Chapter III

Super-Critical Boiler Material

Selection

3.1 Introduction [6]

Supercritical Boiler materials are advanced alloy to withstand the steam

temperature at above 700’C. And fulfill the all required criteria of boiler material

properties. As now a days well advanced technology is available for the

subcritical boilers. But the technology for the supercritical boilers are under

research, so only few finger counting manufactures are developing the

supercritical Boiler Materials. That companies as follows,

1) Haynes International[21]

2) Special Metals [22]

3.2 Properties of Material For Selection

Here properties of material affecting on the selection criteria as given bellow,

1) Thermal Conductivity (W/m’K)

2) Mean Coefficient of Thermal Expansion(um/m-‘C)

3) 0.2% Yield Strength(MPa)

4) Stress Rupture Strength (Rupture for 10000 Hours)MPa as creep Strength

5) Dynamic Modulus of Elasticity (GPa)

6) Specific Heat (J/Kg-‘K)

7) Density(gm/cm3)

8) Melting Point (‘C)

9) Cost (USD/kg)

3.2.1. Thermal Conductivity (W/m K)

In physics, thermal conductivity, k, is the property of a material's ability to

conduct heat. Heat transfer across materials of high thermal conductivity occurs

at a faster rate than across materials of low thermal conductivity.

Correspondingly materials of high thermal conductivity are widely used in heat

sink applications and materials of low thermal conductivity are used as thermal

insulation.

In Supercritical Boilers selecting the material on the High Conductivity Basis. So

that this property is considered as beneficial property.

Thermal conductivity of materials is temperature dependent. In general,

materials become more conductive to heat as the average temperature

increases.

In the International System of Units (SI), thermal conductivity is measured in

watts per meter kelvin (W/(m·K)).

3.2.2 Mean Coefficient of Thermal Expansion(um/m-‘C)

When a substance is heated, its particles begin moving more and thus usually

maintain a greater average separation. Materials which contract with increasing

temperature are rare; this effect is limited in size, and only occurs within limited

temperature ranges (see examples below). The degree of expansion divided by

the change in temperature is called the material's coefficient of thermal

expansion and generally varies with temperature.

In Supercritical Boilers selecting the material on the Low Mean Coefficient of

Thermal Expansion since boiler is on high fluctuating temperature load. So

that this property is considered as non -beneficial property.

In the International System of Units (SI) um/m-‘C.

3.2.3 0.2% Yield Strength(MPa)

The point in the stress-strain curve at which the curve levels off and plastic

deformation begins to occur.

In Supercritical Boilers selecting the material on the high 0.2% Yield

Strength(MPa). So that this property is considered as beneficial property.

In the International System of Units MPa.

3.2.4 Stress Rupture Strength (Rupture for 10000 Hours)MPa as creep

Strength :-

The ability of a metal to withstand a constant weight or force at elevated

temperatures.

In Supercritical Boilers selecting the material on the high Stress Rupture

Strength (Rupture for 10000 Hours)MPa as creep Strength So that this property

is considered as beneficial property. In the International System of Units MPa.

3.2.5 Dynamic Modulus of Elasticity (GPa)

An elastic modulus, or modulus of elasticity, is the mathematical description of

an object or substance's tendency to be deformed elastically (i.e., non-

permanently) when a force is applied to it. The elastic modulus of an object is

defined as the slope of its stress–strain curve in the elastic deformation region:[1]

As such, a stiffer material will have a higher elastic modulus.

where lambda (λ) is the elastic modulus;

In Supercritical Boilers selecting the material on the high Dynamic Modulus of

Elasticity, So that this property is considered as beneficial property. In the

International System of Units GPa.

3.2.6 Specific Heat

Heat capacity (usually denoted by a capital C, often with subscripts), or

thermal capacity, is the measurable physical quantity that characterizes

the amount of heat required to change a substance's temperature by a

given amount.

In Supercritical Boilers selecting the material on the Low Specific Heat Capacity,

So that this property is considered as Non - beneficial property.

In the International System of Units (SI), heat capacity is expressed in

units of joule(s) (J) per kelvin (K).

3.2.7 Density (gm/cm3)

The mass density or density of a material is defined as its mass per unit

volume.

This is generally measured by taking a cubic centimeter of a substance (cm^-3).

In Supercritical Boilers selecting the material on the Low Density, So that this

property is considered as Non-beneficial property.

In the International System of Units gm/cm3 .

3.2.8 Melting Point(‘C)

The melting point of a solid is the temperature at which it changes state

from solid to liquid. At the melting point the solid and liquid phase exist in

equilibrium. The melting point of a substance depends (usually slightly) on

pressure and is usually specified at standard atmospheric pressure.

In Supercritical Boilers selecting the material on the High Melting Point, So that

this property is considered as beneficial property

In the International System of Units Degree Celsius .

3.2.9 Cost (USD/kg)

It is the cost price per unit mass.

Unit is USD/kg

3.3 Material Alternatives for Selection & Composition of

Material

1) 120-Haynes HR-120;

2) 214-Haynes 214;

3) 230-Haynes 230;

4) 602-RA 602 CA;

5) 321-Incoloy-321-347;

6) 617- Incoloy-617;

7) 625- Inconel alloy 625;

8) 718 - Incoloy-718;

9) 800H-Incoloy-800H-800HT;

10) 160 Haynes HR-160 R;

11) 242 Haynes 242 alloy;

12) 556 Haynes 556 Alloy;

13) X Hastelloy X alloy.

3.3.1.Material Composition

Material composition of Haynes HR-120 is Fe 33%, Ni 37%, Co 3%, Cr 25%, Mo

2.5%, W 2.5%, Cb 0.7%, Mn 0.7%, Si 0.6%, N 0.2%, Al 0.1%, C 0.05%, B0.004%,

[23] furnished in the solution annealed condition, unless otherwise specified.

Depending on the product form, the alloy is solution annealed at a temperature

ranging from 2150 to 2250 deg. F (1175 to 1230 deg. C) and rapidly cooled.

provides excellent strength at elevated temperature combined with very good

resistance to carburizing and sulfidizing environments. Its oxidation resistance is

comparable to other widely used Fe-Ni-Cr materials; Applications include those

which require high strength combined with good resistance to carburizing and

sulfidizing environments.

Material composition of Haynes (HR-214) is Ni 75%, Cr 16%, Al 4.5%, Fe 3%, Mn

0.5%, Si 0.2%, Zr 0.1%, C 0.05%, B 0.01%, Y 0.01%[24] the solution heat-treated

condition, unless otherwise specified. The alloy is normally solution heat-treated

at2000°F (1095°C HAYNES 214 alloy combines properties which make it very

suitable for service in relatively low-stress, high temperature oxidizing

environments, where the utmost in resistance to oxidation or scale exfoliation is

needed. Its resistance to such environments persists to temperatures as high as

2400°F (1315°C),

Haynes 230 is composed of Ni 57%, Cr 22%, W 14%, Mo 2%, Fe 3%, Co 5%, Mn

0.5%, Si 0.4%, Al 0.3%, C 0.10%, La 0.02%, B 0.015% [25]. HAYNES® 230® alloy

is a nickel chromium-tungsten-molybdenum alloy that combines excellent high-

temperature strength, outstanding resistance to oxidizing environments up to

2100°F (1149°C) for prolonged exposures, premier resistance to nitriding

environments, and excellent long-term thermal stability. Also it has excellent

forming and welding characteristics. HAYNES 230 alloy combines properties

which make it ideally suited for a wide variety of component applications in the

aerospace and power industries.

Nominal Chemical Composition, Weight Percent321-Incoloy-321-347 is composed of C 0.10%, Si 0.75%, Mn 2.00%, P 0.04%, S

0.03%, Cr 20.0%, Ni 13.0%, Nb & Ta 1% OMINAL[26] CHEMICAL

Material composition of 602-RA 602 CA is Cr 26.0%, C 0.25%, Al 2.4%, Ta 0.02%,

Y 0.12%, Zr 0.10%, Mn 0.15%, Si 0.5%, Fe 11.0% and balance is Nickel [27]. RA

602 CA provides some of the best combined high temperature properties of any

nickel alloy available. RA 602 CA is one of the most oxidation resistant nickel

alloys. A high chromium content, along with aluminum and yttrium additions,

permits the alloy to develop a tightly adherent oxide scale. RA 602 CA may be

considered for applications where it is important to minimize product

contamination while maintaining high mechanical integrity at extreme

temperatures.

Material composition of 617-Incoloy-617 comes as Ni 54%, Cr 22%, Mo 9%, Fe

1%, Co 12.5%, Ti 0.3%, Al 1.2%, C 0.07% [28]. This alloy is a nickel – chromium –

cobalt – molybdenum alloy with a good combination of metallurgical stability,

strength & oxidation resistance at high temperature. This alloy is readily formed

& welded by conventional techniques.

Inconel alloy 625 has the following materials in composition - Ni 62%, Co 1%, Fe

5%, Cr 21%, Mo 9%, Cb & Ta 3.7%, Mn 0.5%, Si 0.5%, Al 0.4%, Ti 0.4%, C 0.10%

[29]. Alloy 625 has good oxidation resistance at temperatures up to

1800°F(980°C) and provides good resistance to aqueous corrosion, but generally

not as effectively as modern HASTELLOY® corrosion resistant alloys. It provides

excellent service in short term applications at temperatures up to approximately

1500°F (815°C); however, for long-term elevated temperature service, use of

alloy 625 is best restricted to a maximum of 1100°F (595°C). Long-term thermal

exposure of alloy 625 above 1100°F (595°C) will result in significant

embrittlement.

Material composition of 718 Incoloy-718 is Ni 52%, Co 1%, Fe 19%, Cr 18%, Mo

3%, Cb & Ta 5%, Mn 0.35%, Si 0.35%, Al 0.5%, Ti 0.9%, C 0.05%, B 0.009%, Cu

0.1% [21]. HAYNES 718 alloy is normally only used for component applications

up to 1200°F (650°C); however, its oxidation resistance is comparable to that for

other gamma-prime strengthened super alloys. HAYNES 718 alloy is produced in

the form of sheet, strip, plate, bar, billet, wire, and tubular products.

Material composition of Haynes 160 is Ni 37%, Co29%, Cr 28%, Fe 2%, Si 2.75%,

Mn 0.5%, Ti 0.5%, C 0.05%, W 1%, Mo 1%, Cb 1% [30]. HR-160alloy is furnished

in the solution annealed condition, unless otherwise specified. The alloy is

solution annealed at 2050°F (1121°C) and rapidly cooled for optimum properties.

HAYNES HR-160alloy is covered by ASME Vessel Code case No. 2162 for Section

VIII Division 1 construction to 1500°F (816°C). HAYNESHR-160 alloy combines

properties which make it highly useful for service in severe high-temperature

corrosive environments.

Material composition of 800 Incoloy-800H-800HT comes as Ni 35%, Fe 39.5%, Cr

23%, Mo 3%, Cb & Ta 5%, C 0.10%, Al 0.60%, Ti 0.60% [31]

Material composition of Haynes HR-160 comes as Ni 37%, Co 29%, Cr 28%, Si

2.75%, Fe 2%, Mo 1%, W 1%, Cb 1%, Mn 0.5%, Ti 0.5%, C 0.05% [32]. It has

excellent resistance to sulfidation and chloride attack in both reducing and

oxidizing atmospheres The alloy also has exceptionally good resistance to

oxidation, hot corrosion, carburization, metal dusting, nitridation, and corrosion

attack by low melting point compounds such as those formed by phosphorus,

vanadium, and other impurities. HAYNESHR-160 alloy combines properties which

make it highly useful for service in severe high-temperature corrosive

environments.

Material composition of Haynes -242 becomes Ni 65%, Mo 26%, Cr 9.0%, Fe

2.0%, Co 2.5%, Mn 0.80%, Si 0.80%, Al 0.50%, C 0.03%, B 0.006%, Cu 0.50%

[33], that alloy is an age-hardenable nickel molybdenum-chromium alloy which

derives its strength from a long-range ordering reaction upon aging. It has

tensile and creep strength properties up to 13000F (7050C) which are as much

as double those for solid solution strengthened alloys, but with high ductility in

the aged condition. HAYNES 242 alloy combines properties which make it ideally

suited for a variety of component applications in the aerospace industry

Material composition of Haynes -556 is Fe 31%, Ni 20%, Co 18%, Cr 22%, Mo 3%,

W 2.5%, Ta 0.6%, N 0.20%, Si 0.4%, Mn 1%, Al 0.2%, C 0.10%, La 0.02%, Zr

0.02% [34], HAYNES® 556™ alloy is an iron-nickel-chromium-cobalt alloy that

combines effective resistance to sulfidizing, carburizing and chlorine-bearing

environments at high temperatures with good oxidation resistance, fabricability,

and excellent high-temperature strength. It has also been found to resist

corrosion by molten chloride salts and other salts, and is resistant to corrosion

from molten zinc. HAYNES 556 alloy combines properties which make it highly

useful for service at elevated temperature in moderately to severely corrosive

environments.

