# Fluid flow & heat transfer using PDE toolbox

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patilak on 14 Jul 2016
Edited: Precise Simulation on 3 Mar 2019
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?
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 on 15 Jun 2017
Edited: QuickerSim on 15 Jun 2017
For flow and heat transfer simulation (both in 2-D and 3-D) QuickerSim CFD Toolbox for MATLAB can be used. Links here:
or here: https://www.mathworks.com/matlabcentral/fileexchange/53993-quickersim-cfd-toolbox

Precise Simulation on 5 Aug 2017
Edited: Precise Simulation on 3 Mar 2019
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.

michio on 31 Aug 2016
Edited: michio on 31 Aug 2016
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.