Table 7 Constants of the mathematical models and their goodness-of-fit parameters at different slice thicknesses and drying tray positions.

From: Modeling, environmental and economic analysis of drying of orange slice in an automatic indirect mixed mode solar dryer

Thin layer models

Layer thickness, mm

Models’ constants values

Goodness of fit indices

Constants

Values

Standard Error

p-value*

RMSE

R2

R2adj.

Tray no. 1 (Lower tray)

Aghbashlo

4

k1

0.1146

0.0138

2.65 × 10− 6

0.0549

0.9688

0.9662

K2

-0.0195

0.0117

0.1218

6

k1

0.0932

0.0093

9.17 × 10− 8

0.0451

0.9733

0.9714

K2

-0.0088

0.0089

0.3388

8

k1

0.0651

0.0039

3.63 × 10− 13

0.0330

0.9846

0.9838

K2

-0.0101

0.0036

0.0120

Henderson - Pabis

4

k

0.1478

0.0083

5.02 × 10− 10

0.0499

0.9743

0.9721

a

1.0806

0.0349

8.07 × 10− 13

6

k

0.1078

0.0051

4.78 × 10− 12

0.0424

0.9764

0.9748

a

1.0458

0.0271

1.25 × 10− 15

8

k

0.0781

0.0027

7.06 × 10− 18

0.0352

0.9824

0.9815

a

1.0319

0.0197

7.16 × 10− 23

Lewis (Newton)

4

k

0.1349

0.0068

4.44 × 10− 11

0.0579

0.9624

0.9624

6

k

0.1017

0.0037

3.48 × 10− 14

0.0450

0.9716

0.9716

8

k

0.0750

0.0019

3.38 × 10− 21

0.0365

0.9801

0.9801

Logarithmic (Asymptotic)

4

k

0.1371

0.0296

0.0007

0.0517

0.9746

0.9700

a

1.1131

0.0980

2.05 × 10− 7

c

-0.0395

0.1117

0.7300

6

k

0.1049

0.0224

0.0004

0.0440

0.9765

0.9729

a

1.0582

0.0998

9.07 × 10− 8

c

-0.0148

0.1133

0.8980

8

k

0.0576

0.0103

2.07 × 10− 7

0.0329

0.9853

0.9838

a

1.1925

0.1112

1.69 × 10− 9

c

-0.1844

0.1225

0.1487

Midilli

4

k

0.0730

0.0199

0.0043

0.0371

0.9881

0.9845

a

1.0195

0.0323

2.41 × 10− 11

b

0.0125

0.0032

0.0028

n

1.4996

0.1618

3.17 × 10− 6

6

k

0.0934

0.0298

0.0086

0.0452

0.9771

0.9713

a

1.0319

0.0420

1.25 × 10− 11

b

0.0028

0.0075

0.7123

n

1.0951

0.2022

0.0002

8

k

0.0778

0.0214

0.0019

0.0330

0.9861

0.9838

a

1.0246

0.0309

1.36 × 10− 17

b

-0.0080

0.0062

0.2120

n

0.8792

0.1695

6.21 × 10− 5

Modified Midilli (I)

4

k

0.0650

0.0122

0.0002

0.0361

0.9876

0.9854

b

0.0130

0.0028

0.0008

n

1.5588

0.1250

7.81 × 10− 8

6

k

0.0783

0.0160

0.0003

0.0446

0.9757

0.9720

b

0.0042

0.0066

0.5412

n

1.1769

0.1578

4.77 × 10− 6

8

k

0.0653

0.0099

2.48 × 10− 6

0.0327

0.9855

0.9840

b

-0.0067

0.0054

0.2354

n

0.9538

0.1271

4.28 × 10− 7

Modified Midilli (II)