Material composition of hastelloy X alloy is Ni 47%, Cr 22%, Fe 18%, Mo 9%, Co

1.5%, W 0.6%, C 0.10%, Mn 1%, Si 1%, B 0.008% [35]. X alloy exhibits good

ductility after prolonged exposure at temperatures of 1200, 1400, 1600°F (650,

760 and 870°C) for 16,000 hours. X alloy has excellent forming and welding

characteristics. It can be forged and, because of its good ductility, can be cold

worked. Wrought forms of HASTELLOY X alloy are furnished in the solution heat-

treated condition unless otherwise specified. X alloy is solution heat-treated at

2150°F (1177°C) and rapid cooled. Bright annealed products are cooled in

hydrogen.

Here the “Alternatives” and “Criteria” are given below:

A1 120-Haynes HR

120;

C1 Thermal Conductivity

A2

214-Haynes 214; C2 Mean Coeff. Of Thermal Expansion

A3

230-Haynes 230; C3

0.2% Yield Strength

A4

602-RA 602 CA; C4 Stress-Rupture Strength (Rupture For 10000

Hours) as Creep Strength

A5

321-Incoloy-321-

347;

C5 Dynamic Modulus of Elasticity

A6

617- Incoloy-617; C6 Specific Heat

A7

625- Inconel alloy

625

C7 Density

A8

718 - Incoloy-718 C8 Melting Point

A9

800H-Incoloy-

800H-800HT;

C9 Cost

A10

160 Haynes HR-

160 R

A11

242 Haynes 242

alloy

A12

556 Haynes 556

Alloy

A13

X Hastelloy X alloy

3.4 Applying the Fuzzy Methods for the System

3.4.1 Preparation of Fuzzy Matrix.

Matrix of “Alternatives” vs. “Criteria” is given in table 6.3

Table 3.1: Alternatives vs. Criteria for Super critical boiler material selection

C1 C2 C3 C4 C5 C6 C7 C8 C9

A1 23.1 16.9 175

83 152

526.5

8.07

1300

10

A2 26.9 15.8 680

115

195

668 8.05

1400

10

A3 22.4 14.8 253

130

171

574 8.97

1370

10

A4 21.4 18.9 205

90 193

500 7.92

1446

65

A5 22.2 15.7 257

155

169

630 7.9 1400

80

A6 23.9 14.8 486

165

166

586 8.36

1380

4

A7 19.99

15.05

639

73 165

577 8.44

1350

60

A8 22.2 15.5 875

204

159

435 8.23

1336

1000

A9 22.8 17.5 93 76 150

460 7.94

1385

75

A10

24.7 15.7 353

75 163

653 8.08

1370

10

A11

22.5 13 925

166

185

595 9.05

1375

200

A12

24 16.4 205

86 115

561 8.23

1415

10

A13

22.9 14 423

82 188

607 8.22

1355

100

Now 10-35% deviation has been taken and DATA MATRIX has been found as in table 6.4

Table 3.2: Data for Super critical boiler material selection

C1 C2 C3 C4 C5 C6 C7 C8 C9

A1(18.48, 23.1,

27.72)(13.52,16.9,20.

28) (140,175,210) (66.4,83,99.6) (121.6,152,182.4) (421.2,526.5,631.8) (6.456,8.07,9.684) (1040,1300,1560) (8,10,12)

A2(18.83, 26.9,

34.97)(11.06,15.8,20.

54) (476,680,884) (80.5,115,149.5) (136.5,195,253.5) (467.6,668,868.4) (5.635,8.05,10.47) (980,1400,1820) (7,10,13)

A3(15.68, 22.4,

29.12)(10.36,14.8,19.

24) (177.1,253,328.9) (91,130,169) (119.7,171,222.3) (401.8,574,746.2) (6.279,8.97,11.66) (959,1370,1781) (7,10,13)

A4(16.05, 21.4,

26.75)(14.18,18.9,23.

63) (153.8,205,256.3) (67.5,90,112.5) (144.8,193,241.3) (375,500,625) (5.94,7.92,9.9) (1085,1446,1808) (48.75,65,81.25)

A5(18.87, 22.2,

25.53)(13.35,15.7,18.

06) (218.5,257,295.6) (131.8,155,178.3) (143.7,169,194.4) (535.5,630,724.5) (6.715,7.9,9.085) (1190,1400,1610) (68,80,92)

A6(21.51, 23.9,

26.29)(13.32,14.8,16.

28) (437.4,486,534.6) (148.5,165,181.5) (149.4,166,182.6) (527.4,586,644.6) (7.524,8.36,9.196) (1242,1380,1518) (3.6,4,4.4)

A7(14.99,19.99,24

.99)(11.29,15.05,18

.81) (479.3,639,798.8) (54.75,73,91.25) (123.8,165,206.3) (432.8,577,721.3) (6.33,8.44,10.55) (1013,1350,1688) (45,60,75)

A8(17.76,22.2,26.

64) (12.4,15.5,18.6) (700,875,1050) (163.2,204,244.8) (127.2,159,190.8) (348,435,522) (6.584,8.23,9.876) (1069,1336,1603) (800,1000,1200)

A9(19.38,22.8,26.

22)(14.88,17.5,20.

13) (79.05,93,107) (64.6,76,87.4) (127.5,150,172.5) (391,460,529) (6.749,7.94,9.131) (1177,1385,1593) (63.75,75,86.25)

A10(17.29,24.7,32.

11)(10.99,15.7,20.

41) (247.1,353,458.9) (52.5,75,97.5) (114.1,163,211.9) (457.1,653,848.9) (5.656,8.08,10.5) (959,1370,1781) (7,10,13)

A11 (18,22.5,27) (10.4,13,15.6) (740,925,1110) (132.8,166,199.2) (148,185,222) (476,595,714) (7.24,9.05,10.86) (1100,1375,1650) (160,200,240)

A12 (18,24,30) (12.3,16.4,20.5) (153.8,205,256.3) (64.5,86,107.5) (86.25,115,143.8) (420.8,561,701.3) (6.173,8.23,10.29) (1061,1415,1769) (7.5,10,12.5)

A13(16.03,22.9,29.

77) (9.8,14,18.2) (296.1,423,549.9) (57.4,82,106.6) (131.6,188,244.4) (424.9,607,789.1) (5.754,8.22,10.69) (948.5,1355,1762) (70,100,130)

3.5 Material Selection By Application Of Fuzzy AHP

Now pair wise comparison matrices for each criteria as follows:

Table 3.3: Pair wise comparison matrix W.R.T. Thermal Conductivity for Super critical boiler material selection

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 W

A1 (1,1,1)(0.793,0.859,0.

981)(0.952,1.03

1,1.179)(1.036,1.07

9,1.151)(1.086,1.04

1,0.979)(1.054,0.96

7,0.859)(1.109,1.15

6,1.233)(1.041,1.04

1,1.041)(1.057,1.01

3,0.954)(0.863,0.93

5,1.069)(1.027,1.02

7,1.027)(0.924,0.96

3,1.027)(0.931,1.00

9,1.153)

0.076,0.077,0.08

A2(1.019,1.16

5,1.262) (1,1,1)(1.201,1.20

1,1.201)(1.307,1.25

7,1.173)(1.37,1.212

,0.998)(1.33,1.126

,0.875)(1.399,1.34

6,1.256)(1.313,1.21

2,1.06)(1.334,1.18

,0.972)(1.089,1.08

9,1.089)(1.295,1.19

6,1.046)(1.166,1.12

1,1.046)(1.175,1.17

5,1.175)

0.095,0.09,0.082

A3(0.848,0.97

,1.051)(0.833,0.833,0.

833) (1,1,1)(1.089,1.04

7,0.977)(1.141,1.00

9,0.831)(1.108,0.93

7,0.729)(1.165,1.12

1,1.046)(1.093,1.00

9,0.883)(1.111,0.98

2,0.809)(0.907,0.90

7,0.907)(1.079,0.99

6,0.871)(0.971,0.93

3,0.871)(0.978,0.97

8,0.978)

0.079,0.075,0.069

A4(0.869,0.92

6,0.965)(0.852,0.796,0.

765)(1.024,0.95

5,0.919) (1,1,1)(1.048,0.96

4,0.851)(1.017,0.89

5,0.746)(1.071,1.07

1,1.071)(1.004,0.96

4,0.904)(1.02,0.939

,0.828)(0.833,0.86

6,0.928)(0.991,0.95

1,0.892)(0.892,0.89

2,0.892)(0.899,0.93

4,1.001)

0.074,0.072,0.069

A5(1.021,0.96

1,0.921)(1.002,0.825,0.

73)(1.203,0.99

1,0.877)(1.176,1.03

7,0.954) (1,1,1)(0.971,0.92

9,0.877)(1.022,1.11

1,1.259)(0.958,1,1.

063)(0.974,0.97

4,0.974)(0.795,0.89

9,1.091)(0.946,0.98

7,1.048)(0.851,0.92

5,1.048)(0.858,0.96

9,1.177)

0.075,0.074,0.076

A6(1.164,1.03

5,0.948)(1.142,0.888,0.

752)(1.372,1.06

7,0.903)(1.34,1.117

,0.983)(1.14,1.077

,1.03) (1,1,1)(1.052,1.19

6,1.435)(0.987,1.07

7,1.211)(1.003,1.04

8,1.11)(0.819,0.96

8,1.244)(0.974,1.06

2,1.195)(0.876,0.99

6,1.195)(0.883,1.04

4,1.342)

0.081,0.08,0.083

A7(0.811,0.86

5,0.901)(0.796,0.743,0.

715)(0.956,0.89

2,0.858)(0.934,0.93

4,0.934)(0.795,0.9,

0.979)(0.697,0.83

6,0.95) (1,1,1)(0.938,0.9,

0.844)(0.953,0.87

7,0.774)(0.778,0.80

9,0.867)(0.925,0.88

8,0.833)(0.833,0.83

3,0.833)(0.839,0.87

3,0.935)

0.067,0.067,0.067

A8(0.961,0.96

1,0.961)(0.943,0.825,0.

762)(1.133,0.99

1,0.915)(1.107,1.03

7,0.996)(0.941,1,1.

043)(0.826,0.92

9,1.013)(1.185,1.11

1,1.066) (1,1,1)(1.016,0.97

4,0.916)(0.83,0.899

,1.027)(0.987,0.98

7,0.987)(0.888,0.92

5,0.987)(0.895,0.96

9,1.108)

0.075,0.074,0.075

A9(1.049,0.98

7,0.946)(1.029,0.848,0.

