Flow through Chamfered Ducts
Flow through Chamfered Ducts
Consider the fluid flow through a chamfered duct. The flow velocity in the cross section satisfies the equation:
2
∂
v
z
∂
2
x
2
∂
v
z
∂
2
y
1
μ
∂P
∂z
The associated boundary conditions are =0 (no slip condition) on the walls of the chamfered duct (colored black in the snapshots). These walls are defined by the implicit equation , where is a parameter that determines the shape of the duct.
v
z
α+=1
6
x
4
y
α
This Demonstration uses the finite element method in Mathematica's built-in function NDSolve to display the velocity distribution for values of set by the user.
α