4

k

0.0640

0.0209

0.0119

0.0343

0.9899

0.9868

a

0.8214

0.0438

4.02 × 10− 9

b

0.1932

0.0264

2.55 × 10− 5

n

1.6848

0.2023

8.28 × 10− 6

6

k

0.0958

0.0294

0.0069

0.0449

0.9774

0.9717

a

0.9302

0.1611

8.81 × 10− 5

b

0.1000

0.1410

0.4916

n

1.1379

0.2301

0.0003

8

k

0.0571

0.0166

0.0030

0.0331

0.9860

0.9836

a

1.5360

0.7239

0.0480

b

-0.5115

0.7090

0.4799

n

0.8760

0.1603

3.44 × 10− 5

Modified Page

4

k

0.1369

0.0048

2.38 × 10− 12

0.0473

0.9768

0.9749

n

1.2303

0.0949

2.04 × 10− 8

6

k

0.1031

0.0035

5.29 × 10− 14

0.0436

0.9751

0.9733

n

1.1019

0.0782

1.16 × 10− 9

8

k

0.0758

0.0017

1.65 × 10− 21

0.0341

0.9835

0.9827

n

1.1005

0.0515

3.03 × 10− 15

Page

4

k

0.0866

0.0166

0.0002

0.0473

0.9768

0.9749

n

1.2303

0.0949

2.04 × 10− 8

6

k

0.0818

0.0141

4.56 × 10− 5

0.0436

0.9751

0.9733

n

1.1019

0.0782

1.16 × 10− 9

8

k

0.0585

0.0076

2.02 × 10− 7

0.0341

0.9835

0.9827

n

1.1005

0.0515

3.03 × 10− 15

Wang-Sigh

4

b

-0.1145

0.0074

2.88 × 10− 9

0.0530

0.9709

0.9685

a

0.0038

0.0007

0.0002

6

b

-0.0875

0.0053

1.29 × 10− 10

0.0462

0.9720

0.9700

a

0.0023

0.0004

0.0001

8

b

-0.0621

0.0024

5.15 × 10− 17

0.0338

0.9838

0.9829

a

0.0011

0.0001

2.13 × 10− 7

Weibullian (I)

4

β

1.2303

0.0949

2.04 × 10− 8

0.0473

0.9768

0.9749

α

7.3060

0.2584

2.38 × 10− 12

6

β

1.1019

0.0782

1.16 × 10− 9

0.0436

0.9751

0.9733

α

9.6968

0.3288

5.29 × 10− 14

8

β

1.1005

0.0515

3.03 × 10− 15

0.0341

0.9835

0.9827

α

13.1896

0.2953

1.65 × 10− 21

Weibullian (II)

4

n

1.2303

0.0949

2.04 × 10− 8

0.0473

0.9768

0.9749

δ

14.3914

0.9296

2.71 × 10− 9

6

n

1.1019

0.0782

1.16 × 10− 9

0.0436

0.9751

0.9733

δ

20.6702

1.4533

1.03 × 10− 9

8

n

1.1005

0.0515

3.03 × 10− 15

0.0341

0.9835

0.9827

δ

28.1434

1.2941

2.17 × 10− 15

Tray no. 2 (Middel tray)

Aghbashlo

4

k1

0.1140

0.0117

1.27 × 10− 7

0.0488

0.9732

0.9713

K2

-0.0080

0.0098

0.4290

6

k1

0.0836

0.0073

4.02 × 10− 9

0.0417

0.9757

0.9742

K2

-0.0066

0.0070

0.3587

8

k1

0.0606

0.0029

6.51 × 10− 17

0.0280

0.9881

0.9877

K2

-0.0044

0.0027

0.1182

Henderson - Pabis

4

k

0.1316

0.0061

3.83 × 10− 12

0.0432

0.9790

0.9775

a

1.0622

0.0289

2.54 × 10− 15

6

k

0.0939

0.0041

1.06 × 10− 13

0.0405

0.9770

0.9756

a

1.0326

0.0246

8.34 × 10− 18

8

k

0.0666

0.0017

3.07 × 10− 23

0.0282

0.9880

0.9875

a

1.0208

0.0148

3.85 × 10− 29

Lewis (Newton)

