# Heat Equation in CFD Simulation

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 December 2, 2019, 14:58 Heat Equation in CFD Simulation #1 Member   Join Date: Apr 2016 Posts: 91 Rep Power: 10 Hi, in CFD simulations, you can solve for momentum (Navier-Stokes), mass balance, gas equation and energy equation to get the solution of a heat transfer problem for example (gas flowing over hot stone). But I am wondering: 1) there are more equations for solving heat transfer problems: how does for example the advection diffusion equation come into CFD simulation? 2) Or just the heat equation (this is I think just for heat conduction?) I only read all the time "energy equation". So 1) and 2) are a kind of energy equation, but I do not think that they are used? Thanks for any hints

December 2, 2019, 15:59
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Filippo Maria Denaro
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 Originally Posted by CellZone Hi, in CFD simulations, you can solve for momentum (Navier-Stokes), mass balance, gas equation and energy equation to get the solution of a heat transfer problem for example (gas flowing over hot stone). But I am wondering: 1) there are more equations for solving heat transfer problems: how does for example the advection diffusion equation come into CFD simulation? 2) Or just the heat equation (this is I think just for heat conduction?) I only read all the time "energy equation". So 1) and 2) are a kind of energy equation, but I do not think that they are used? Thanks for any hints

In the Navier-Stokes equations for compressible flows, the conserved variables are mass, momentum and total energy. This latter is the sum of the kinetic, internal (that is related to temperature) and any other form of energy required for the problem.
For the incompressible flow model, the energy equation is not coupled to mass and momentum apart the case of buoyancy effects. In such a case you can solve the internal energy equation that is a convection-diffusion equation for the temperature.

 December 3, 2019, 11:27 #3 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,686 Rep Power: 66 The heat diffusion equation and advection-diffusion equation are simpler forms of the energy equation. If you want to solve a pure heat diffusion equation using CFD, you'd still cast the problem in the realm the mass, momentum, and energy equations, but you would assign a 0 velocity everywhere and hold it fixed. I.e. you'd assign and freeze the flow variables and you could even skip solving the continuity and momentum equations altogether. Likewise for advection-diffusion problems, just prescribe the background flow, hold it fixed.