75)(1.236,1.01

8,0.9)(1.207,1.06

5,0.98)(1.027,1.02

7,1.027)(0.901,0.95

4,0.997)(1.293,1.14

1,1.049)(1.091,1.02

7,0.984) (1,1,1)(0.817,0.92

3,1.121)(0.971,1.01

3,1.077)(0.874,0.95

,1.077)(0.881,0.99

6,1.209)

0.079,0.076,0.076

A10

(0.936,1.069,1.158)

(0.918,0.918,0.918)

(1.103,1.103,1.103)

(1.077,1.154,1.2)

(0.916,1.113,1.258)

(0.804,1.033,1.221)

(1.153,1.236,1.285)

(0.974,1.113,1.205)

(0.892,1.083,1.225) (1,1,1)

(1.189,1.098,0.961)

(1.07,1.029,0.961)

(1.079,1.079,1.079)

0.077,0.083,0.085

A11

(0.974,0.974,0.974)

(0.956,0.836,0.772)

(1.148,1.004,0.927)

(1.121,1.051,1.009)

(0.954,1.014,1.058)

(0.837,0.941,1.027)

(1.201,1.126,1.081)

(1.014,1.014,1.014)

(0.929,0.987,1.03)

(1.041,0.911,0.841) (1,1,1)

(0.9,0.938,1)

(0.504,0.655,0.936)

0.073,0.073,0.074

A12

(0.974,1.039,1.082)

(0.956,0.892,0.858)

(1.148,1.071,1.03)

(1.121,1.121,1.121)

(0.954,1.081,1.175)

(0.837,1.004,1.141)

(1.201,1.201,1.201)

(1.014,1.081,1.126)

(0.929,1.053,1.144)

(1.041,0.972,0.934)

(1,1.067,1.111) (1,1,1)

(1.008,1.048,1.123)

0.078,0.08,0.082

A13

(0.867,0.991,1.074)

(0.851,0.851,0.851)

(1.022,1.022,1.022)

(0.999,1.07,1.113)

(0.849,1.032,1.166)

(0.745,0.958,1.132)

(1.069,1.146,1.191)

(0.903,1.032,1.117)

(0.827,1.004,1.135)

(0.927,0.927,0.927)

(1.069,1.527,1.985)

(0.891,0.954,0.992) (1,1,1)

0.071,0.079,0.084

Table 3.4: Pair wise comparison matrix W.R.T. Mean Coefficient of Thermal Expansion for Super critical boiler material selection

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 W

A1 (1,1,1)(0.987,1.07,

1.222)(1.054,1.14

2,1.305)(0.858,0.89

4,0.954)(1.123,1.07

6,1.013)(1.246,1.14

2,1.015)(1.078,1.12

3,1.198)(1.09,1.09,1

.09)(1.008,0.96

6,0.909)(0.994,1.07

6,1.23) (1.3,1.3,1.3)(0.989,1.03,

1.099)(1.114,1.20

7,1.38)

0.081,0.083,0.086

A2(0.818,0.93

5,1.013) (1,1,1)(1.068,1.06

8,1.068)(0.869,0.83

6,0.78)(1.138,1.00

6,0.829)(1.262,1.06

8,0.83)(1.092,1.05,

0.98)(1.104,1.01

9,0.892)(1.021,0.90

3,0.744)(1.006,1.00

6,1.006)(1.317,1.21

5,1.063)(1.002,0.96

3,0.899)(1.129,1.12

9,1.129)

0.081,0.077,0.071

A3(0.766,0.87

6,0.949)(0.937,0.93

7,0.937) (1,1,1)(0.814,0.78

3,0.731)(1.066,0.94

3,0.776)(1.182,1,0.7

78)(1.023,0.98

3,0.918)(1.034,0.95

5,0.835)(0.956,0.84

6,0.696)(0.943,0.94

3,0.943)(1.233,1.13

8,0.996)(0.939,0.90

2,0.842)(1.057,1.05

7,1.057)

0.076,0.073,0.067

A4(1.048,1.11

8,1.165)(1.282,1.19

6,1.15)(1.368,1.27

7,1.228) (1,1,1)(1.309,1.20

4,1.062)(1.451,1.27

7,1.064)(1.256,1.25

6,1.256)(1.27,1.219,

1.143)(1.174,1.08,

0.953)(1.158,1.20

4,1.29)(1.514,1.45

4,1.363)(1.152,1.15

2,1.152)(1.298,1.35,

1.446)

0.096,0.093,0.089

A5(0.987,0.92

9,0.89)(1.207,0.99

4,0.879)(1.288,1.06

1,0.938)(0.941,0.83

1,0.764) (1,1,1)(1.109,1.06

1,1.002)(0.96,1.043,

1.182)(0.971,1.01

3,1.076)(0.897,0.89

7,0.897)(0.885,1,1.2

14)(1.157,1.20

8,1.283)(0.881,0.95

7,1.085)(0.992,1.12

1,1.362)

0.078,0.077,0.079

A6(0.985,0.87

6,0.803)(1.204,0.93

7,0.793)(1.286,1,0.8

46)(0.94,0.783,

0.689)(0.998,0.94

3,0.902) (1,1,1)(0.865,0.98

3,1.18)(0.875,0.95

5,1.074)(0.809,0.84

6,0.895)(0.798,0.94

3,1.212)(1.044,1.13

8,1.281)(0.794,0.90

2,1.083)(0.895,1.05

7,1.359)

0.073,0.073,0.075

A7(0.835,0.89

1,0.928)(1.021,0.95

3,0.916)(1.09,1.017,

0.978)(0.796,0.79

6,0.796)(0.846,0.95

9,1.042)(0.847,1.01

7,1.156) (1,1,1)(1.011,0.97

1,0.91)(0.935,0.86,

0.759)(0.922,0.95

9,1.027)(1.206,1.15

8,1.085)(0.918,0.91

8,0.918)(1.034,1.07

5,1.152)

0.073,0.074,0.074

A8(0.917,0.91

7,0.917)(1.121,0.98

1,0.906)(1.197,1.04

7,0.967)(0.875,0.82,

0.787)(0.929,0.98

7,1.03)(0.931,1.04

7,1.143)(1.099,1.03,

0.989) (1,1,1)(0.924,0.88

6,0.834)(0.911,0.98

7,1.128)(1.192,1.19

2,1.192)(0.907,0.94

5,1.008)(1.022,1.10

7,1.265)

0.077,0.076,0.076

A9(1.1,1.036,0

.992)(1.345,1.10

8,0.98)(1.436,1.18

2,1.046)(1.049,0.92

6,0.852)(1.115,1.11

5,1.115)(1.117,1.18

2,1.236)(1.318,1.16

3,1.07)(1.2,1.129,1

.082) (1,1,1)(0.986,1.11

5,1.354)(1.29,1.346,

1.43)(0.982,1.06

7,1.209)(1.106,1.25,

1.518)

0.088,0.086,0.086

A10

(0.813,0.929,1.006)

(0.994,0.994,0.994)

(1.061,1.061,1.061)

(0.775,0.831,0.864)

(0.824,1,1.13)

(0.825,1.061,1.254)

(0.974,1.043,1.085)

(0.886,1.013,1.097)

(0.739,0.897,1.014) (1,1,1)

(1.308,1.208,1.057)

(0.996,0.957,0.893)

(1.121,1.121,1.121)

0.072,0.077,0.079

A11

(0.769,0.769,0.769)

(0.94,0.823,0.759)

(1.004,0.878,0.811)

(0.734,0.688,0.66)

(0.779,0.828,0.864)

(0.781,0.878,0.958)

(0.921,0.864,0.829)

(0.839,0.839,0.839)

(0.699,0.743,0.775)

(0.946,0.828,0.764) (1,1,1)

(0.761,0.793,0.846)

(0.857,0.929,1.061)

0.065,0.064,0.064

A12

(0.91,0.97,1.011)

(1.112,1.038,0.998)

(1.187,1.108,1.065)

(0.868,0.868,0.868)

(0.922,1.045,1.135)

(0.923,1.108,1.259)

(1.09,1.09,1.09)

(0.992,1.058,1.102)

(0.827,0.937,1.019)

(1.119,1.045,1.004)

(1.183,1.262,1.314) (1,1,1)

(1.126,1.171,1.255)

0.078,0.08,0.082

A13

(0.725,0.828,0.897)

(0.886,0.886,0.886)

(0.946,0.946,0.946)

(0.691,0.741,0.77)

(0.734,0.892,1.008)

(0.736,0.946,1.118)

(0.868,0.93,0.967)

(0.79,0.903,0.978)

(0.659,0.8,0.904)

(0.892,0.892,0.892)

(0.942,1.077,1.167)

(0.797,0.854,0.888) (1,1,1)

0.063,0.069,0.072

Table 3.5: Pair wise comparison matrix W.R.T. 0.2% Yield Strength for Super critical boiler material selectionA1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A13 A14 W

A1 (1,1,1)(0.238,0.25

7,0.294)(0.638,0.69

2,0.791)(0.82,0.854,

0.911)(0.711,0.68

1,0.641)(0.393,0.36,

0.32)(0.263,0.27

4,0.292) (0.2,0.2,0.2)(1.964,1.88

2,1.771)(0.458,0.49

6,0.567)(0.189,0.18

9,0.189)(0.82,0.854,

0.911)(0.382,0.41

4,0.473)

0.031,0.031,0.033

A2(3.4,3.886,4

.21) (1,1,1)(2.688,2.68

8,2.688)(3.45,3.317,

3.096)(2.991,2.64

6,2.179)(1.654,1.39

9,1.088)(1.107,1.06

4,0.993)(0.842,0.77

7,0.68)(8.266,7.31

2,6.022)(1.926,1.92

6,1.926)(0.796,0.73

5,0.643)(3.45,3.317,

3.096)(1.608,1.60

8,1.608)

0.128,0.122,0.112

A3(1.265,1.44

6,1.566)(0.372,0.37

2,0.372) (1,1,1)(1.284,1.23

4,1.152)(1.113,0.98

4,0.811)(0.615,0.52

1,0.405)(0.412,0.39

6,0.37)(0.313,0.28

9,0.253)(3.075,2.72,

2.24)(0.717,0.71

7,0.717)(0.296,0.27

4,0.239)(1.284,1.23

4,1.152)(0.598,0.59

8,0.598)

0.048,0.045,0.042

A4(1.098,1.17

1,1.22)(0.323,0.30

1,0.29)(0.868,0.81,

0.779) (1,1,1)(0.867,0.79

8,0.704)(0.479,0.42

2,0.352)(0.321,0.32

1,0.321)(0.244,0.23

4,0.22)(2.396,2.20

4,1.945)(0.558,0.58

1,0.622)(0.231,0.22

2,0.208) (1,1,1)(0.466,0.48

5,0.519)

0.038,0.037,0.035

A5(1.56,1.469,

1.407)(0.459,0.37

8,0.334)(1.233,1.01

6,0.899)(1.421,1.25

4,1.153) (1,1,1)(0.553,0.52

9,0.499)(0.37,0.402,

0.456)(0.281,0.29

4,0.312)(2.763,2.76

3,2.763)(0.644,0.72

8,0.884)(0.266,0.27

8,0.295)(1.153,1.25

4,1.421)(0.537,0.60

8,0.738)

0.047,0.046,0.047

A6(3.124,2.77

7,2.546)(0.919,0.71

5,0.605)(2.47,1.921,

1.625)(2.845,2.37

1,2.086)(2.002,1.89

1,1.809) (1,1,1)(0.669,0.76

1,0.913)(0.509,0.55

5,0.625)(4.999,5.22

6,5.533)(1.165,1.37

7,1.77)(0.482,0.52

5,0.591)(2.086,2.37

1,2.845)(0.972,1.14

9,1.477)

0.088,0.087,0.091

A7(3.423,3.65

1,3.804)(1.007,0.94,

0.904)(2.706,2.52

6,2.429)(3.117,3.11

7,3.117)(2.194,2.48

6,2.703)(1.096,1.31

5,1.494) (1,1,1)(0.761,0.73,

0.685)(7.468,6.87

1,6.063)(1.741,1.81,

1.939)(0.72,0.691,

0.648)(3.117,3.11

7,3.117)(1.453,1.51

1,1.619)

0.114,0.115,0.115

A8 (5,5,5)(1.471,1.28

7,1.188)(3.953,3.45

8,3.192)(4.553,4.26

8,4.098)(3.204,3.40

5,3.553)(1.6,1.8,1.9

64)(1.461,1.36

9,1.315) (1,1,1)(9.818,9.40

9,8.855)(2.288,2.47

9,2.833)(0.946,0.94

6,0.946)(4.098,4.26

8,4.553)(1.909,2.06

9,2.364)

0.158,0.157,0.159

A9(0.565,0.53

1,0.509)(0.166,0.13

7,0.121)(0.446,0.36

8,0.325)(0.514,0.45

4,0.417)(0.362,0.36

2,0.362)(0.181,0.19

1,0.2)(0.165,0.14

6,0.134)(0.113,0.10

6,0.102) (1,1,1)(0.233,0.26

3,0.32)(0.096,0.10

1,0.107)(0.417,0.45

4,0.514)(0.194,0.22,

0.267)

0.017,0.017,0.017

A10

(1.765,2.017,2.185)

(0.519,0.519,0.519)

(1.395,1.395,1.395)

(1.607,1.722,1.791)

(1.131,1.374,1.553)

(0.565,0.726,0.858)

(0.516,0.552,0.575)

(0.353,0.403,0.437)

(3.126,3.796,4.291) (1,1,1)

(0.413,0.382,0.334)

(1.791,1.722,1.607)

