The heat conduction is expressed by a classic heat equation like
$p(x) u_t + div (A(x) u) = f(x,t) $.
If I look at a porous medium like this (solid+gas) the heat equation should apply too (in a related form).
But what if there's a gas M in the open space of the medium and now there is another gas N flowing into the same space? Can the heat conduction still be expressed in a single equation? Or does this require a system of equations?
How would such an equation or system of equations look like?