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I have a system of PDEs in cylindrical coordinates that needs to be solved: 1. Continuity equation 2. Incompressible Navier stokes ( in r & z coordinates) 3. Heat transfer equation with both conduction and convection terms

Is it possible to solve these equations using PDE toolbox?

This is the link from the MATLAB website I referred to: http://www.mathworks.com/help/pde/ug/equations-you-can-solve.html

However, I do not think my equations would fit into this form.

Is discretization by the finite difference method a better way? Is application of the SIMPLE algorithm by Patankar necessary?

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    $\begingroup$ I don't know about the toolbox, but in general solving a 2D PDE in Matlab can be rather slow. Some important questions relevant to this: compressible or incompressible? What Reynolds number? Laminar or turbulent? $\endgroup$ – David Ketcheson Jul 15 '16 at 13:27
  • $\begingroup$ Incompressible Newtonian fluid and laminar flow $\endgroup$ – patilak Jul 15 '16 at 15:28
  • $\begingroup$ Thanks; it's best if you edit the question to include that kind of information. I've done so for you. $\endgroup$ – David Ketcheson Jul 15 '16 at 19:22
  • $\begingroup$ At first glance, I think the answer is no, since you can't fit the convective term into that form. $\endgroup$ – David Ketcheson Jul 15 '16 at 19:25
  • $\begingroup$ What if the convective term were to be neglected? Do the other equations fit into that form? Thanks for your help $\endgroup$ – patilak Jul 15 '16 at 21:14
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The cylindrical coordinate form of PDE equations are not available as default equations with the PDE Toolbox, but should be able to be entered as a custom PDE equation form.

Alternatively, both the Navier-Stokes equations and heat transfer (heat conduction with convection/advection) is also available for MATLAB as pre-defined (axisymmetric) PDE equations with the FEATool Multiphysics toolbox.

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There is a book on the finite volume method (FVM), which is widely used to solve flow problems. Aside from presenting the theory behind the method, the authors demonstrate the finite volume method on a Matlab-based FVM code and on OpenFOAM, which is a C++ library implementing the finite volume method.

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