(0.835,0.835,0.835)

0.059,0.063,0.065

A11

(5.286,5.286,5.286)

(1.555,1.36,1.256)

(4.178,3.656,3.375)

(4.813,4.512,4.332)

(3.388,3.599,3.756)

(1.692,1.903,2.076)

(1.544,1.448,1.39)

(1.057,1.057,1.057)

(9.361,9.946,10.38)

(2.995,2.62,2.419) (1,1,1)

(4.332,4.512,4.813)

(2.019,2.187,2.499)

0.169,0.166,0.166

A12

(1.098,1.171,1.22)

(0.323,0.301,0.29)

(0.868,0.81,0.779) (1,1,1)

(0.704,0.798,0.867)

(0.352,0.422,0.479)

(0.321,0.321,0.321)

(0.22,0.234,0.244)

(1.945,2.204,2.396)

(0.622,0.581,0.558)

(0.208,0.222,0.231) (1,1,1)

(0.466,0.485,0.519)

0.036,0.037,0.038

A13

(2.115,2.417,2.619)

(0.622,0.622,0.622)

(1.672,1.672,1.672)

(1.926,2.063,2.146)

(1.355,1.646,1.861)

(0.677,0.87,1.029)

(0.618,0.662,0.688)

(0.423,0.483,0.524)

(3.746,4.548,5.142)

(1.198,1.198,1.198)

(0.4,0.457,0.495)

(1.926,2.063,2.146) (1,1,1)

0.069,0.076,0.08

Table 3.6: Pair wise comparison matrix W.R.T. Stress-Rupture Strength (Rupture For 10000 Hours) as Creep Strength for Super critical boiler material selection

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 W

A1 (1,1,1)(0.666,0.72

2,0.825)(0.589,0.63

8,0.73)(0.885,0.92

2,0.984)(0.559,0.53

5,0.504)(0.549,0.50

3,0.447)(1.092,1.13

7,1.213)(0.407,0.40

7,0.407)(1.14,1.092,

1.028)(1.022,1.10

7,1.265) (0.5,0.5,0.5)(0.927,0.96

5,1.029)(0.934,1.01

2,1.157)

0.054,0.055,0.057

A2(1.212,1.38

6,1.501) (1,1,1)(0.885,0.88

5,0.885)(1.329,1.27

8,1.193)(0.839,0.74

2,0.611)(0.824,0.69

7,0.542)(1.638,1.57

5,1.47)(0.611,0.56

4,0.493)(1.711,1.51

3,1.246)(1.533,1.53

3,1.533)(0.751,0.69

3,0.606)(1.391,1.33

7,1.248)(1.402,1.40

2,1.402)

0.08,0.077,0.07

A3(1.37,1.566,

1.697)(1.13,1.13,1

.13) (1,1,1)(1.502,1.44

4,1.348)(0.948,0.83

9,0.691)(0.931,0.78

8,0.613)(1.852,1.78

1,1.662)(0.69,0.637,

0.558)(1.934,1.71

1,1.409)(1.733,1.73

3,1.733)(1.572,1.51

2,1.411)(1.572,1.51

2,1.411)(1.585,1.58

5,1.585)

0.095,0.091,0.084

A4(1.017,1.08

4,1.13)(0.839,0.78

3,0.753)(0.742,0.69

2,0.666) (1,1,1)(0.631,0.58

1,0.512)(0.62,0.545,

0.455)(1.233,1.23

3,1.233)(0.46,0.441,

0.414)(1.287,1.18

4,1.045)(1.154,1.2,1

.286)(0.565,0.54

2,0.508)(1.047,1.04

7,1.047)(1.055,1.09

8,1.176)

0.062,0.06,0.058

A5(1.984,1.86

7,1.79)(1.637,1.34

8,1.192)(1.448,1.19

2,1.055)(1.952,1.72

2,1.584) (1,1,1)(0.982,0.93

9,0.887)(1.953,2.12

3,2.406)(0.728,0.76,

0.807)(2.039,2.03

9,2.039)(1.828,2.06

7,2.51)(0.895,0.93

4,0.992)(1.658,1.80

2,2.043)(1.672,1.89,

2.295)

0.105,0.103,0.105

A6(2.236,1.98

8,1.822)(1.845,1.43

5,1.214)(1.632,1.26

9,1.074)(2.2,1.833,1

.613)(1.127,1.06

5,1.018) (1,1,1)(1.989,2.26,

2.712)(0.741,0.80

9,0.91)(2.077,2.17

1,2.299)(1.862,2.2,2

.829)(0.911,0.99

4,1.118)(1.688,1.91

9,2.302)(1.703,2.01

2,2.587)

0.111,0.11,0.114

A7(0.825,0.88,

0.916)(0.68,0.635,

0.61)(0.602,0.56

2,0.54)(0.811,0.81

1,0.811)(0.416,0.47

1,0.512)(0.369,0.44

2,0.503) (1,1,1)(0.373,0.35

8,0.335)(1.044,0.96

1,0.848)(0.936,0.97

3,1.043)(0.458,0.44,

0.412)(0.849,0.84

9,0.849)(0.856,0.89,

0.954)

0.048,0.049,0.049

A8(2.458,2.45

8,2.458)(2.027,1.77

4,1.637)(1.793,1.56

9,1.449)(2.418,2.26

7,2.176)(1.239,1.31

6,1.373)(1.099,1.23

6,1.349)(2.981,2.79

5,2.683) (1,1,1)(2.801,2.68

4,2.526)(2.511,2.72,

3.109)(1.229,1.22

9,1.229)(2.277,2.37

2,2.53)(2.296,2.48

8,2.843)

0.137,0.136,0.137

A9(0.973,0.91

6,0.878)(0.802,0.66

1,0.585)(0.71,0.585,

0.517)(0.957,0.84

4,0.777)(0.49,0.49,0

.49)(0.435,0.46

1,0.482)(1.18,1.041,

0.958)(0.396,0.37

3,0.357) (1,1,1)(0.896,1.01

3,1.23)(0.439,0.45

8,0.486)(0.813,0.88

4,1.002)(0.82,0.927,

1.125)

0.052,0.051,0.051

A10

(0.791,0.904,0.979)

(0.652,0.652,0.652)

(0.577,0.577,0.577)

(0.778,0.833,0.867)

(0.398,0.484,0.547)

(0.354,0.455,0.537)

(0.959,1.027,1.068)

(0.322,0.368,0.398)

(0.813,0.987,1.116) (1,1,1)

(0.489,0.452,0.395)

(0.605,0.756,1.008)

(0.915,0.915,0.915)

0.045,0.049,0.052

A11 (2,2,2)

(1.65,1.443,1.332)

(0.709,0.662,0.636)

(1.967,1.844,1.771)

(1.008,1.071,1.118)

(0.894,1.006,1.098)

(2.426,2.274,2.183)

(0.814,0.814,0.814)

(2.056,2.184,2.279)

(2.53,2.213,2.043) (1,1,1)

(1.853,1.93,2.059)

(1.869,2.024,2.314)

0.106,0.105,0.105

A12

(0.971,1.036,1.079)

(0.801,0.748,0.719)

(0.709,0.662,0.636)

(0.956,0.956,0.956)

(0.49,0.555,0.603)

(0.434,0.521,0.592)

(1.178,1.178,1.178)

(0.395,0.422,0.439)

(0.998,1.132,1.23)

(0.992,1.323,1.654)

(0.486,0.518,0.54) (1,1,1)

(1.008,1.049,1.124)

0.055,0.058,0.06

A13

(0.864,0.988,1.07)

(0.713,0.713,0.713)

(0.631,0.631,0.631)

(0.85,0.911,0.948)

(0.436,0.529,0.598)

(0.387,0.497,0.587)

(1.048,1.123,1.168)

(0.352,0.402,0.435)

(0.889,1.079,1.22)

(1.093,1.093,1.093)

(0.432,0.494,0.535)

(0.89,0.953,0.992) (1,1,1)

0.05,0.055,0.058

Table 3.7: Pair wise comparison matrix W.R.T. Dynamic Modulus of Elasticity for Super critical boiler material selection

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 W

A1 (1,1,1)(0.72,0.779,

0.891)(0.821,0.88

9,1.016)(0.756,0.78

8,0.84)(0.939,0.89

9,0.847)(0.999,0.91

6,0.814)(0.884,0.92

1,0.983)(0.956,0.95

6,0.956)(1.057,1.01

3,0.954)(0.861,0.93

3,1.066)(0.822,0.82

2,0.822)(1.269,1.32

2,1.41)(0.746,0.80

9,0.924)

0.069,0.07,0.072

A2(1.123,1.28

3,1.39) (1,1,1)(1.14,1.14,1

.14)(1.051,1.01,

0.943)(1.304,1.15

4,0.95)(1.388,1.17

5,0.914)(1.229,1.18

2,1.103)(1.329,1.22

6,1.073)(1.47,1.3,1.

071)(1.196,1.19

6,1.196)(1.142,1.05

4,0.922)(1.763,1.69

6,1.583)(1.037,1.03

7,1.037)

0.094,0.09,0.083

A3(0.984,1.12

5,1.219)(0.877,0.87

7,0.877) (1,1,1)(0.921,0.88

6,0.827)(1.144,1.01

2,0.833)(1.217,1.03,

0.801)(1.078,1.03

6,0.967)(1.165,1.07

5,0.941)(1.289,1.14,

0.939)(1.049,1.04

9,1.049)(1.001,0.92

4,0.809)(1.546,1.48

7,1.388)(0.91,0.91,0

.91)

0.082,0.079,0.072

A4(1.19,1.27,1

.323)(1.06,0.99,0

.952)(1.209,1.12

9,1.085) (1,1,1)(1.241,1.14

2,1.008)(1.321,1.16

3,0.969)(1.17,1.17,1

.17)(1.264,1.21

4,1.138)(1.399,1.28

7,1.135)(1.139,1.18

4,1.269)(1.087,1.04

3,0.978)(1.678,1.67

8,1.678)(0.987,1.02

7,1.1)

0.092,0.089,0.085

A5(1.181,1.11

2,1.066)(1.052,0.86

7,0.767)(1.2,0.988,0

.874)(0.992,0.87

6,0.806) (1,1,1)(1.064,1.01

8,0.962)(0.942,1.02

4,1.161)(1.019,1.06

3,1.129)(1.127,1.12

7,1.127)(0.917,1.03

7,1.259)(0.875,0.91

4,0.971)(1.352,1.47,

1.666)(0.795,0.89

9,1.092)

0.079,0.078,0.08

A6(1.229,1.09

2,1.001)(1.095,0.85

1,0.72)(1.248,0.97

1,0.821)(1.032,0.86,

0.757)(1.04,0.982,

0.94) (1,1,1)(0.885,1.00

6,1.207)(0.957,1.04

4,1.175)(1.059,1.10

7,1.172)(0.862,1.01

8,1.309)(0.823,0.89

7,1.009)(1.27,1.443,

1.732)(0.747,0.88

3,1.135)

0.077,0.076,0.08

A7(1.018,1.08

6,1.131)(0.907,0.84

6,0.814)(1.034,0.96

5,0.928)(0.855,0.85

5,0.855)(0.861,0.97

6,1.061)(0.828,0.99

4,1.13) (1,1,1)(1.081,1.03

8,0.973)(1.196,1.1,0

.971)(0.973,1.01

2,1.085)(0.929,0.89

2,0.836)(1.435,1.43

5,1.435)(0.844,0.87

8,0.94)

0.075,0.076,0.076

A8(1.046,1.04

6,1.046)(0.932,0.81

5,0.753)(1.063,0.93,

0.858)(0.879,0.82

4,0.791)(0.885,0.94

1,0.982)(0.851,0.95

8,1.045)(1.028,0.96

4,0.925) (1,1,1)(1.106,1.06,

0.998)(0.9,0.975,1

.115)(0.859,0.85

9,0.859)(1.327,1.38

3,1.475)(0.781,0.84

6,0.967)

0.074,0.073,0.074

A9(1.049,0.98

7,0.946)(0.934,0.76

9,0.68)(1.065,0.87

7,0.776)(0.881,0.77

7,0.715)(0.888,0.88

8,0.888)(0.853,0.90

4,0.945)(1.03,0.909,

0.836)(1.002,0.94

3,0.904) (1,1,1)(0.814,0.92,

1.117)(0.777,0.81

1,0.861)(1.2,1.304,1

.478)(0.706,0.79

8,0.969)

