Table 6 Mathematical models’ constants values and goodness of fit indices results of Henna leaves for DDSD at different layer thicknesses.

From: Mathematical modeling, drying kinetics, and economic analysis of a hybrid photovoltaic thermal solar dryer for henna leaves

MMs

LT

Models’ constants values

Goodness of fit indices

Parameters

Estimates

Standard error

p value

Sign./insign

RMSE

R2

R2adj

Aghbashlo

2

k1

0.2766

0.0207

5.84*10–9

Sign

0.033593

0.988174

0.987264

k1

− 0.0003

0.0125

0.9841

InSign

   

4

k1

0.0400

0.0277

0.1710

InSign

0.343264

− 0.422381

− 0.523980

k1

− 0.0667

0.0245

0.0167

Sign

   

6

k1

0.0401

0.0192

0.0547

InSign

0.245140

0.384318

0.343273

k1

− 0.0625

0.0168

0.0021

Sign

   

Henderson—Pabis

2

k

0.2762

0.0124

9.59*10–12

Sign

0.033578

0.988185

0.987276

a

0.9970

0.0275

1.93*10–14

Sign

   

4

k

0.2657

0.0161

1.43*10–10

Sign

0.043503

0.977155

0.975523

a

0.9400

0.0353

2.13*10–13

Sign

   

6

k

0.1983

0.0061

2.45*10–15

Sign

0.026686

0.992704

0.992217

a

1.0306

0.0199

2.50*10–18

Sign

   

Lewis (Newton)

2

k

0.2770

0.0095

6.22*10–14

Sign

0.032372

0.988174

0.988174

4

k

0.2831

0.0139

2.48*10–12

Sign

0.046034

0.972592

0.972592

6

k

0.1924

0.0048

1.84*10–17

Sign

0.027825

0.991539

0.991539

Logarithmic (Asymptotic)

2

k

0.2841

0.0231

3.64*10–8

Sign

0.034671

0.988372

0.986434

a

0.9916

0.0310

5.60*10–13

Sign

   

c

0.0092

0.0210

0.6691

InSign

   

4

k

0.2815

0.0297

3.31*10–7

Sign

0.044431

0.977871

0.974467

a

0.9315

0.0390

3.95*10–12

Sign

   

c

0.0166

0.0245

0.5098

InSign

   

6

k

0.1914

0.0129

6.12*10–10

Sign

0.027277

0.992885

0.991869

a

1.0385

0.0243

3.08*10–16

Sign

   

c

− 0.0129

0.0221

0.5691

InSign

   

Midilli

2

k

0.2472

0.0391

5.72*10–5

Sign

0.034850

0.989231

0.986294

a

0.9847

0.0339

9.45*10–12

Sign

   

b

0.0020

0.0018

0.2947

InSign

   

n

1.0967

0.1047

4.66*10–7

Sign

   

4

k

0.3628

0.0564

3.24*10–5

Sign

0.042238

0.981541

0.976926

a

0.9853

0.0419

2.08*10–11

Sign

   

b

− 0.0018

0.0028

0.5321

InSign

   

n

0.8021

0.1076

7.69*10–6

Sign

   

6

k

0.1737

0.0244

7.68*10–6

Sign

0.027386

0.993341

0.991804

a

1.0136

0.0261

7.79*10–15

Sign

   

b

0.0004

0.0016

0.7988

InSign

   

n

1.0706

0.0819

7.49*10–9

Sign

   

Modified Midilli I

2

k

0.2603

0.0282

8.42*10–7

Sign

0.033653

0.989045

0.987219

b

0.0018

0.0017

0.3213

InSign

   

n

1.0692

0.0843

2.60*10–8

Sign

   

4

k

0.3772

0.0417

5.63*10–7

Sign

0.040776

0.981363

0.978496

b

− 0.0020

0.0028

0.4716

InSign

   

n

0.7829

0.0923

1.17*10–6

Sign

   

6

k

0.1650

0.0159

5.79*10–8

Sign

0.026682

0.993192

0.992219

b

0.0006

0.0015

0.6951

InSign

   

n

1.0943

0.0662

1.39*10–10

Sign

   

