UNSTEADY VISCOUS FLOW u p g Dt u D 2 2 2 1 y u x p t u Viscous effects confined to within some finite area near the boundary → boundary layer In unsteady viscous flows at low Re the boundary layer thickness δ grows with time; but in periodic flows, it remains constant If the pressure gradient is zero, Navier-Stokes equation (in x) reduces to: 2 2 y u t u Assume linear, horizontal motion
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UNSTEADY VISCOUS FLOW Viscous effects confined to within some finite area near the boundary → boundary layer In unsteady viscous flows at low Re the boundary.
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UNSTEADY VISCOUS FLOW
upgDt
uD
2
2
21
y
u
x
p
t
u
Viscous effects confined to within some finite area near the boundary → boundary layer
In unsteady viscous flows at low Re the boundary layer thickness δ grows with time; but in periodic flows, it remains constant
If the pressure gradient is zero, Navier-Stokes equation (in x) reduces to:
2
2
y
u
t
u
Assume linear, horizontal motion
2
2
y
u
t
u
Heat Equation– parabolic partial differential equation - linear
Requires one initial condition and two boundary conditions