0.071,0.069,0.069

A10

(0.938,1.072,1.162)

(0.836,0.836,0.836)

(0.953,0.953,0.953)

(0.788,0.845,0.878)

(0.794,0.964,1.09)

(0.764,0.982,1.16)

(0.922,0.988,1.027)

(0.897,1.025,1.111)

(0.895,1.087,1.228) (1,1,1)

(0.955,0.881,0.771)

(1.474,1.417,1.323)

(0.867,0.867,0.867)

0.07,0.075,0.077

A11

(1.217,1.217,1.217)

(1.084,0.949,0.876)

(1.236,1.082,0.999)

(1.022,0.959,0.92)

(1.03,1.095,1.142)

(0.991,1.114,1.216)

(1.196,1.121,1.076)

(1.164,1.164,1.164)

(1.161,1.233,1.287)

(1.297,1.135,1.048) (1,1,1)

(1.544,1.609,1.716)

(0.908,0.984,1.125)

0.087,0.085,0.085

A12

(0.709,0.757,0.788)

(0.632,0.59,0.567)

(0.721,0.673,0.647)

(0.596,0.596,0.596)

(0.6,0.68,0.74)

(0.577,0.693,0.787)

(0.697,0.697,0.697)

(0.678,0.723,0.753)

(0.676,0.767,0.833)

(0.756,0.706,0.678)

(0.583,0.622,0.648) (1,1,1)

(0.588,0.612,0.655)

0.051,0.053,0.054

A13

(1.082,1.237,1.34)

(0.964,0.964,0.964)

(1.099,1.099,1.099)

(0.909,0.974,1.013)

(0.916,1.112,1.258)

(0.881,1.133,1.338)

(1.063,1.139,1.185)

(1.035,1.182,1.281)

(1.032,1.253,1.417)

(1.153,1.153,1.153)

(0.889,1.016,1.101)

(1.526,1.635,1.7) (1,1,1)

0.079,0.087,0.092

Table 3.8: Pair wise comparison matrix W.R.T. Specific Heat for Super critical boiler material selection

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 W

A1 (1,1,1)(0.728,0.78

8,0.901)(0.847,0.91

7,1.048)(1.011,1.05

3,1.123)(0.872,0.83

6,0.787)(0.98,0.898,

0.799)(0.876,0.91

2,0.973)(1.21,1.21,1

.21)(1.194,1.14

5,1.077)(0.744,0.80

6,0.921)(0.885,0.88

5,0.885)(0.901,0.93

9,1.001)(0.801,0.86

7,0.991)

0.07,0.071,0.074

A2(1.11,1.269,

1.374) (1,1,1)(1.164,1.16

4,1.164)(1.389,1.33

6,1.247)(1.199,1.06,

0.873)(1.347,1.14,

0.887)(1.204,1.15

8,1.081)(1.664,1.53

6,1.344)(1.642,1.45

2,1.196)(1.023,1.02

3,1.023)(1.216,1.12

3,0.982)(1.238,1.19

1,1.111) (1.1,1.1,1.1)

0.095,0.091,0.083

A3(0.954,1.09,

1.181)(0.859,0.85

9,0.859) (1,1,1)(1.194,1.14

8,1.071)(1.03,0.911,

0.75)(1.158,0.98,

0.762)(1.035,0.99

5,0.928)(1.43,1.32,1

.155)(1.411,1.24

8,1.028)(0.879,0.87

9,0.879)(1.045,0.96

5,0.844)(1.064,1.02

3,0.955)(0.946,0.94

6,0.946)

0.082,0.078,0.072

A4(0.89,0.95,0

.989)(0.802,0.74

9,0.72)(0.933,0.87

1,0.838) (1,1,1)(0.863,0.79

4,0.7)(0.97,0.853,

0.711)(0.867,0.86

7,0.867)(1.197,1.14

9,1.078)(1.181,1.08

7,0.959)(0.736,0.76

6,0.82)(0.875,0.84,

0.788)(0.891,0.89

1,0.891)(0.792,0.82

4,0.883)

0.07,0.068,0.065

A5(1.271,1.19

7,1.147)(1.145,0.94

3,0.834)(1.333,1.09

8,0.971)(1.428,1.26,

1.159) (1,1,1)(1.124,1.07

5,1.015)(1.005,1.09

2,1.237)(1.388,1.44

8,1.539)(1.37,1.37,1

.37)(0.853,0.96

5,1.172)(1.015,1.05

9,1.125)(1.033,1.12

3,1.273)(0.918,1.03

8,1.26)

0.087,0.085,0.087

A6(1.252,1.11

3,1.02)(1.128,0.87

7,0.742)(1.313,1.02

1,0.864)(1.406,1.17

2,1.031)(0.985,0.93,

0.89) (1,1,1)(0.894,1.01

6,1.219)(1.235,1.34

7,1.516)(1.219,1.27

4,1.349)(0.759,0.89

7,1.154)(0.903,0.98

5,1.108)(0.919,1.04

5,1.253)(0.817,0.96

5,1.241)

0.08,0.079,0.083

A7(1.027,1.09

6,1.142)(0.925,0.86

4,0.831)(1.077,1.00

5,0.967)(1.154,1.15

4,1.154)(0.808,0.91

6,0.996)(0.821,0.98

5,1.119) (1,1,1)(1.382,1.32

6,1.244)(1.363,1.25

4,1.107)(0.85,0.884,

0.947)(1.01,0.97,0

.909)(1.029,1.02

9,1.029)(0.914,0.95

1,1.018)

0.078,0.078,0.078

A8(0.826,0.82

6,0.826)(0.744,0.65

1,0.601)(0.866,0.75

8,0.7)(0.928,0.87,

0.835)(0.65,0.69,0

.72)(0.66,0.742,

0.81)(0.804,0.75

4,0.724) (1,1,1)(0.987,0.94

6,0.89)(0.615,0.66

6,0.761)(0.731,0.73

1,0.731)(0.744,0.77

5,0.827)(0.662,0.71

7,0.819)

0.06,0.059,0.059

A9(0.928,0.87

4,0.837)(0.836,0.68

9,0.609)(0.973,0.80

1,0.709)(1.043,0.92,

0.846)(0.73,0.73,0

.73)(0.741,0.78

5,0.821)(0.904,0.79

7,0.733)(1.124,1.05

7,1.013) (1,1,1)(0.623,0.70

4,0.855)(0.741,0.77

3,0.821)(0.754,0.82,

0.929)(0.67,0.758,

0.92)

0.064,0.062,0.063

A10

(1.085,1.24,1.344)

(0.978,0.978,0.978)

(1.138,1.138,1.138)

(1.219,1.306,1.358)

(0.854,1.037,1.172)

(0.867,1.114,1.317)

(1.056,1.132,1.177)

(1.314,1.501,1.626)

(1.169,1.42,1.605) (1,1,1)

(1.189,1.097,0.96)

(1.211,1.164,1.086)

(1.076,1.076,1.076)

0.083,0.089,0.091

A11

(1.13,1.13,1.13)

(1.018,0.891,0.822)

(1.185,1.037,0.957)

(1.269,1.19,1.142)

(0.889,0.944,0.986)

(0.903,1.015,1.108)

(1.1,1.031,0.99)

(1.368,1.368,1.368)

(1.217,1.293,1.35)

(1.041,0.911,0.841) (1,1,1)

(1.018,1.061,1.131)

(0.905,0.98,1.12)

0.082,0.081,0.081

A12

(0.999,1.066,1.11)

(0.9,0.84,0.808)

(1.047,0.977,0.94)

(1.122,1.122,1.122)

(0.786,0.89,0.968)

(0.798,0.957,1.088)

(0.972,0.972,0.972)

(1.209,1.29,1.343)

(1.076,1.22,1.326)

(0.92,0.859,0.826)

(0.884,0.943,0.982) (1,1,1)

(0.889,0.924,0.99)

0.074,0.076,0.078

A13

(1.009,1.153,1.249)

(0.909,0.909,0.909)

(1.057,1.057,1.057)

(1.133,1.214,1.263)

(0.793,0.963,1.089)

(0.806,1.036,1.224)

(0.982,1.052,1.094)

(1.221,1.395,1.512)

(1.087,1.32,1.492)

(0.93,0.93,0.93)

(0.893,1.02,1.105)

(1.01,1.082,1.125) (1,1,1)

0.075,0.082,0.087

Table 3.9: Pair wise comparison matrix W.R.T. Density for Super critical boiler material selection

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 W

A1 1,1,10.925,1.002

,1.1460.83,0.9,1.0

280.978,1.019

,1.0871.066,1.022

,0.9611.053,0.965

,0.8580.918,0.956

,1.020.981,0.981

,0.9811.061,1.016

,0.9570.922,0.999

,1.1410.892,0.892

,0.8920.941,0.981

,1.0460.906,0.982

,1.122

0.074,0.075,0.078

A20.873,0.998

,1.081 1,1,10.897,0.897

,0.8971.057,1.016

,0.9491.152,1.019

,0.8391.138,0.963

,0.7490.992,0.954

,0.891.06,0.978,

0.8561.146,1.014

,0.8350.996,0.996

,0.9960.964,0.89,

0.7781.017,0.978

,0.9130.979,0.979

,0.979

0.078,0.075,0.069

A30.973,1.112

,1.2041.114,1.114

,1.114 1,1,11.178,1.133

,1.0571.284,1.135

,0.9351.268,1.073

,0.8351.105,1.063

,0.9921.181,1.09,

0.9541.277,1.13,

0.931.11,1.11,1.

111.074,0.991

,0.8671.134,1.09,

1.0171.091,1.091

,1.091

0.087,0.083,0.077

A40.92,0.981,

1.0221.054,0.984

,0.9460.946,0.883

,0.849 1,1,11.09,1.003,

0.8851.077,0.947

,0.7890.938,0.938

,0.9381.002,0.962

,0.9021.084,0.997

,0.880.942,0.98,

1.050.912,0.875

,0.820.962,0.962

,0.9620.926,0.964

,1.032

0.076,0.074,0.071

A51.04,0.979,

0.9381.192,0.981

,0.8681.069,0.881

,0.7791.13,0.997,

0.918 1,1,10.988,0.945

,0.8920.861,0.936

,1.0610.92,0.96,1.

020.995,0.995

,0.9950.865,0.978

,1.1870.837,0.873

,0.9270.883,0.96,

1.0880.85,0.961,

1.167

0.074,0.074,0.075

A61.165,1.036

,0.951.335,1.039

,0.8791.198,0.932

,0.7891.267,1.056

,0.9291.12,1.058,

1.012 1,1,10.872,0.991

,1.1890.931,1.016

,1.1431.007,1.053

,1.1150.875,1.035

,1.330.847,0.924

,1.0390.894,1.016

,1.2190.861,1.017

,1.308

0.078,0.078,0.081

A70.98,1.046,

1.0891.123,1.048

,1.0081.008,0.941

,0.9051.066,1.066

,1.0660.943,1.068

,1.1610.841,1.01,

1.147 1,1,11.068,1.026

,0.9611.155,1.063

,0.9381.004,1.045

,1.1190.971,0.933

,0.8741.026,1.026

,1.0260.987,1.027

,1.1

0.078,0.079,0.078

A81.02,1.02,1.