4

k

0.1225

0.0048

1.00 × 10− 13

0.0482

0.9719

0.9719

6

k

0.0900

0.0029

1.70 × 10− 16

0.041

0.9745

0.9745

8

k

0.0649

0.0012

1.46 × 10− 27

0.0287

0.9870

0.9870

Logarithmic (Asymptotic)

4

k

0.1406

0.0221

2.45 × 10− 5

0.0445

0.9793

0.9761

a

1.0384

0.0595

2.09 × 10− 10

c

0.0309

0.0676

0.6553

6

k

0.0869

0.0181

0.0002

0.0417

0.9772

0.9742

a

1.0681

0.1019

2.67 × 10− 8

c

-0.0419

0.1152

0.7212

8

k

0.0600

0.0071

1.75 × 10− 8

0.0282

0.9885

0.9875

a

1.0679

0.0569

1.94 × 10− 15

c

-0.0564

0.0651

0.3949

Midilli

4

k

0.0854

0.0215

0.0019

0.0371

0.9867

0.9834

a

1.0271

0.0329

7.30 × 10− 13

b

0.0097

0.0029

0.0058

n

1.3270

0.1426

7.72 × 10− 7

6

k

0.0956

0.0298

0.0064

0.0428

0.9775

0.9727

a

1.0323

0.0406

4.00 × 10− 13

b

-0.0037

0.0084

0.6689

n

0.9437

0.2036

0.0004

8

k

0.0709

0.0164

0.0003

0.0285

0.9887

0.9872

a

1.0225

0.0258

5.69 × 10− 22

b

-0.0028

0.0032

0.3812

n

0.9305

0.1190

8.62 × 10− 8

Modified Midilli I

4

k

0.0737

0.0129

7.29 × 10− 5

0.0367

0.9859

0.9837

b

0.0103

0.0026

0.0017

n

1.3960

0.1127

1.42 × 10− 8

6

k

0.0793

0.0150

9.11 × 10− 5

0.0425

0.9763

0.9731

b

-0.0024

0.0076

0.7573

n

1.0234

0.1608

1.27 × 10− 5

8

k

0.0601

0.0078

8.39 × 10− 8

0.0285

0.9883

0.9873

b

-0.0019

0.0027

0.5013

n

0.9978

0.0859

4.18 × 10− 11

Modified Midilli II

4

k

0.0816

0.0236

0.0047

0.0350

0.9882

0.9852

a

0.8419

0.0485

7.19 × 10− 10

b

0.1812

0.0301

5.97 × 10− 5

n

1.4536

0.1734

2.32 × 10− 6

6

k

0.0882

0.0216

0.0011

0.0430

0.9774

0.9725

a

1.1399

0.3726

0.0085

b

-0.1084

0.3544

0.7641

n

0.9529

0.2112

0.0005

8

k

0.0641

0.0102

2.55 × 10− 6

0.0286

0.9887

0.9872

a

1.1778

0.2362

5.44 × 10− 5

b

-0.1554

0.2229

0.4930

n

0.9262

0.1229

1.56 × 10− 7

Modified Page

4

k

0.1233

0.0042

4.79 × 10− 14

0.0450

0.9771

0.9755

n

1.1276

0.0783

8.77 × 10− 10

6

k

0.0908

0.0028

6.17 × 10− 16

0.0413

0.9761

0.9746

n

1.0668

0.0683

4.20 × 10− 11

8

k

0.0652

0.0011

4.33 × 10− 27

0.0282

0.9880

0.9875

n

1.0507

0.0376

8.07 × 10− 20

Page

4

k

0.0944

0.0158

3.35 × 10− 5

0.0450

0.9771

0.9755

n

1.1276

0.0783

8.77 × 10− 10

6

k

0.0773

0.0123

1.03 × 10− 5

0.0413

0.9761

0.9746

n

1.0668

0.0683

4.20 × 10− 11

8

k

0.0568

0.0057

5.31 × 10− 10

0.0282

0.9880

0.9875

n

1.0507

0.0376

8.07 × 10− 20

Wang-Sigh

4

b

-0.1068

0.0053

9.06 × 10− 12

0.0463

0.9758

0.9741

a

0.0035

0.0004

1.70 × 10− 6

6

b

-0.0769

0.0041

3.11 × 10− 12

0.0437

0.9732

0.9716

a

0.0018

0.0003

3.03 × 10− 5

8

b

-0.0561

0.0016

2.60 × 10− 22

0.0292

0.9872

0.9866

a

0.0010

7.96E-05

1.35 × 10− 11

Weibullian (I)

