▸ 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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Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

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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

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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