021.168,1.022

,0.9441.049,0.918

,0.8471.108,1.039

,0.9980.98,1.042,

1.0870.875,0.984

,1.0741.04,0.975,

0.936 1,1,11.082,1.037

,0.9760.94,1.019,

1.1640.909,0.909

,0.9090.96,1,1.06

70.924,1.001

,1.144

0.077,0.077,0.077

A91.045,0.984

,0.9431.198,0.986

,0.8731.075,0.885

,0.7831.136,1.003

,0.9221.005,1.005

,1.0050.897,0.95,

0.9931.066,0.941

,0.8651.025,0.965

,0.925 1,1,10.869,0.983

,1.1930.841,0.877

,0.9320.888,0.965

,1.0930.854,0.966

,1.173

0.076,0.074,0.074

A10

0.876,1.001,1.085

1.004,1.004,1.004

0.901,0.901,0.901

0.952,1.02,1.061

0.842,1.023,1.156

0.752,0.967,1.142

0.894,0.957,0.996

0.859,0.982,1.064

0.838,1.018,1.15 1,1,1

0.967,0.893,0.781

1.021,0.982,0.916

0.983,0.983,0.983

0.07,0.075,0.077

A11

1.121,1.121,1.121

1.285,1.124,1.038

1.153,1.009,0.931

1.219,1.143,1.097

1.078,1.146,1.195

0.962,1.083,1.181

1.144,1.072,1.029 1.1,1.1,1.1

1.073,1.14,1.189

1.28,1.12,1.034 1,1,1

1.056,1.1,1.173

1.016,1.101,1.258

0.086,0.084,0.084

A12

0.956,1.02,1.062

1.095,1.022,0.983

0.983,0.918,0.882

1.039,1.039,1.039

0.919,1.042,1.132

0.82,0.984,1.119

0.975,0.975,0.975

0.938,1,1.042

0.915,1.037,1.127

1.091,1.019,0.979

0.853,0.909,0.947 1,1,1

0.963,1.001,1.073

0.074,0.077,0.078

A13

0.891,1.019,1.103

1.021,1.021,1.021

0.916,0.916,0.916

0.969,1.038,1.079

0.857,1.041,1.176

0.765,0.983,1.162

0.909,0.974,1.013

0.874,0.999,1.082

0.853,1.035,1.17

1.017,1.017,1.017

0.795,0.908,0.984

0.932,0.999,1.039 1,1,1

0.07,0.076,0.081

Table 3.10: Pair wise comparison matrix W.R.T. Melting Point for Super critical boiler material selection

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 W

A1 1,1,10.857,0.929

,1.0610.876,0.949

,1.0840.863,0.899

,0.9590.969,0.929

,0.8741.028,0.942

,0.8370.924,0.963

,1.0270.973,0.973

,0.9730.979,0.939

,0.8830.876,0.949

,1.0840.945,0.945

,0.9450.882,0.919

,0.980.886,0.959

,1.096

0.071,0.073,0.075

A20.942,1.077

,1.167 1,1,11.022,1.022

,1.0221.007,0.968

,0.9041.13,1,0.82

41.199,1.014

,0.7891.079,1.037

,0.9681.135,1.048

,0.9171.143,1.011

,0.8321.022,1.022

,1.0221.103,1.018

,0.8911.029,0.989

,0.9231.033,1.033

,1.033

0.082,0.078,0.072

A30.922,1.054

,1.1420.979,0.979

,0.979 1,1,10.985,0.947

,0.8841.106,0.979

,0.8061.173,0.993

,0.7721.055,1.015

,0.9471.111,1.025

,0.8971.118,0.989

,0.815 1,1,11.079,0.996

,0.8721.007,0.968

,0.9041.011,1.011

,1.011

0.08,0.077,0.07

A41.043,1.112

,1.1591.107,1.033

,0.9931.131,1.055

,1.015 1,1,11.123,1.033

,0.9111.191,1.048

,0.8731.071,1.071

,1.0711.127,1.082

,1.0151.135,1.044

,0.9211.015,1.055

,1.1311.095,1.052

,0.9861.022,1.022

,1.0221.026,1.067

,1.143

0.084,0.081,0.078

A51.144,1.077

,1.0321.214,1,0.8

851.241,1.022

,0.9041.097,0.968

,0.891 1,1,11.061,1.014

,0.9580.954,1.037

,1.1751.004,1.048

,1.1131.011,1.011

,1.0110.904,1.022

,1.2410.976,1.018

,1.0820.91,0.989,

1.1210.914,1.033

,1.255

0.079,0.078,0.08

A61.194,1.062

,0.9731.267,0.986

,0.8341.295,1.007

,0.8521.145,0.954

,0.841.044,0.986

,0.943 1,1,10.9,1.022,1.

2270.947,1.033

,1.1620.953,0.996

,1.0550.852,1.007

,1.2950.92,1.004,

1.1290.858,0.975

,1.170.862,1.018

,1.309

0.078,0.077,0.08

A70.974,1.038

,1.0821.033,0.964

,0.9271.056,0.985

,0.9480.934,0.934

,0.9340.851,0.964

,1.0480.815,0.978

,1.112 1,1,11.053,1.01,

0.9471.059,0.975

,0.860.948,0.985

,1.0561.023,0.982

,0.920.954,0.954

,0.9540.958,0.996

,1.067

0.075,0.075,0.075

A81.028,1.028

,1.0281.091,0.954

,0.8811.114,0.975

,0.90.986,0.924

,0.8870.898,0.954

,0.9960.861,0.968

,1.0561.056,0.99,

0.95 1,1,11.007,0.965

,0.9080.9,0.975,1.

1140.972,0.972

,0.9720.906,0.944

,1.0070.91,0.986,

1.127

0.075,0.075,0.075

A91.132,1.065

,1.0211.201,0.989

,0.8751.228,1.011

,0.8941.086,0.958

,0.8810.989,0.989

,0.9890.948,1.004

,1.0491.163,1.026

,0.9441.101,1.037

,0.993 1,1,10.894,1.011

,1.2280.965,1.007

,1.070.9,0.979,1.

1090.904,1.022

,1.241

0.08,0.077,0.078

A10

0.922,1.054,1.142

0.979,0.979,0.979 1,1,1

0.884,0.947,0.985

0.806,0.979,1.106

0.772,0.993,1.173

0.947,1.015,1.055

0.897,1.025,1.111

0.815,0.989,1.118 1,1,1

1.079,0.996,0.872

1.007,0.968,0.904

1.011,1.011,1.011

0.072,0.077,0.079

A11

1.058,1.058,1.058

1.122,0.982,0.907

1.147,1.004,0.926

1.014,0.951,0.913

0.924,0.982,1.025

0.886,0.996,1.087

1.086,1.019,0.978

1.029,1.029,1.029

0.934,0.993,1.036

1.147,1.004,0.926 1,1,1

0.933,0.972,1.037

0.937,1.015,1.16

0.078,0.077,0.077

A12

1.02,1.088,1.134

1.083,1.011,0.972

1.107,1.033,0.993

0.979,0.979,0.979

0.892,1.011,1.099

0.854,1.025,1.165

1.048,1.048,1.048

0.993,1.059,1.103

0.901,1.022,1.111

1.107,1.033,0.993

0.965,1.029,1.072 1,1,1

1.004,1.044,1.119

0.077,0.079,0.081

A13

0.912,1.042,1.129

0.968,0.968,0.968

0.989,0.989,0.989

0.875,0.937,0.975

0.797,0.968,1.094

0.764,0.982,1.16

0.937,1.004,1.044

0.887,1.014,1.099

0.806,0.978,1.106

0.989,0.989,0.989

0.862,0.985,1.068

0.894,0.958,0.996 1,1,1

0.069,0.076,0.08

Table 3.11: Pair wise comparison matrix W.R.T. Cost for Super critical boiler material selection

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 W

A1 1,1,1 0.923,1,1.1 0.923,1,1.1 0.148,0.154, 0.13,0.125,0 2.727,2.5,2. 0.16,0.167,0 0.01,0.01,0. 0.139,0.133, 0.923,1,1.1 0.05,0.05,0. 0.96,1,1.0 0.092,0.1,0. 0.006,0.006,

43 43 0.164 .118 222 .178 01 0.125 43 05 67 1140.006

A20.875,1,1.

083 1,1,1 1,1,10.16,0.154,0

.1440.141,0.125,

0.1032.955,2.5,1.

9440.173,0.167,

0.1560.011,0.01,0

.0090.151,0.133,

0.11 1,1,10.054,0.05,0

.0441.04,1,0.9

33 0.1,0.1,0.1

0.006,0.006,0.006

A30.875,1,1.

083 1,1,1 1,1,10.16,0.154,0

.1440.141,0.125,

0.1032.955,2.5,1.

9440.173,0.167,

0.1560.011,0.01,0

.0090.151,0.133,

0.11 1,1,10.054,0.05,0

.0441.04,1,0.9

33 0.1,0.1,0.1

0.006,0.006,0.006

A46.094,6.5,

6.7716.964,6.5,6

.256.964,6.5,6

.25 1,1,10.883,0.813,

0.71718.47,16.25,

13.541.083,1.083,

1.0830.068,0.065,

0.0610.942,0.867,

0.7656.25,6.5,6.

9640.339,0.325,

0.3056.5,6.5,6.

50.625,0.65,

0.696

0.041,0.04,0.038

A58.5,8,7.66

79.714,8,7.0

779.714,8,7.0

771.395,1.231,

1.132 1,1,120.91,20,18.

891.227,1.333,

1.5110.077,0.08,0

.0851.067,1.067,

1.0677.077,8,9.7

140.383,0.4,0.

4257.36,8,9.0

670.708,0.8,0.

971

0.049,0.049,0.05

A60.45,0.4,0.

3670.514,0.4,0

.3380.514,0.4,0

.3380.074,0.062,

0.0540.053,0.05,0

.048 1,1,10.059,0.067,

0.080.004,0.004,

0.0050.051,0.053,

0.0560.338,0.4,0

.5140.018,0.02,0

.0230.352,0.4,

0.480.034,0.04,

0.051

0.002,0.002,0.003

A75.625,6,6.

256.429,6,5.7

696.429,6,5.7

690.923,0.923,

0.9230.662,0.75,0

.81512.5,15,17.0

5 1,1,10.063,0.06,0

.0560.87,0.8,0.7

065.769,6,6.4

290.313,0.3,0.

281 6,6,60.577,0.6,0.

643

0.036,0.037,0.036

A8100,100,1

00114.3,100,

92.31114.3,100,

92.3116.41,15.38,

14.7711.76,12.5,1

3.04222.2,250,2

72.717.78,16.67,

16 1,1,113.91,13.33,

12.5592.31,100,

114.3 5,5,596,100,10

6.79.231,10,11

.43

0.614,0.612,0.612

A97.969,7.5,

7.1889.107,7.5,6

.6359.107,7.5,6

.6351.308,1.154,

1.0620.938,0.938,

0.93817.71,18.75,

19.61.417,1.25,1

.150.08,0.075,0

.072 1,1,16.635,7.5,9

.1070.359,0.375,

0.3986.9,7.5,8.

50.663,0.75,

0.911

0.047,0.046,0.046

A10

0.875,1,1.083 1,1,1 1,1,1

0.144,0.154,0.16

0.103,0.125,0.141

1.944,2.5,2.955

0.156,0.167,0.173

0.009,0.01,0.011

0.11,0.133,0.151 1,1,1

0.054,0.05,0.044

1.04,1,0.933 0.1,0.1,0.1

0.006,0.006,0.006

A11 20,20,20

22.86,20,18.46

22.86,20,18.46

3.282,3.077,2.954

2.353,2.5,2.609

44.44,50,54.55

3.556,3.333,3.2 0.2,0.2,0.2

2.51,2.667,2.783

22.86,20,18.46 1,1,1

19.2,20,21.33

1.846,2,2.286

0.124,0.122,0.121

A12

0.938,1,1.042

1.071,1,0.962

1.071,1,0.962

0.154,0.154,0.154

0.11,0.125,0.136

2.083,2.5,2.841

0.167,0.167,0.167

0.009,0.01,0.01

0.118,0.133,0.145

1.071,1,0.962

0.047,0.05,0.052 1,1,1

0.096,0.1,0.107

0.006,0.006,0.006

A13

8.75,10,10.83 10,10,10 10,10,10

1.436,1.538,1.6

1.029,1.25,1.413

19.44,25,29.55

1.556,1.667,1.733

0.088,0.1,0.108

1.098,1.333,1.507 10,10,10

0.438,0.5,0.542

9.333,10,10.4 1,1,1

0.056,0.061,0.064

Table 3.12: Positive decision matrix for Super critical boiler material selection

A1 0.8507

0.8404

0.9378

0.8919

0.8641

0.8615

0.8547

0.8592

0.9878

A2 0.8300

0.8528

0.7731

0.8542

0.8302

0.8288

0.8574

0.8512

0.9880

A3 0.8573

0.8617

0.9122

0.8279

0.8503

0.8519

0.8418

0.8543

0.9880

A4 0.8623

0.8238

0.9279

0.8839

0.8305

0.8692

0.8584

0.8452

0.9225

A5 0.8555

0.8505

0.9088

0.8021

0.8487

0.8346

0.8568

0.8479

0.9038

A6 0.8442

0.8581

0.8306

0.7892

0.8507

0.8450

0.8482

0.8494

0.9951

A7 0.8711

0.8583

0.7842

0.9054

0.8541

0.8499

0.8495

0.8551

0.9284

A8 0.8563

0.8532

0.7091

0.7454

0.8582

0.8849

0.8520

0.8555

0.1499

A9 0.8517

0.8341

0.9665

0.9002

0.8651

0.8777

0.8561

0.8495

0.9097

A10

0.8434

0.8537

0.8786

0.9044

0.8571

0.8326

0.8569

0.8543

0.9880

A11

0.8586

0.8760

0.6940

0.7999

0.8360

0.8443

0.8379

0.8514

0.7699

A12

0.8463

0.8461

0.9279

0.8880

0.8971

0.8539

0.8531

0.8484

0.9879

A13

0.8499

0.8689

0.8554

0.8949

0.8360

0.8437

0.8544

0.8557

0.8830

Table 3.13: Negative decision matrix for Super critical boiler material selection

