# Can I model laminar incompressible fluid flow and heat transfer in MATLAB's PDE toolbox?

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?

• 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? – David Ketcheson Jul 15 '16 at 13:27
• Incompressible Newtonian fluid and laminar flow – patilak Jul 15 '16 at 15:28
• Thanks; it's best if you edit the question to include that kind of information. I've done so for you. – David Ketcheson Jul 15 '16 at 19:22
• At first glance, I think the answer is no, since you can't fit the convective term into that form. – David Ketcheson Jul 15 '16 at 19:25
• What if the convective term were to be neglected? Do the other equations fit into that form? Thanks for your help – patilak Jul 15 '16 at 21:14