Fluid flow & heat transfer using PDE toolbox

The equations describing my system in 2-D (r,z) in cylindrical coordinates are: 1. Continuity equation 2. Navier stokes equations in r & z coordinates 3. Heat conduction equation

i.e. the velocity has components in r & z directions

Can PDE toolbox be used to solve these equations?

I figured this link might be useful: http://www.mathworks.com/help/pde/ug/solve-problems-using-pdemodel-objects.html

However, I am not sure whether the continuity & Navier stokes equation can fit in this general form

What approach should I follow here? One idea I had was to use finite difference method to discretize the equations. Is that workable?

[QuickerSim]

For flow and heat transfer simulation (both in 2-D and 3-D) QuickerSim CFD Toolbox for MATLAB can be used. Links here:

http://www.quickersim.com/cfd-toolbox-for-matlab/index.html

or here: https://www.mathworks.com/matlabcentral/fileexchange/53993-quickersim-cfd-toolbox

Answer 1

[Precise Simulation]

Coupled axisymmetric Matlab CFD and heat transfer problems can relatively easily be set up and solved with the FEATool Multiphysics, either by defining your own PDE problem or using the built-in pre defined equations.

Relevant to your question is for example this axisymmetric tutorial describing how to set up and solve an axisymmetric fluid problem using the Navier-Stokes equations.

Answer 2

[michio]

I assume that you are trying to solve a system of equations in an axisymmetric cylindrical domain, 2D r-z. Currently, PDE Toolbox only supports the equations in the Cartesian coordinate system, so may not be a good fit for your problem.

Implementing finite difference method for the spatial derivatives is one way. You can let MATLAB built-in functions do the time integration.