of stem/hr/m2 of heating surface area

� kg of stem/hr/m3 of heating surface volume

� Kg of stem/hr/kg of fuel burnt

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Equivalent Evaporation

Equivalent of evaporation of one kg of water at 100 oC at

standard atmospheric pressure of 101.3 kPa. Hence, equivalent

evaporation of 1 kg of water needs 2257 kJ of energy.

� =�� ℎ� − ℎ�

2257

Ms = kg of steam/kg of fuel

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Factor of Evaporation

Ratio of heat absorbed by 1 kg of feed water under working

conditions to that absorbed by 1 kg of water from and at 100 oC

and 101.3 kPa pressure.

� =ℎ� − ℎ�

2257

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Boiler Efficiency

Ratio of heat energy utilized by feed water for steam formation to

the generation of heat energy supplied by fuel.

� =�� ℎ� − ℎ�

� ��

Ma mass of steam/h

Mf mass of fuel/h

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 82

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Heat Loss in Boilers

� Hot flue gases

� Radiation from furnace

� Incomplete combustion

� Presence of moisture in fuel

� Unburnt fuel going to ash pit

� Boiler design

� Properties and characteristics of fuel

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Boiler Power

ASME has recommended a unit called boiler power which may be

used to measure the capacity of boiler.

������ ����� =�������� ����������� ��� ℎ��� ��� �� 100 �"

21.296

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Numerical #1

Calculate the equivalent evaporation and efficiency of the boiler for the following data:

Pressure of steam 900 kPa

Quality 0.9

Quantity of steam 5000 kg/h

Feed water temperature 30 oC

Coal consumption 700 kg/h

C.V. of coal 31.4 MJ/kg

What will be the saving in coal consumption per hour if the by puttingan economizers the temperature of feed water is raised to 95 oC andother data remains the same except the boiler efficiency by 5%.

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Numerical #2

A boiler generates steam at 1.6 MPa pressure and 320 oCtemperature. The feed water temperature is 60 oC. Thecalorific value of fuel fired in the boiler is 46.8 MJ/kg. theultimate analysis of fuel gives C=85% and H2=15%. Calculate:

• minimum quantity of air required for complete combustionof the fuel

• Gross Calorific value of fuel

• overall efficiency of boiler if the steam produced is 13 kg/kgof fuel fired.

Latent heat of water vaour in the flue gases may be assumedas 2510 kJ/kg.

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Boiler Trial

� To determine the efficiency of boiler.

� To estimate evaporative capacity of boiler.

� To draw up the heat balance sheet of the boiler.

� CV OF Fuel

� Heat utilized for steam raising

� Heat carried away by flue dry gases

� Heat carried away by the moisture

� Heat to surrounding air and unburnt fuel

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Numerical #3

� During the boiler trial following data were obtained:

� Coal analysis dry: C=85.2%, H=4.8%, ash = 10%, GCV of dry coal

35 MJ/kg; moisture content 1.8%; coal consumption 1450 kg/h;

Boiler room temperature 25 oC; feed water temperature 55 oC;

steam pressure 1.2 MPa, steam temperature 250 oC; steam

raised 12500 kg/h; Analysis of dry flue gases by volume of

gases: CO2 =9.4%, O2 =11.1%, N2= 79.5%. The temperature of

gases in the uptake was 300 oC. Mean specific of dry gases

1.005 kJ/kg.

� Prepare a complete balance sheet per kg of dry coal.

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…boiler trial� Steam generated per kg of coal

� Heat supplied per kg of coal

� 9:���� ��� ;����< = =>?

@@ ?">A?"kg/kg of coal

� Minimum air required per kg of dry coal

� Excess air

� Mass of flue gases = air + fuel (0.9)

� Mass of water in products = H2 conversion + moisture

� Mass of dry gas

� Mass of dry gasses excluding excess air

� Heat Loss in dry products

� Heat loss in excess air

� Heat loss in vapour in flue gases

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…boiler trial

� Heat supplied by coal

� Heat in steam

� Heat in dry products

� Heat in vapour and gas

� Heat in excess air

� Heat unaccounted

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DRAUGHT

� Small pressure difference causing flow of air and gases

through the boiler.

� It is essential to supply a sufficient quantity of air for

combustion and to remove the product of combustion.

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Type of Draught

� Natural

� Artificial

�Steam Jet

⁻ Induced

⁻ Forced

�Mechanical Jet

⁻ Induced

⁻ Forced

⁻ Forced

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Natural Draught

Difference between the pressure of column of hot gases in

chimney or stack and equal column if cold outside air.

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…draught

� + CD = �CD

2ED + CD=EDO

� = FGH

I

� = F0.287 × 273

101.3= 0.7734 F@

� = F0.287 × HN

101.3= F

HN

353

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Calculation of Chimney Height and Cross-section

Volume of air at NTP=GH

�= 0.7734 F@

Volume per kg of air at HN = 0.7734HN

273

Volume m kg of air at HN=0.7734HN

273F

Volume 1+m kg of air at H =0.7734H

273F + 1

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…calculation of chimney height and cross-section

Volume m kg of air at HN=0.7734HN

273F

���;��< �O ��� PN =273 × F

0.7734 × F × HN

PN = 1.293273

HN

PN =353

HN

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering

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…calculation of chimney height and cross-section

���;��< �O :ℎ�F��< Q�;�; P =273 × F + 1

0.7734 × F × H

P = 1.293F + 1

F

273

H

=F + 1

F

353

H

For the chimney height ‘H’ pressure drop

∆� = QE PN − P

∆� = 353QE1

HN

−F + 1

F

1

H

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Height of Hot gases Column

E =∆�

P Q

E = 353QE

1HN

−F + 1F

1H

F + 1F

.353HN

. Q

E = EF

F + 1

H

HN− 1

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Cross Section Area of Chimney

� = 2Q E − ∆E S

� = 4.43 E 1 −∆E

E

S

� = T E S

K = 1.1 for steel chimney and 0.825 for brick chimney

1.1 = 4.3 1 −∆E

E

S

∆E

E

=18.4

19.6

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Artificial draught

� Advantages

� Capable of consuming low grade fuel

� Increase in evaporative power of boiler

� Easy control of combustion and evaporation

� Reduction of chimney height

� Prevention of smoke

� Improved efficiency

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Draft

� Induced Draft Fan type

� Forced Draft Fan Type

Advantages of forced draft over induced draft

Small fan size

No water cooled bearing

Less leakage

No heat loss

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THE END

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Chimney Efficiency

Ratio of the energy equivalent of draught produced by the fan

and the additional heat carried away by the gases in natural

draught system.

UVWXYZ[\ =E

:] H − H ,

February 16, 2016 Prof. Ravi Kumar, Department of Mechanical & Industrial Engineering 103


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