Ns

Char and Chiang [28]

Present study

Char and Chiang [28]

Present study

Free, isothermal

Free, isothermal

Free, insulated

Free, insulated

( $Bi\to \infty$ )

( $Bi\to \infty$ )

( $Bi=0$ )

( $Bi=0$ )

$R_{tc}$

$a_c$

$R_{tc}$

$a_c$

$R_{tc}$

$a_c$

$R_{tc}$

$a_c$

0

1100.684

2.682

1100.671

2.682

669.013

2.086

669.003

2.085

0.5

1055.612

2.679

1055.574

2.679

608.758

2.070

608.764

2.070

1

1011.471

2.680

1011.434

2.679

557.618

2.060

557.640

2.059

5

725.639

2.773

725.897

2.732

328.590

2.035

328.678

2.034

10

518.346

2.803

518.346

2.802

215.415

2.033

215.508

2.032

15

398.695

2.849

399.216

2.847

159.957

2.034

160.040

2.033

20

323.111

2.880

323.617

2.877

127.144

2.036

127.217

2.034

30

233.637

2.916

234.077

2.914

90.116

2.038

90.174

2.036

40

182.746

2.937

183.125

2.935

69.778

2.039

69.825

2.038

70

110.369

2.967

110.627

2.965

41.598

2.042

41.628

2.040

100

79.020

2.980

79.2141

2.978

29.629

2.043

29.651

2.041