ANALYSIS OF CASSON FLUID MODEL FOR BLOOD FLOW IN EXTERNALLY APPLIED MAGNETIC FIELD - Theoretical and Computational Research in the 21st Century - page 243

3

π

R

( )

2

Q = τ

1/ 2

− τ

1/ 2

(12)

H

2

3

2

Again, from Eqs. (9) and (10),

1 ∂ ∂ p ∂ B

() r τ =− m

1

rr ∂ ∂ z ∂ z

∂ u 1 ⎛ r ∂ p ∂ B ⎞

⎛ ⎞

= 2 ττ − τ − − m

⎜ ⎜ ⎟ ⎟

HH 1

2

∂ rm 2 ∂ z ∂ z

⎝ ⎠

⎝ ⎠ 2

⎛ 1 r

2

∂ p ∂ B ⎞

⎛ ⎞

u = 2 ττ . r − τ r − − m

⎜ ⎜ ⎟ ⎟

(13)

H H 1

m

2

4 ∂ z ∂ z

⎝ ⎠

⎝ ⎠

2

Again, from volumetric flow rate and Eq. (13),

Rz ()

∫

2

Q = 2 π rudr = π R u

(14)

0

⎛

2

⎞

1 r ⎛ ∂ p ∂ B ⎞ 2

QR = π 2 ττ . r − τ r − − m

⎜ ⎜ ⎟ ⎟

(15)

H H 1

2

m 4 ∂ z ∂ z

⎝ ⎠

⎝ ⎠

2

ττ = When r = R , then

R

⎛

2

⎞

1 Rp ∂ ∂ B

⎛ ⎞

QR = π

2

2 ττ . R R − τ − − m

(16)

⎜ ⎟

⎜ ⎟

H H 1

2

m 4 ∂ z ∂ z

⎝ ⎠

⎝ ⎠

2

Therefore, from Eqs. (11) and (14),

R

Rdp
dz

rdp
dz

dr = d τ

τ =−

where

τ =−

and gives

R

τ

2

2

R

τ

2

τ R

R

∫

2

Qf = πτ () R d τ

ττ

2

RR

0