Free convection
I have had a big problem trying to simulate free convection over a vertical plate. One of my problems is i want to control the pressure gradient, I mean one of the unknown variables is the pressure p. But, in free convection or at least, in my model I don't take into account the xmomentum equation. In fact, my equations are the following
With this boundary conditions This is the problem, http://s7.postimage.org/xobd7x255/image.png Link: http://s7.postimage.org/xobd7x255/image.png I take and And I compute as, . Replacing, . I will initially define: . Finally, . In fact, is it possible to compute this in a COMSOL? Mi unknown are only u,v and T not P. Because I assume the pressure gradient as I explained before. 
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No but in the model you have presented here you have taken the xmomentum equation into account. I'm afraid your model is completely rubbish. Free convection is a kind of flow which is vertically dominated as it is induced by gravity. So taking x momentum equation does not make sense. If you assume that your flow is unidirectional then choose rather the y momentum because the buoyancy force which drives such flow is oriented along y axis. I even do not undertand how you can have your buoyancy term in the x momentum or I have missed something.:confused: f= rho*g with vector g=9.81y where here f g and y are vectors. Quote:
Then you could verify a posteriory if your assumptions were right or not especially concerning the pressure gradient, but I guess it won't ;) 
I turned over the axes, look at my axes. I will follow you advice. But I want to compute also a solution for those equations because I want to learn about it.
What is the simplest way to compute it ? With a good solution (exact) it doesnt matter if the convergence takes to much for the algorithm jaja 
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Better keep the usual notations well mastered by every one here Quote:
It should be easy if you can extract the v componnent from integrating the continuity equation. 
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You have to learn howto discetize a partial derivative equation based on finite difference, finite volume or finite element. Just choose your method. If you want to use finite volume books of Versteek or Peric are great http://www.amazon.com/AnIntroductio.../dp/0131274988 http://www.amazon.com/Computational...keywords=peric for finite differences or finite element I don't have particular books in mind but you can find many lecture notes on internet. once you discretized your equations, in one time step solve: your momentum equation, then use continuity equation to obtain the second velocity component, then solve heat equation finaly advance time step.. 
Efficiency
I solved the problem in MATLAB.
Now I'm going to compare my results with COMSOL results. But I see this weird behaviour and I don't know why ? http://s10.postimage.org/5q2xjuz2v/Temperature.png Imagen: http://s10.postimage.org/5q2xjuz2v/Temperature.png http://s12.postimage.org/mmjk7giq3/velocity.png Imagen: http://s12.postimage.org/mmjk7giq3/velocity.png Here is my COMSOL file: http://www.mediafire.com/?fsdkoqa1uumm3cc Thanks ! 
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