Free convection -- CFD Online Discussion Forums

August 17, 2012, 11:29	Free convection	#1
ebrattr New Member Join Date: Jul 2012 Posts: 4 Rep Power: 13	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 x-momentum equation. In fact, my equations are the following $\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0$ $u \frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y}=\zeta \beta g(T-T_{\infty})+\nu \frac{\partial^2 u}{\partial y^2}$ $u\frac{\partial T}{\partial x}+ v\frac{\partial T}{\partial y} = \alpha \frac{\partial^2 T}{\partial y^2}$ With this boundary conditions $u(x,\infty) = 0$ $T(x,\infty) = T_{\infty}$ This is the problem, Link: http://s7.postimage.org/xobd7x255/image.png I take $F_x = -\zeta\rho g$ and $\frac{\partial p}{\partial x} = -\zeta \rho_{\infty}g$ And I compute $\rho$ as, $\rho = \rho_{\infty}+\left(\frac{\partial \rho}{\partial T} \right)_P (T-T_{\infty})$ . Replacing, $\beta=-\frac{1}{\rho} \left(\frac{\partial \rho}{\partial T}\right)_P$ . I will initially define: $T_w(x), \, u_w(x)$ . Finally, $\zeta \in \{-1,0,1\}$ . 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. Last edited by ebrattr; August 17, 2012 at 14:39.

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