Porous media convection UDS equations
I am modeling the convective heat transfer in a heated porous media. The convection is included as a source term (hv*(Ts-Tg)). Thermal non-equilibrium is considered and the solid phase equation is implemented via UDS. I define an additional UDS for local porosity (motivated by Greg Perkins). I am solving for the steady state solid temperature distribution. My question is concerned with the implementation of the steady state UDS equations in Fluent.
The general solid medium energy equation is:
d/dt((1-epsi)*rho_s*c_s*T) = d/dx(KdT/dt) + S
epsi->porosity; Scalar -> h = c_s*T; T-> Solid medium temperature, S -> Source term
From this, in order to get steady state equations, I think that there are 2 ways:
Set the left hand side to zero, we get,
d/dt(KdT/dt) + S = 0 in W/m3
Take out the constants from left hand side,
(1-epsi)*rho_s*c_s*dT/dt = d/dx(KdT/dt) + S
Divide the entire equation by these constants,
dT/dt = d/dx(KdT/dt)/(1-epsi)*rho_s*c_s + S/(1-epsi)*rho_s*c_s in K/s
Now set the left hand side to zero, we get:
d/dx(KdT/dt)/(1-epsi)*rho_s*c_s + S/(1-epsi)*rho_s*c_s = 0
This means that:
my diffusion coefficient is: K/(1-epsi)*rho_s*c_s
and source term is: S/(1-epsi)*rho_s*c_s
I ran the Fluent case using the above-mentioned 2 methods. One would expect the same answer from both the cases. But, that did not happen to me.
Does anybody see any problem in my formulation and implementation in Fluent?
Thanks in advance,
Re: Porous media convection UDS equations
There is a small typo in my previous post.
The diffusion term is defined as:
d/dx(KdT/dx) and NOT d/dx(KdT/dt) as posted.
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