Presentation of Transport Phenomena Problem Group 6 Abu Bakar Adeni Feizal Ibrahim Mohammad Sofa Khodi
Jan 21, 2016
Presentation ofTransport Phenomena Problem
Group 6Abu Bakar AdeniFeizal IbrahimMohammad Sofa Khodi
Problem(solve with Navier Stokes equations)
Water at 60oC flows between two large flat plates. The lower plate moves to the left at a speed of 0.3 m/sec. The plate spacing is 3 mm and the flow is laminar. Determine the pressure gradient (dp/dx) required to produce zero net flow at the cross-section (= 4.7 x 10-4 Ns/m at 60o)
b=3mm
y
x
U=-0.3m/s
Profile and Shell
Arah Perubahan Momentum
Arah KecepatanShell
y
XVx
Shell
(πΏπ )π π¦π₯|π¦
(πΏπ )π π¦π₯|π¦+β π¦
(π΅π )ππ£π₯|π₯+βπ₯ (π΅π )ππ£π₯|π₯
Derivation of Equation
Equation of Continuity Equation of Motion
The Equation of Continuity
konstan . tidak ada kecepatan ke arah y, maka : tidak ada kecepatan ke arah z, maka : Jadi : β¦(1)
The Equation of MotionConstan Ο and ΞΌ (Navier Stokes)
Karena arah kecepatannya menuju x (negatif), maka Equation of Motion (Navier-Stokes) yang dipakai searah x.(Bird First Edition, Tabel 3.4-2 (D))
Equation of Motion (cont)
Tidak ada percepatan, maka: pada equation of motion = 0
konstan Tidak ada kecepatan ke arah y, maka: Tidak ada kecepatan ke arah z, maka:
(Cont) konstan pada arah x, maka : konstan pada arah z, maka : Tidak ada gaya gravitasi searah x, maka
:
Diperoleh Rumus Pressure Gradient:
β¦.(2)
Tapiβ¦.
Next Steps
Didapat:..(3)
Boundary ConditionKetika :Y=0, Vx=VmaxY=b, Vx=0
1st Boundary Conditiony=0, Vx=Vmax
β¦(4)
2nd Boundary Conditiony=b, vx=0
β¦(5)
SubstitutionSubstitusikan persamaan (4) dan (5) ke persamaan (3):
β¦(6)
Flow Rate (Q)
Substitusikan persamaan(6).
Didapat:β¦(7)
Get back to the problem
Determine the pressure gradient (dp/dx) required to produce zero net flow at the cross-section!
Zero net Flow Q=0
Q=0
Last Equation:
πππ π₯
=π£πππ₯(3 π2π2 )
Solving the Problem
kecepatan plat bagian bawah
Thank You For Your Attention