MATLAB PDE TOOL for Newtonian Fluid
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For a Newtonian fluid (like water) in a duct with cross section, A and Length L = 2.0m. The governing equation is given by:
Mu*d2u/dx2 = Delta P/L
Mu = dynamic viscosity = 10*10E-04 Pa-s Delta P/L = 10 kPa/m is the pressure gradient that drives the flow.
What will be the coefficients c,a and f? What will be the Neumann and Dirichlet B.C?
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Mukul Rao
el 24 de Abr. de 2017
Editada: Mukul Rao
el 24 de Abr. de 2017
Hello,
As far as I can see, your equation is a one dimensional description of Newtonian Fluid flow (unless the d stands for some other operator). For this simple scenario, especially when there is no time derivative, I would recommend using the MATLAB ODE suite to solve this problem. A solver like ode45 should suffice.
As far as the boundary conditions are concerned, it would depend on the problem at hand. Most pipe flows will have the inlet velocity specified. Essentially, u is known at the inlet and the mass flux d(rho*A*u)/dx will probably be specified.
If you would still like to use the PDE tool, you can refer the following page to learn how to specify coefficients :
In your case, formatting the governing equation to the standard PDE toolbox equation form, leaves us with ( m = 0 , d = 0, c = -Mu, a = 0, f = DeltaP/L
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