Table 5 Mathematical models’ constants values and goodness of fit indices results of Henna leaves for OAD 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

0.0400

0.0252

0.1349

InSign

0.312176

− 0.100011

− 0.178584

k1

− 0.0667

0.0223

0.0098

Sign

   

4

k1

0.1770

0.0064

6.28*10–15

Sign

0.018496

0.995938

0.995684

k1

0.0040

0.0042

0.3569

InSign

   

6

k1

0.1708

0.0094

4.74*10–13

Sign

0.029169

0.989280

0.988684

k1

0.0091

0.0062

0.1584

InSign

   

Henderson—Pabis

2

k

0.2472

0.0056

1.79*10–16

Sign

0.017358

0.996599

0.996356

a

0.9854

0.0138

2.42*10–19

Sign

   

4

k

0.1677

0.0034

6.01*10–19

Sign

0.017556

0.996340

0.996112

a

0.9791

0.0124

3.81*10–22

Sign

   

6

k

0.1514

0.0047

2.57*10–17

Sign

0.027904

0.990190

0.989645

a

0.9600

0.0191

8.00*10–21

Sign

   

Lewis (Newton)

2

k

0.2509

0.0044

6.17*10–19

Sign

0.017407

0.996336

0.996336

4

k

0.1714

0.0027

1.25*10–21

Sign

0.018467

0.995698

0.995698

6

k

0.1581

0.0039

6.80*10–20

Sign

0.030238

0.987840

0.987840

Logarithmic (Asymptotic)

2

k

0.2688

0.0087

1.39*10–13

Sign

0.013894

0.997977

0.997665

a

0.9722

0.0121

6.75*10–19

Sign

   

c

0.0255

0.0081

0.0074

Sign

   

4

k

0.1633

0.0081

2.60*10–12

Sign

0.017935

0.996419

0.995942

a

0.9851

0.0165

2.89*10–19

Sign

   

c

− 0.0095

0.0165

0.5716

InSign

   

6

k

0.1468

0.0112

2.67*10–10

Sign

0.028563

0.990292

0.989149

a

0.9665

0.0249

4.79*10–18

Sign

   

c

− 0.0108

0.0249

0.6695

InSign

   

Midilli

2

k

0.2822

0.0160

6.17*10–10

Sign

0.013830

0.998149

0.997687

a

1.0060

0.0136

2.43*10–17

Sign

   

b

0.0006

0.0008

0.4475

InSign

   

n

0.9394

0.0370

8.39*10–12

Sign

   

4

k

0.2019

0.0144

1.19*10–9

Sign

0.014385

0.997850

0.997390

a

0.9995

0.0140

2.44*10–19

Sign

   

b

− 0.0033

0.0012

0.0180

Sign

   

n

0.8683

0.0427

8.72*10–12

Sign

   

6

k

0.2201

0.0210

1.40*10–8

Sign

0.020191

0.995434

0.994578

a

1.0034

0.0198

4.29*10–19

Sign

   

b

− 0.0055

0.0017

0.0056

Sign

   

n

0.7586

0.0561

3.58*10–10

Sign

   

Modified Midilli I

2

k

0.2775

0.0113

2.88*10–12

Sign

0.013396

0.998119

0.997830

b

0.0007

0.0008

0.3847

InSign

   

n

0.9472

0.0314

2.03*10–13

Sign

   

4

k

0.2023

0.0092

8.40*10–13

Sign

0.013898

0.997850

0.997563

b

− 0.0033

0.0012

0.0116

Sign

   

n

0.8674

0.0343

1.02*10–13

Sign

   

6

k

0.2175

0.0134

8.62*10–12

Sign

0.019607

0.995425

0.994887

b

− 0.0055

0.0016

0.0037

Sign

   

n

0.7636

0.0462

6.50*10–12

Sign

   

Modified Midilli I I

2

k

0.2835

0.0152

3.09*10–10

Sign

0.013643

0.998199

0.997749

a

0.9914

0.0206

4.27*10–15

Sign

   

b

0.0140

0.0134

0.3182

InSign

   

n

0.9500

0.0409

2.38*10–11

Sign

   

4

k

0.1887

0.0111

9.07*10–11

Sign

0.014666

0.997765

0.997286

a

1.0888

0.0476

1.72*10–12

Sign

   

b

− 0.0890

0.0415

0.0502

InSign

   

n

0.8566

0.0470

3.79*10–11

Sign

   

6

k

0.1857

0.0145

8.30*10–10

Sign

0.020711

0.995196

0.994295

a

1.2145

0.1100

6.83*10–9

Sign

   

b

− 0.2107

0.1025

0.0565

InSign

   

n

0.7389

0.0622

2.38*10–9

Sign

   

Modified Page

2

k

0.2550

0.0038

6.70*10–19

Sign

0.013282

0.998009

0.997866

n

0.9267

0.0207

1.63*10–16

Sign

   

4

k

0.1729

0.0028

1.43*10–20

Sign

0.017379

0.996414

0.996190

n

0.9552

0.0246

3.00*10–17

Sign

   

6

k

0.1611

0.0039

2.92*10–19

Sign

0.026609

0.991079

0.990584

n

0.9097

0.0344

7.47*10–16

Sign

   

Page

2

k

0.2819

0.0101

1.14*10–13

Sign

0.013282

0.998009

0.997866

n

0.9267

0.0207

1.63*10–16

Sign

   

4

k

0.1870

0.0093

8.76*10–13

Sign

0.017379

0.996414

0.996190

n

0.9552

0.0246

3.00*10–17

Sign

   

6

k

0.1900

0.0138

5.38*10–11

Sign

0.026609

0.991079

0.990584

n

0.9097

0.0344

7.47*10–16

Sign

   

Wang-Sigh

2

b

− 0.1722

0.0075

1.74*10–12

Sign

0.066132

0.950635

0.947109

a

0.0076

0.0006

9.07*10–9

Sign

   

2

b

− 0.1291

0.0046

5.43*10–15

Sign

0.048802

0.971721

0.969953

a

0.0045

0.0003

5.97*10–10

Sign

   

2

b

− 0.1167

0.0050

6.36*10–15

Sign

0.061907

0.951712

0.949030

a

0.0036

0.0003

2.11*10–9

Sign

   

Weibullian

2

β

0.9267

0.0207

1.63*10–16

Sign

0.013282

0.998009

0.997866

α

3.9210

0.0591

6.70*10–19

Sign

   

4

β

0.9552

0.0246

3.00*10–17

Sign

0.017379

0.996414

0.996190

α

5.7851

0.0922

1.43*10–20

Sign

   

6

β

0.9097

0.0344

7.47*10–16

Sign

0.026609

0.991079

0.990584

α

6.2055

0.1508

2.92*10–19

Sign

   

Weibullian I

2

n

0.9267

0.0207

1.63*10–16

Sign

0.013282

0.998009

0.997866

δ

9.6438

0.1950

4.06*10–17

Sign

   

4

n

0.9552

0.0246

3.00*10–17

Sign

0.017379

0.996414

0.996190

δ

13.8516

0.3280

7.70*10–18

Sign

   

6

n

0.9097

0.0344

7.47*10–16

Sign

0.026609

0.991079

0.990584

δ

15.5227

0.5559

2.84*10–16

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.
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