A1 0.0060

0.0069

0.0010

0.0031

0.0050

0.0052

0.0057

0.0053

0.0000

A2 0.0079

0.0059

0.0146

0.0058

0.0079

0.0081

0.0055

0.0060

0.0000

A3 0.0055

0.0052

0.0020

0.0081

0.0061

0.0059

0.0068

0.0058

0.0000

A4 0.0051

0.0085

0.0013

0.0036

0.0079

0.0046

0.0054

0.0065

0.0016

A5 0.0056

0.0061

0.0022

0.0109

0.0062

0.0075

0.0055

0.0063

0.0024

A6 0.0066

0.0054

0.0079

0.0125

0.0060

0.0065

0.0062

0.0061

0.0000

A7 0.0044

0.0054

0.0131

0.0024

0.0057

0.0061

0.0061

0.0057

0.0013

A8 0.0056

0.0058

0.0249

0.0187

0.0054

0.0035

0.0059

0.0056

0.3755

A9 0.0059

0.0075

0.0003

0.0026

0.0049

0.0040

0.0056

0.0061

0.0021

A10

0.0067

0.0058

0.0039

0.0024

0.0055

0.0077

0.0055

0.0057

0.0000

A11

0.0054

0.0041

0.0279

0.0112

0.0073

0.0066

0.0072

0.0060

0.0150

A12

0.0064

0.0064

0.0013

0.0033

0.0028

0.0058

0.0058

0.0062

0.0000

A13

0.0061

0.0046

0.0057

0.0029

0.0074

0.0067

0.0057

0.0056

0.0036

Table 3.14: Resultant matrix for Super critical boiler material selection

D* D- CC rank

A1 8.45497182 0.54514955 0.06057136 12

A2 8.30210677 0.69900319 0.07765744 3

A3 8.39999681 0.60093272 0.06676341 9

A4 8.38954807 0.61074868 0.06785873 8

A5 8.32802812 0.67199585 0.07466601 5

A6 8.32660081 0.67349974 0.07483247 4

A7 8.35290225 0.64710265 0.07190026 7

A8 7.65667681 1.34333072 0.14925884 1

A9 8.43578858 0.5642637 0.0626956 11

A10 8.41296191 0.58759176 0.06528396 10

A11 8.13868613 0.8613409 0.09570426 2

A12 8.455226 0.54495505 0.06054934 13

A13 8.34687314 0.65444791 0.07270576 6

3.6 Material Selection By Application Of Fuzzy TOPSIS

In this method, Table 6.4 has been taken as data matrix and normalized decision matrix (Table 3.15), weighted decision

matrix (Table 3.17), positive decision matrix (Table 3.18), negative decision matrix (Table 3.19), distance matrices (Table

3.20 & 3.21) and results (Table 3.22) are determined according to the method described in Chapter 2. Criteria weights are

also determined in Table 3.16 as discussed in Chapter 2.

Table 3.15: Fuzzy normalized decision matrix for Super critical boiler material selection

C1 C2 C3 C4 C5 C6 C7 C8 C9

A1

(0.535,0.45,0.274)

(0.267,0.339,0.417)

(0.092,0.099,0.103)

(0.126,0.076,0.078)

(0.56,0.463,0.352)

(0.61,0.607,0.683)

(0.565,0.852,0.767) (0.312,0,0.139) (0.006,0.006,0.

006)

A2(0.589,1,1) (0.752,0.525,0.

384)(0.601,0.706,0.

775)(0.253,0.321,0.

395) (0.796,1,1) (0.362,0,0) (1,0.87,0.464) (0.107,0.685,1) (0.004,0.006,0.007)

A3

(0.105,0.349,0.414)

(0.89,0.695,0.546)

(0.148,0.192,0.221)

(0.348,0.435,0.518)

(0.53,0.7,0.716)

(0.713,0.403,0.353) (0.659,0.07,0) (0.036,0.479,0.

871)(0.004,0.006,0.

007)

A4

(0.162,0.204,0.177) (0.138,0,0) (0.113,0.135,0.

149)(0.136,0.13,0.1

59)(0.926,0.975,0.

888)(0.856,0.721,0.

703)(0.839,0.983,0.

684) (0.463,1,0.959) (0.057,0.061,0.064)

A5

(0.595,0.32,0.054)

(0.301,0.542,0.694)

(0.211,0.197,0.188)

(0.716,0.626,0.577)

(0.909,0.675,0.461)

(0,0.163,0.415) (0.428,1,1) (0.823,0.685,0.

305)(0.081,0.076,0.

073)

A6(1,0.566,0.13) (0.306,0.695,0.

915)(0.542,0.472,0.

426)(0.867,0.702,0.

598)(1,0.638,0.354

)(0.043,0.352,0.

646) (0,0.6,0.957) (1,0.548,0) (0,0,0)

A7(0,0,0) (0.707,0.653,0.

6)(0.605,0.656,0.

69) (0.02,0,0.024) (0.594,0.625,0.569)

(0.548,0.391,0.425)

(0.632,0.53,0.431)

(0.218,0.342,0.561)

(0.052,0.056,0.059)

A8

(0.425,0.32,0.166)

(0.488,0.576,0.626)

(0.939,0.94,0.94) (1,1,1) (0.648,0.55,0.4

29) (1,1,1) (0.498,0.713,0.693)

(0.41,0.247,0.282) (1,1,1)

A9

(0.673,0.407,0.123)

(0,0.237,0.436) (0,0,0) (0.109,0.023,0) (0.653,0.438,0.

262)(0.771,0.893,0.

98)(0.41,0.965,0.9

82)(0.779,0.582,0.

248)(0.076,0.071,0.

068)

A10

(0.353,0.682,0.713)

(0.766,0.542,0.401)

(0.254,0.313,0.351) (0,0.015,0.064) (0.441,0.6,0.62

1)(0.418,0.064,0.

056)(0.989,0.843,0.

449)(0.036,0.479,0.

871)(0.004,0.006,0.

007)

A11

(0.461,0.363,0.202) (0.882,1,1) (1,1,1) (0.725,0.71,0.7

1)(0.978,0.875,0.

713)(0.317,0.313,0.

446) (0.15,0,0.311) (0.516,0.514,0.437)

(0.196,0.197,0.197)

A12

(0.461,0.58,0.502)

(0.507,0.424,0.389)

(0.113,0.135,0.149)

(0.108,0.099,0.128) (0,0,0) (0.612,0.459,0.

483)(0.715,0.713,0.

533)(0.384,0.788,0.

83)(0.005,0.006,0.

007)

A13

(0.159,0.421,0.479)

(1,0.831,0.676)

(0.328,0.397,0.442)

(0.044,0.069,0.122)

(0.718,0.913,0.917)

(0.59,0.262,0.229)

(0.937,0.722,0.378) (0,0.377,0.806) (0.083,0.096,0.

105)

Table 3.16: Criteria weights for Super critical boiler material selection

C1 C2 C3 C4 C5 C6 C7 C8 C9 Weight

C1 11.46

50.05

40.19

90.13

80.04

12.782

0.017

0.183

0.008158

C20.68

21

0.037

0.136

0.094

0.028

1.8990.01

10.12

50.0055

67

C318.626

27.292

13.71

32.56

50.75

551.82

40.31

13.40

80.1519

44

C45.01

77.35

10.26

91

0.691

0.203

13.959

0.084

0.918

0.040926

C57.26

110.640

0.390

1.447

10.20

320.20

30.12

11.32

90.0568

49

C624.658

36.131

1.324

4.915

3.396

168.60

70.41

24.51

20.2011

51

C70.35

90.52

70.01

90.07

20.04

90.01

51

0.006

0.066

0.002932

C859.808

87.635

3.211

11.921

8.237

2.426

166.406

110.944

0.487891

C95.46

58.00

80.29

31.08

90.75

30.22

215.20

60.09

11

0.044582

Table 3.17: Fuzzy weighted normalized decision matrix for Super critical boiler material selection

C1 C2 C3 C4 C5 C6 C7 C8 C9

A1 0.004,0.004,0.002

0.002,0.002,0.003

0.014,0.015,0.016

0.005,0.003,0.003

0.032,0.026,0.02

0.123,0.122,0.137

0.002,0.003,0.002 0.152,0,0.068 0.000,0.000,0

.000

A2 0.005,0.008,0.008

0.005,0.003,0.002

0.091,0.107,0.118

0.01,0.013,0.016

0.045,0.057,0.057 0.073,0,0 0.003,0.003,0

.0010.052,0.334,0

.4880.000,0.000,0

.000

A3 0.001,0.003,0.003

0.005,0.004,0.003

0.023,0.029,0.034

0.014,0.018,0.021

0.03,0.04,0.041

0.143,0.081,0.071 0.002,0.000,0 0.017,0.234,0

.4250.000,0.000,0

.000

A4 0.001,0.002,0.001 0.001,0,0, 0.017,0.02,0.

0230.006,0.005,0

.0070.053,0.056,0

.0510.172,0.145,0

.1410.003,0.003,0

.0020.226,0.488,0

.4680.003,0.003,0

.003

A5 0.005,0.003,0.000

0.002,0.003,0.004

0.032,0.03,0.029

0.029,0.026,0.024

0.052,0.038,0.026 0,0.033,0.083 0.001,0.003,0

.0030.402,0.334,0

.1490.004,0.003,0

.003

A6 0.008,0.005,0.001

0.002,0.004,0.005

0.082,0.072,0.065

0.036,0.029,0.025

0.057,0.036,0.02

0.009,0.071,0.13 0,0.002,0.003 0.488,0.267,0 0.000,0.000,0

.000

A7 0,0,0 0.004,0.004,0.004

0.092,0.1,0.105 0.001,0,0.001 0.034,0.036,0

.0320.11,0.079,0.

0850.002,0.002,0

.0010.106,0.167,0

.2740.002,0.003,0

.003

A8 0.003,0.003,0.001

0.003,0.003,0.004

0.143,0.143,0.143

0.041,0.041,0.041

0.037,0.031,0.024

0.201,0.201,0.201

0.001,0.002,0.002

0.2,0.12,0.138

0.045,0.045,0.045

A9 0.005,0.003,0.001 0,0.001,0.003 0,0,0 0.004,0.001,0 0.037,0.025,0

.0150.155,0.179,0

.1970.001,0.003,0

.0030.38,0.284,0.

