▸ An incompressible Newtonian fluid flows between two parallel plates (distance b). The bottom plate is fixed while the upper one moves at a constant velocity V (assuming linear velocity distribution). The surfaces of the lower and upper plates are maintained at T = T₁ and T = To, respectively. Find T(y). Assume fluid viscosity and conductivity k are known. μ
▸ An incompressible Newtonian fluid flows between two parallel plates (distance b). The bottom plate is fixed while the upper one moves at a constant velocity V (assuming linear velocity distribution). The surfaces of the lower and upper plates are maintained at T = T₁ and T = To, respectively. Find T(y). Assume fluid viscosity and conductivity k are known. μ
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Please can you assist me with this example.
Thank you
B H
![Example
▸ An incompressible Newtonian fluid flows between two parallel
plates (distance b). The bottom plate is fixed while the upper one
moves at a constant velocity V, (assuming linear velocity
distribution). The surfaces of the lower and upper plates are
maintained at T = To and T = T, respectively. Find T(y). Assume fluid
viscosity and conductivity k are known.
μ
13
y
V₂
b
Tb
To
pressure V](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F776fde46-0e13-4f4b-965e-6a3678bd5960%2F31636bb2-6e63-47c0-bf7d-724e3122a081%2Fpq0bkfo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Example
▸ An incompressible Newtonian fluid flows between two parallel
plates (distance b). The bottom plate is fixed while the upper one
moves at a constant velocity V, (assuming linear velocity
distribution). The surfaces of the lower and upper plates are
maintained at T = To and T = T, respectively. Find T(y). Assume fluid
viscosity and conductivity k are known.
μ
13
y
V₂
b
Tb
To
pressure V
![BCS y=o, T=To
y=b, T³ Tb
26
Try) = - (V₂)² + (+ (0) + (2 → C₂ = To
- V² + b + To = T₂C₁- (Tb - To ) + M V₂²
Ty. -21 (V) ²³y² + (T-ToMV² y + To
Example An incompressible Newtonian fluid flows between two parallel
2bk
plates (distance b). The bottom plate is fixed while the upper one
moves at constant velocity V₂. The surfaces of the lower and upper
plates are maintained at T = To and T = Tf, respectively, find
Tly). Assume fluid velocity Mand conductivity Kareshown
T= T(y)
Vx =
Dissipation
Function
ń fu
(di-
An incom-
Vy= V₂=0
Cartesian coordinates (x, y, z)
X momentum
Vxzy) = Ky - Vb-0
b-o
Vx = Vb y
BCS @yo
[Vxly) =>
y,
x
no programient
O
exhorizontal
P(ae, V. Ve vyt ) ve Zvez
at
ax
dvx = C₁ integrate V₁ly) = C₁ Y + C₂
from X momentum equen
d²vx
→
dy²
dy²
Vx=0 ⇒ C₂-0
y=b₁ V x = Vb ⇒ C₁ = b = Vy (₁ = Vb
Vb y
O
integrate dry
Cartesian coordinates (x, y, z) T(y)
stead of
Vyso
ScplST MOST VST NUST) KOD ST
>t
Energy Eqnkd¹²T + MO₁ = 0 Valy)
dyz
BCS @yso, T₂ To
@yib, TTb
e
22²
V.
V.
Tb
subinto Energy Ear Kot, M. (²
K.
To
2Vy= V2=0/2
(34³] [DK², JV; ], [ ] [ ] [ ]
tax
ay
incomparsible
Cartesian Coordinate
3,22
dissipation p= (dvs ² = (V₂)²
d'I
; - - M (Vb) ² integrate dr = _M (Vb) y + C, Integrate [ly)= - M (Vb Jy²r Cy+C₂
K
dy²
ou c](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F776fde46-0e13-4f4b-965e-6a3678bd5960%2F31636bb2-6e63-47c0-bf7d-724e3122a081%2Ff00m0m9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:BCS y=o, T=To
y=b, T³ Tb
26
Try) = - (V₂)² + (+ (0) + (2 → C₂ = To
- V² + b + To = T₂C₁- (Tb - To ) + M V₂²
Ty. -21 (V) ²³y² + (T-ToMV² y + To
Example An incompressible Newtonian fluid flows between two parallel
2bk
plates (distance b). The bottom plate is fixed while the upper one
moves at constant velocity V₂. The surfaces of the lower and upper
plates are maintained at T = To and T = Tf, respectively, find
Tly). Assume fluid velocity Mand conductivity Kareshown
T= T(y)
Vx =
Dissipation
Function
ń fu
(di-
An incom-
Vy= V₂=0
Cartesian coordinates (x, y, z)
X momentum
Vxzy) = Ky - Vb-0
b-o
Vx = Vb y
BCS @yo
[Vxly) =>
y,
x
no programient
O
exhorizontal
P(ae, V. Ve vyt ) ve Zvez
at
ax
dvx = C₁ integrate V₁ly) = C₁ Y + C₂
from X momentum equen
d²vx
→
dy²
dy²
Vx=0 ⇒ C₂-0
y=b₁ V x = Vb ⇒ C₁ = b = Vy (₁ = Vb
Vb y
O
integrate dry
Cartesian coordinates (x, y, z) T(y)
stead of
Vyso
ScplST MOST VST NUST) KOD ST
>t
Energy Eqnkd¹²T + MO₁ = 0 Valy)
dyz
BCS @yso, T₂ To
@yib, TTb
e
22²
V.
V.
Tb
subinto Energy Ear Kot, M. (²
K.
To
2Vy= V2=0/2
(34³] [DK², JV; ], [ ] [ ] [ ]
tax
ay
incomparsible
Cartesian Coordinate
3,22
dissipation p= (dvs ² = (V₂)²
d'I
; - - M (Vb) ² integrate dr = _M (Vb) y + C, Integrate [ly)= - M (Vb Jy²r Cy+C₂
K
dy²
ou c
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