4

β

1.1276

0.0783

8.77 × 10− 10

0.0450

0.9771

0.9755

α

8.1109

0.2731

4.79 × 10− 14

6

β

1.0668

0.0683

4.20 × 10− 11

0.0413

0.9761

0.9746

α

11.0145

0.3441

6.17 × 10− 16

8

β

1.0506

0.0376

8.07 × 10− 20

0.0282

0.9880

0.9875

α

15.3284

0.2701

4.33 × 10− 27

Weibullian (II)

4

n

1.1276

0.0783

8.77 × 10− 10

0.0450

0.9771

0.9755

δ

16.9937

1.0591

2.08 × 10− 10

6

n

1.0668

0.0683

4.20 × 10− 11

0.0413

0.9761

0.9746

δ

24.0717

1.5808

6.10 × 10− 11

8

n

1.0506

0.0376

8.07 × 10− 20

0.0282

0.9880

0.9875

δ

33.9041

1.2352

1.23 × 10− 19

Tray no. 3 (Upper tray)

Aghbashlo

4

k1

0.1126

0.0097

1.64 × 10− 9

0.0431

0.9765

0.9751

k1

0.0050

0.0082

0.5472

6

k1

0.0841

0.0070

5.08 × 10− 10

0.0419

0.9751

0.9737

k1

-0.0012

0.0066

0.8529

8

k1

0.0519

0.0023

4.74 × 10− 19

0.0258

0.9882

0.9877

k1

-0.0004

0.0024

0.8721

Henderson - Pabis

4

k

0.1118

0.0047

1.87 × 10− 14

0.0415

0.9783

0.9770

a

1.0359

0.0261

3.29 × 10− 18

6

k

0.0881

0.0037

3.90 × 10− 15

0.0407

0.9764

0.9751

a

1.0248

0.0239

1.43 × 10− 19

8

k

0.0524

0.0012

2.29 × 10− 26

0.0259

0.9881

0.9877

a

1.0016

0.0125

1.21 × 10− 33

Lewis (Newton)

4

k

0.1071

0.0034

3.82 × 10− 17

0.0425

0.9759

0.9759

6

k

0.0853

0.0025

2.06 × 10− 18

0.0408

0.9750

0.9750

8

k

0.0523

0.0008

4.05 × 10− 32

0.0254

0.9881

0.9881

Logarithmic (Asymptotic)

4

k

0.1424

0.0157

1.05 × 10− 7

0.0376

0.9832

0.9811

a

0.9669

0.0360

9.87 × 10− 15

c

0.0990

0.0383

0.0200

6

k

0.0933

0.0158

1.76 × 10− 5

0.0418

0.9766

0.9738

a

1.0019

0.0681

4.23 × 10− 11

c

0.0285

0.0789

0.7224

8

k

0.0498

0.0060

9.17 × 10− 9

0.0263

0.9882

0.9873

a

1.0252

0.0584

6.27 × 10− 16

c

-0.0275

0.0662

0.6807

Midilli

4

k

0.0937

0.0204

0.0004

0.0342

0.9869

0.9843

a

1.0325

0.0305

1.42 × 10− 15

b

0.0082

0.0021

0.0015

n

1.2008

0.1144

2.63 × 10− 8

6

k

0.0974

0.0293

0.0043

0.0430

0.9767

0.9723

a

1.0354

0.0402

1.89 × 10− 14

b

-0.0007

0.0058

0.9026

n

0.9524

0.1747

5.34 × 10− 5

8

k

0.0717

0.0157

0.0001

0.0250

0.9898

0.9885

a

1.0248

0.0231

2.69 × 10− 25

b

-0.0046

0.0031

0.1495

n

0.8155

0.1152

2.01 × 10− 7

Modified Midilli (I)

