Thermal Convection in a Cylindrical Enclosure withWavy Sidewall - Selected Topics of Computational and Experimental Fluid Mechanics - page 393

Appendix: Coefficients and Parameters

Ta b l e 1 Coefficients of Eqs. 12 and 13
Name Coefficient Name Coefficient

2
r 3 ∂ˈ

1
r

2 ʵ

−

A I

∂ z

r 2 ∂ˈ

2
r 2 ∂ˈ

2
r 2

1 ʵ

−

B J

∂ z ∂ r

r 3 ∂ˈ

4
r

3 3

r 3

− ʵ −

C K

∂ z

4

r 4 ∂ˈ

3 3

r 4

Ra ʵ

D

− +

L

∂ z Pr

2

2 ʵ Pr

r

∂ˈ
∂ r

E

−

N

r

Pr ∂ ∂ z

1

2
r 2 ∂ˈ

2
r 2

− ʵ

2 ʵ 1

r

+ − + F O

∂ z

r 2 ∂ˈ

1

G P

− 1

∂ r

r 3 ∂ˈ

1

2

H

−

Q

− ʵ

∂ r

Ta b l e 2 Coefficients of Eqs. 16 and 17
Name Coefficient

b

I

c J

d

K

3 ʷʓ ʩ

2 cos 2 2 sin 2

2 ʩʓ sin (ʩʾ) 2 ʷʓ ʩ sin (ʩʾ) (ʩʾ) 6 ʷʓ ʩ (ʩʾ)

e

+ ʳ + I

F

+ J +

ʳ

2

ʳ ʳ ʳ

2

− 4 ʷʓ ʩ

3 sin 2 3 cos 3 3 sin 3

(ʩʾ) 24 ʷʓ ʩ (ʩʾ) sin (ʩʾ) 24 ʷʓ ʩ (ʩʾ)

+ K + +

ʳ

2 3

ʳ ʳ

6 ʷʓ ʩ

2 cos 2 2 sin 2

3 ʷʓ ʩ sin (ʩʾ) (ʩʾ) 12 ʷʓ ʩ (ʩʾ)

F
ʳ + J

f + K +

ʳ ʳ

2

ʳ

4 ʷʓ ʩ sin (ʩʾ)

g

K

ʳ

2 2 2 sin 2

4 ʓʩ sin (ʩʾ) 2 ʷʓ ʩ sin (ʩʾ) 3 ʷ ʓ ʩ (ʩʾ)

h

+ ʳ 2

E

+ F + J

ʳ

3

12 ʷ

ʳ

2

ʳ

2

2 2 3 sin 2 3 3 sin 3

ʓ ʩ (ʩʾ) cos (ʩʾ) 24 ʷ ʓ ʩ (ʩʾ)

+ K +

ʳ

2

ʳ

3

3 3 3 sin 3

2 ʷʓ ʩ sin (ʩʾ) 4 ʷ ʓ ʩ (ʩʾ)

i

E

+ K

ʳ

3

ʳ

3

2 2 2 sin 2

6 ʷ ʓ ʩ (ʩʾ)

E
ʳ

j + K

2 2

ʳ

ʓʩ

2 cos 2 2 sin 2

(ʩʾ) 2 ʓ ʩ (ʩʾ)

+ H ʓʩ sin (ʩʾ)
ʳ

D
ʳ + F

+

k

ʳ

2

ʳ

3 2

ʷʓ ʩ

2 cos 2 2 sin 2

(ʩʾ) 2 ʷʓ ʩ (ʩʾ)

+ I +

ʳ

2

− ʷʓ ʩ

ʳ

3 sin 3 3 sin 3 2 3 cos

(ʩʾ) 6 ʷʓ ʩ (ʩʾ) 6 ʷʓ ʩ (ʩʾ) sin (ʩʾ)

+ J + +

ʳ

3 2

ʳ ʳ

− ʷʓ ʩ

4 cos 2 4 sin 2 3 4 sin 2

(ʩʾ) 8 ʷʓ ʩ (ʩʾ) 36 ʷʓ ʩ (ʩʾ) cos (ʩʾ)

+ K − +

ʳ ʳ

2

ʳ

3

24 ʷʓ

4 4 sin 4 2 4 cos 2

ʩ (ʩʾ) 6 ʷʓ ʩ (ʩʾ)

+ K +

4 2

ʳ ʳ

(continued)