drir
Mechanical
- Aug 17, 2011
- 47
Hi,
I'm solving a problem which determines the flow between a porous material and an impermeable material, using the slip-flow boundary conditions as proposed by Beavers and Joseph in '67. I can solve the whole problem as stated below, which gives the velocity 'u' of the fluid in the x-direction over the gap height (y-direction). However, in this equation I still have one unknown namely 'ub' which is the slip velocity. How can I write this 'ub' in function of the other variables so that this unknown disappear in my equation of 'u' ? A hint can maybe be enough!
Poiseuille motion:
d^2u/dy^2 = 1/mu dP/dx
boundary conditions:
1. u = 0 at y = h
2. du/dy = alpha/k^(1/2) ub at y = 0
Solution of this PDE is:
u = 1/2mu dP/dx (y^2-h^2) + alpha/k^(1/2) ub (y-h)
I'm solving a problem which determines the flow between a porous material and an impermeable material, using the slip-flow boundary conditions as proposed by Beavers and Joseph in '67. I can solve the whole problem as stated below, which gives the velocity 'u' of the fluid in the x-direction over the gap height (y-direction). However, in this equation I still have one unknown namely 'ub' which is the slip velocity. How can I write this 'ub' in function of the other variables so that this unknown disappear in my equation of 'u' ? A hint can maybe be enough!
Poiseuille motion:
d^2u/dy^2 = 1/mu dP/dx
boundary conditions:
1. u = 0 at y = h
2. du/dy = alpha/k^(1/2) ub at y = 0
Solution of this PDE is:
u = 1/2mu dP/dx (y^2-h^2) + alpha/k^(1/2) ub (y-h)