4

k

0.0794

0.0121

6.65 × 10− 6

0.0346

0.9858

0.9840

b

0.0087

0.0019

0.0004

n

1.2721

0.0920

2.57 × 10− 10

6

k

0.0799

0.0151

5.86 × 10− 5

0.0429

0.9753

0.9724

b

0.0004

0.0052

0.9445

n

1.0334

0.1380

8.86 × 10− 7

8

k

0.0590

0.0070

6.23 × 10− 9

0.0252

0.9892

0.9884

b

-0.0036

0.0028

0.2094

n

0.8908

0.0849

7.75 × 10− 11

Modified Midilli (II)

4

k

0.0934

0.0227

0.0009

0.0323

0.9884

0.9860

a

0.8443

0.0442

6.10 × 10− 12

b

0.1843

0.0264

4.48 × 10− 6

n

1.3052

0.1373

9.67 × 10− 8

6

k

0.0957

0.0233

0.0008

0.0430

0.9766

0.9722

a

1.0354

0.2221

0.0003

b

-0.0011

0.2031

0.9959

n

0.9685

0.1888

0.0001

8

k

0.0534

0.0112

7.09 × 10 − 5

0.0251

0.9897

0.9884

a

1.4592

0.5168

0.0092

b

-0.4346

0.5049

0.3976

n

0.8145

0.1126

1.40 × 10− 7

Modified Page

4

k

0.1072

0.0035

2.30 × 10− 16

0.0436

0.9760

0.9746

n

1.0164

0.0639

1.20 × 10− 11

6

k

0.0856

0.0026

1.57 × 10− 17

0.0417

0.9753

0.9739

n

1.0254

0.0625

2.83 × 10− 12

8

k

0.0522

0.0009

3.95 × 10− 30

0.0258

0.9882

0.9877

n

0.9928

0.0325

1.74 × 10− 22

Page

4

k

0.1033

0.0151

2.80 × 10− 6

0.0436

0.9760

0.9746

n

1.0164

0.0639

1.20 × 10− 11

6

k

0.0804

0.0121

2.99 × 10− 6

0.0417

0.9753

0.9739

n

1.0254

0.0625

2.83 × 10− 12

8

k

0.0533

0.0049

1.86 × 10− 11

0.0258

0.9882

0.9877

n

0.9928

0.0325

1.74 × 10− 22

Wang-Sigh

4

b

-0.0966

0.0036

2.13 × 10− 15

0.0410

0.9788

0.9775

a

0.0029

0.0002

1.67 × 10− 9

6

b

-0.0748

0.0036

5.22 × 10− 14

0.0447

0.9715

0.9700

a

0.0017

0.0002

1.01 × 10− 6

8

b

-0.0467

0.0013

3.87 × 10− 24

0.0290

0.9851

0.9845

a

0.0007

5.99E-05

5.70 × 10− 12

Weibullian (I)

4

β

1.0164

0.0639

1.20 × 10− 11

0.0436

0.9760

0.9746

α

9.3297

0.3025

2.30 × 10− 16

6

β

1.0254

0.0625

2.83 × 10− 12

0.0417

0.9753

0.9739

α

11.6860

0.3553

1.57 × 10− 17

8

β

0.9928

0.0325

1.74 × 10− 22

0.0258

0.9882

0.9877

α

19.1517

0.3232

3.95 × 10− 30

Weibullian (II)

4

n

1.0164

0.0639

1.20 × 10− 11

0.0436

0.9760

0.9746

δ

21.1960

1.2987

8.06 × 10− 12

6

n

1.0254

0.0625

2.83 × 10− 12

0.0417

0.9753

0.9739

δ

26.3568

1.6709

5.54 × 10− 12

8

n

0.9928

0.0325

1.74 × 10− 22

0.0258

0.9882

0.9877

δ

44.3668

1.6469

4.77 × 10− 21

  1. * bold numbers were significant at p ≤ 0.05.
Back to article page