# Grid resolution in porous medium model for heat sink

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 March 27, 2012, 11:59 Grid resolution in porous medium model for heat sink #1 Senior Member   Join Date: Oct 2010 Location: Zurich Posts: 176 Rep Power: 7 Hi I am simulating conjugate heat transfer in a heat sink consisting of a number of parallel microchannels. Since modeling each microchannel is computationally inefficient, I am modeling the heat sink using the porous medium model (this is a well established approach in literature). Now, if I understand correctly, the porous medium model equations are derived for what is called as the Representative Elementary Volume (REV) that is assumed to be much larger than the average pore size. In my case the average pore size is of the order of channel width. So following the above REV assumption, what minimum grid size can I go to while checking for grid Independence? Should I ensure that my average grid size is always much larger than the channel width? If yes, then how much larger it should be than the channel width? Thanks for your inputs.

 March 28, 2012, 12:57 #2 Senior Member   Andrew Join Date: Mar 2009 Location: Washington, DC Posts: 195 Rep Power: 9 are you checking your answer against experimental data? When I did a fluent model based on my physical model, I was comparing the data. Therefore, I could do a grid check based on that. I think you might want to try different different grid densities and see how that affects your answer. It was a few years ago that I did my porous media model. When I did it I had to have various coefficients in order for Fluent to solve the equations. I had to obtain those from my lab experiment. Is this your case too?

 March 30, 2012, 05:26 #3 Senior Member   Join Date: Oct 2010 Location: Zurich Posts: 176 Rep Power: 7 Hello Andrew, Thanks for your reply. No I do not have experimental data to check my simulations against it. However, I have repeated the simulations for three grid densities, of average sizes 0.5h, h and 2h where h is nearly equal to the channel width. And the results of three simulations fall on a trend that is typical of a grid independent study. In other words, the results do not change drastically when i refine my grid. So, is it safe top conclude that the grid size can go below the pore size in porous medium and is independent of the way the differential equations are derived for porous medium?

 April 2, 2012, 10:11 #4 Senior Member   Rami Ben-Zvi Join Date: Mar 2009 Posts: 148 Rep Power: 9 The porous model aloows one to treat the micro-structure (micro-channels in your case) as averaged continuum. Once this was done, refining the grid to check the solution grid independence may use grid smaller than the REV, but do keep in mind that doing so does not mean you resolve the micro-structure - you only validate solution of the continuous equation system is converging.

 April 2, 2012, 10:56 #5 Senior Member   Join Date: Oct 2010 Location: Zurich Posts: 176 Rep Power: 7 Thanks Rami for your reply. Your explanation does make a lot of sense. I will check if I get the same behaviour when I use non-thermal equilibrium model for Porous medium (actually your explanation suggests that I should get the same behaviour) Thanks again Chander

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