1210.003,0.003,0

.003

A10

0.003,0.005,0.006

0.005,0.003,0.002

0.039,0.048,0.053 0,0.001,0.003 0.025,0.034,0

.0350.084,0.013,0

.0110.003,0.003,0

.0010.017,0.234,0

.4250.000,0.000,0

.000

A11

0.004,0.003,0.002

0.005,0.006,0.006

0.152,0.152,0.152

0.03,0.029,0.029

0.056,0.05,0.041

0.064,0.063,0.09 0.000,0,0.001 0.252,0.251,0

.2130.009,0.009,0

.009

A12

0.004,0.005,0.004

0.003,0.003,0.002

0.017,0.02,0.023

0.004,0.004,0.005 0,0,0 0.123,0.092,0

.0970.002,0.002,0

.0020.187,0.384,0

.4050.000,0.000,0

.000

A13

0.001,0.003,0.004

0.006,0.005,0.004

0.05,0.06,0.067

0.002,0.003,0.005

0.041,0.052,0.052

0.119,0.053,0.046

0.003,0.002,0.001 0,0.184,0.393 0.004,0.004,0

.005

Table 3.18: Fuzzy positive decision matrix for Super critical boiler material selection

C1 C2 C3 C4 C5 C6 C7 C8 C9

A1 0.99,0.993,0.996

0.997,0.996,0.995

0.972,0.97,0.969

0.99,0.994,0.994

0.937,0.948,0.96

0.77,0.771,0.744

0.997,0.995,0.995 0.719,1,0.869 1,0.999,0.999

A2 0.991,0.984,0.984

0.991,0.994,0.995

0.826,0.797,0.778

0.979,0.974,0.968

0.911,0.889,0.889 0.86,1,1 0.994,0.995,0

.9970.898,0.443,0

.262 1,0.999,0.999

A3 0.998,0.994,0.993

0.989,0.992,0.993

0.955,0.942,0.934

0.972,0.965,0.958

0.941,0.922,0.92

0.734,0.844,0.863 0.996,1,1 0.965,0.587,0

.331 1,0.999,0.999

A4 0.997,0.997,0.997 0.998,1,1 0.966,0.959,0

.9550.989,0.989,0

.9870.897,0.892,0

.9010.685,0.731,0

.7370.995,0.994,0

.9960.599,0.262,0

.2830.995,0.994,0

.994

A5 0.991,0.995,0.999

0.996,0.994,0.992

0.937,0.941,0.944

0.942,0.949,0.953

0.899,0.925,0.948 1,0.936,0.84 0.997,0.994,0

.9940.358,0.443,0

.7250.993,0.993,0

.993

A6 0.984,0.991,0.998

0.996,0.992,0.989

0.842,0.862,0.875

0.93,0.943,0.952

0.889,0.929,0.96

0.983,0.864,0.757 1,0.996,0.994 0.262,0.537,1 1,1,1

A7 1,1,1 0.992,0.992,0.993

0.824,0.81,0.801 0.998,1,0.998 0.933,0.93,0.

9360.792,0.849,0

.8370.996,0.997,0

.9970.798,0.694,0

.5270.995,0.995,0

.995

A8 0.993,0.995,0,.997

0.994,0.993,0.993

0.735,0.735,0.735

0.92,0.92,0.92

0.927,0.938,0.952

0.638,0.638,0.638

0.997,0.996,0.996

0.64,0.774,0.744

0.912,0.912,0.912

A9 0.989,0.994,0.998 1,0.997,0.995 1,1,1 0.991,0.998,1 0.927,0.951,0

.970.714,0.673,0

.6450.998,0.994,0

.9940.384,0.512,0

.7730.993,0.994,0

.994

A10

0.994,0.989,0.989

0.991,0.994,0.995

0.924,0.907,0.896 1,0.999,0.995 0.95,0.933,0.

930.839,0.974,0

.9770.994,0.995,0

.9970.965,0.587,0

.331 1,0.999,0.999

A11

0.993,0.994,0.997

0.989,0.988,0.988

0.719,0.719,0.719

0.941,0.943,0.943

0.892,0.903,0.92

0.877,0.878,0.829 0.999,1,0.998 0.56,0.561,0.

6190.982,0.982,0

.982

A12

0.993,0.991,0.992

0.994,0.995,0.995

0.966,0.959,0.955

0.991,0.992,0.99 1,1,1 0.769,0.824,0

.8150.996,0.996,0

.9970.66,0.379,0.

354 1,0.999,0.999

A13

0.997,0.993,0.992

0.988,0.99,0.992

0.903,0.883,0.87

0.996,0.994,0.99

0.92,0.899,0.898

0.777,0.898,0.91

0.994,0.996,0.998 1,0.666,0.368 0.993,0.991,0

.991

Table 3.19: Fuzzy negative decision matrix for Super critical boiler material selection

C1 C2 C3 C4 C5 C6 C7 C8 C9

A1 0.0000,0.0000,0.0000

0.0000,0.0000,0.0000

0.0002,0.0002,0.0002

0.0000,0.0000,0.0000

0.0010,0.0007,0.0004

0.0150,0.0149,0.0188

0.0000,0.0000,0.0000

0.0231,0.0000,0.0046

0.0000,0.0000,0.0000

A2 0.0000,0.0001,0.0001

0.0000,0.0000,0.0000

0.0083,0.0115,0.0139

0.0001,0.0002,0.0003

0.0021,0.0032,0.0032

0.0053,0.0000,0.0000

0.0000,0.0000,0.0000

0.0027,0.1117,0.2381

0.0000,0.0000,0.0000

A3 0.0000,0.0000,0.0000

0.0000,0.0000,0.0000

0.0005,0.0009,0.0011

0.0002,0.0003,0.0005

0.0009,0.0016,0.0017

0.0205,0.0066,0.0050

0.0000,0.0000,0.0000

0.0003,0.0547,0.1806

0.0000,0.0000,0.0000

A4 0.0000,0.0000,0.0000

0.0000,0.0000,0.0000

0.0003,0.0004,0.0005

0.0000,0.0000,0.0000

0.0028,0.0031,0.0026

0.0296,0.0210,0.0199

0.0000,0.0000,0.0000

0.0511,0.2381,0.2188

0.0000,0.0000,0.0000

A5 0.0000,0.0000,0.0000

0.0000,0.0000,0.0000

0.0010,0.0009,0.0008

0.0009,0.0007,0.0006

0.0027,0.0015,0.0007

0.0000,0.0011,0.0070

0.0000,0.0000,0.0000

0.1612,0.1117,0.0221

0.0000,0.0000,0.0000

A6 0.0001,0.0000,0.0000

0.0000,0.0000,0.0000

0.0068,0.0052,0.0042

0.0013,0.0008,0.0006

0.0032,0.0013,0.0004

0.0001,0.0050,0.0169

0.0000,0.0000,0.0000

0.2381,0.0715,0.0000

0.0000,0.0000,0.0000

A7 0.0000,0.0000,0.0000

0.0000,0.0000,0.0000

0.0085,0.0100,0.0110

0.0000,0.0000,0.0000

0.0011,0.0013,0.0011

0.0121,0.0062,0.0073

0.0000,0.0000,0.0000

0.0113,0.0279,0.0750

0.0000,0.0000,0.0000

A8 0.0000,0.0000,0.0000

0.0000,0.0000,0.0000

0.0204,0.0204,0.0204

0.0017,0.0017,0.0017

0.0014,0.0010,0.0006

0.0404,0.0404,0.0404

0.0000,0.0000,0.0000

0.0400,0.0145,0.0190

0.0020,0.0020,0.0020

A9 0.0000,0.0000,0.0000

0.0000,0.0000,0.0000

0.0000,0.0000,0.0000

0.0000,0.0000,0.0000

0.0014,0.0006,0.0002

0.0240,0.0322,0.0388

0.0000,0.0000,0.0000

0.1447,0.0807,0.0146

0.0000,0.0000,0.0000

A10

0.0000,0.0000,0.0000

0.0000,0.0000,0.0000

0.0015,0.0023,0.0028

0.0000,0.0000,0.0000

0.0006,0.0012,0.0013

0.0071,0.0002,0.0001

0.0000,0.0000,0.0000

0.0003,0.0547,0.1806

0.0000,0.0000,0.0000

A11

0.0000,0.0000,0.0000

0.0000,0.0000,0.0000

0.0231,0.0231,0.0231

0.0009,0.0008,0.0008

0.0031,0.0025,0.0017

0.0041,0.0040,0.0080

0.0000,0.0000,0.0000

0.0635,0.0628,0.0455

0.0001,0.0001,0.0001

A12

0.0000,0.0000,0.0000

0.0000,0.0000,0.0000

0.0003,0.0004,0.0005

0.0000,0.0000,0.0000

0.0000,0.0000,0.0000

0.0151,0.0085,0.0094

0.0000,0.0000,0.0000

0.0351,0.1478,0.1642

0.0000,0.0000,0.0000

A13

0.0000,0.000,0.0000

0.0000,0.000,0.0000

0.0025,0.0036,0.0045

0.0000,0.0000,0.0000

0.0017,0.0027,0.0027

0.0141,0.0028,0.0021

0.0000,0.0000,0.0000

0.0000,0.0338,0.1548

0.0000,0.0000,0.0000

Table 3.20: Fuzzy distance matrix from positive ideal solution for Super critical boiler material selection

C1 C2 C3 C4 C5 C6 C7 C8 C9

A10.996643

3160.997954

4660.985129

0410.996181

8410.973897

5950.872733

8850.997815

0440.928752

5290.999731

416

A20.993097

7460.996677

270.894639

4190.986772

3840.946897

1440.976340

2090.997666

3840.731064

3310.999737

706

A30.997685

2860.995738

3810.971539

5750.982219

3690.963049

2020.902126

8810.999271

750.792219

2640.999737

706

A40.998552

3660.999724

2140.979914

210.994195

3780.946996

9350.847372

4810.997495

3020.617592

1790.997266

786

A50.997417

2740.996924

6080.969801

1650.973775

9020.961201

6470.961853

6380.997572

0590.713245

6130.996543

443

A60.995480

5180.996167

9770.927023

6920.970390

3560.962279

7740.931554

0110.998443

7930.774349

3561

A7 10.996081

780.901142

4770.999388

0320.966023

1630.908756

7710.998406

2260.820449

5760.997491

128

A80.997573

7180.996619

8110.857141

9230.959

0.969097545

0.7990.998096

4470.848015

8060.955

A90.996792

7890.998653

7221

0.998195061

0.974342039

0.823088673

0.997642688

0.745987111

0.996770931

A10

0.995340504

0.996583381

0.953525608

0.99891502

0.968433395

0.964496356

0.997718727

0.792219264

0.999737706

A11

0.997263583

0.994236509

0.8480.970676

8470.951269

8190.927965

8390.999538

7810.761583

8780.991146

599A12

0.995883019

0.997358992

0.97991421

0.995417168

10.895999

7580.998038

340.681418

970.999734

561A13

0.997175544

0.994987275

0.94091741

0.996789928

0.951608079

0.928178201

0.997963002

0.823408101

0.995727892

Table 3.21: Fuzzy distance matrix from negative ideal solution for Super critical boiler material selection

C1 C2 C3 C4 C5 C6 C7 C8 C9

A10.003468

1710.002078

2790.014885

7040.003932

6790.026558

1160.127490

8670.002214

630.096179

440.000269

024

A20.007075

4930.003444

8930.105986

6790.013441

2190.053401

6030.042024

6330.002432

1010.342835

1850.000267

811

A30.002547

2280.004344

6040.028833

5330.018012

7110.037273

2990.103514

6930.001147

8990.280271

3460.000267

811

A40.001454

2790.000477

8070.020212

7170.005828

6680.053043

7230.153355

9140.002531

4030.411547

9220.002736

821

A50.003129

8710.003225

1620.030233

7210.026332

5170.040229

4390.051789

9940.002559

3440.313611

0310.003459

419

A60.005341

0750.004119

9520.073362

470.029967

1840.040728

9170.085524

1330.001956

280.321271

0670

A7 00.003927

0460.099012

8010.000752

810.034002

3870.092350

170.001612

6660.195168

0550.002512

281

A80.002571

6380.003397

6670.142858

0850.041

0.031337567

0.2010.001925

7830.156462

8950.045

A90.003677

0870.001719

9580

0.002643563

0.027270945

0.177929092

0.002488717

0.282823313

0.003231723

A10

0.00483973

0.003533866

0.046883941

0.001561338

0.031907785

0.049527763

0.002381855

0.280271346

0.000267811

A11

0.002867842

0.005773239

0.1520.029324

6850.049144

930.073168

1670.000598

2260.239298

6080.008853

41A12

0.004135927

0.002657733

0.020212717

0.004608689

00.104974

7110.001978

3350.340132

5170.000267

702A13

0.003036544

0.005075514

0.059531044

0.003475658

0.04869429

0.079464127

0.002150912

0.250741787

0.004290956

Table 3.22: RESULT for Super critical boiler material selection

D* D- CC RANK

A18.74883

9130.27707

6910.0307

13

A28.52289

2590.57090

9620.0628

3

A38.60358

7410.47621

3120.0524

9

A48.37910

9850.65118

9250.0721

1

A58.56833

5350.47457

050.0525

8

A68.55568

9480.56227

1080.0617

5

A78.58773

9150.42933

8210.0476

11

A88.37954

5250.62555

3630.0695

2

A98.53147

3010.50178

440.0555

6

A10

8.66696996

0.42117544

0.0463

12

A11

8.44168186

0.56102911

0.0623

4

A12

8.54376502

0.47896833

0.0531

7

A13

8.62675543

0.45646083

0.0503

10