Modified Midilli I I

2

k

0.2506

0.0399

5.98*10–5

Sign

0.034977

0.989152

0.986194

a

0.9565

0.0453

3.02*10–10

Sign

   

b

0.0276

0.0247

0.2879

InSign

   

n

1.1100

0.1176

1.32*10–6

Sign

   

4

k

0.3527

0.0472

7.52*10–6

Sign

0.041913

0.981824

0.977280

a

1.0315

0.0847

4.09*10–8

Sign

   

b

− 0.0445

0.0673

0.5210

InSign

   

n

0.7782

0.1188

2.73*10–5

Sign

   

6

k

0.1720

0.0234

5.63*10–6

Sign

0.027200

0.993431

0.991915

a

0.9963

0.0432

6.23*10–12

Sign

   

b

0.0158

0.0285

0.5901

InSign

   

n

1.0911

0.0904

1.94*10–8

Sign

   

Modified Page

2

k

0.2765

0.0104

9.92*10–13

Sign

0.033567

0.988193

0.987285

n

1.0090

0.0596

3.07*10–10

Sign

   

4

k

0.2979

0.0158

2.30*10–11

Sign

0.040216

0.980477

0.979082

n

0.8406

0.0601

1.27*10–9

Sign

   

6

k

0.1903

0.0044

3.64*10–17

Sign

0.025911

0.993121

0.992663

n

1.0750

0.0425

1.02*10–13

Sign

   

Page

2

k

0.2733

0.0263

1.13*10–7

Sign

0.033567

0.988193

0.987285

n

1.0090

0.0596

3.07*10–10

Sign

   

4

k

0.3613

0.0363

1.00*10–7

Sign

0.040216

0.980477

0.979082

n

0.8406

0.0601

1.27*10–9

Sign

   

6

k

0.1680

0.0135

2.76*10–9

Sign

0.025911

0.993121

0.992663

n

1.0750

0.0425

1.02*10–13

Sign

   

Wang-Sigh

2

b

− 0.1895

0.0079

3.69*10–12

Sign

0.062592

0.958944

0.955786

a

0.0090

0.0007

9.18*10–9

Sign

   

2

b

− 0.1823

0.0101

4.27*10–11

Sign

0.088616

0.905206

0.898435

a

0.0083

0.0008

1.19*10–7

Sign

   

2

b

− 0.1419

0.0050

1.65*10–14

Sign

0.047803

0.976588

0.975027

a

0.0053

0.0004

7.55*10–10

Sign

   

Weibullian

2

β

1.0090

0.0596

3.07*10–10

Sign

0.033567

0.988193

0.987285

α

3.6166

0.1357

9.92*10–13

Sign

   

4

β

0.8406

0.0601

1.27*10–9

Sign

0.040216

0.980477

0.979082

α

3.3572

0.1775

2.30*10–11

Sign

   

6

β

1.0750

0.0425

1.02*10–13

Sign

0.025911

0.993121

0.992663

α

5.2561

0.1215

3.64*10–17

Sign

   

Weibullian I

2

n

1.0090

0.0596

3.07*10–10

Sign

0.033567

0.988193

0.987285

δ

8.2657

0.4194

4.57*10–11

Sign

   

4

n

0.8406

0.0601

1.27*10–9

Sign

0.040216

0.980477

0.979082

δ

9.0546

0.6087

5.69*10–10

Sign

   

6

n

1.0750

0.0425

1.02*10–13

Sign

0.025911

0.993121

0.992663

δ

11.4183

0.3793

7.89*10–15

Sign

   
  1. *MMs are mathematical models: LT is the layer thickness; cm: k1, k2 and k are the drying constants, h−1: a, b, c, n, ɤ, β and δ are the models constants, dimensionless: RMSE is the root mean square error: R2 is the coefficient of determination R2adj. is the adjusted coefficient of determination at p ≤ 0.05.
  2. Significant values are in bold.
Back to article page