  We present a theory to describe the Nusselt number ($Nu$), corresponding to
the heat or mass flux, as a function of the Rayleigh--Darcy number ($Ra$), the
ratio of buoyant driving force over diffusive dissipation, in convective porous
media flows. First, we derive exact relationships within the system for the
kinetic energy and the thermal dissipation rate. Second, by segregating the
thermal dissipation rate into contributions from the boundary layer and the
bulk, which is inspired by the ideas of the Grossmann and Lohse theory (J.
Fluid Mech., vol. 407, 2000; Phys. Rev. Lett., vol. 86, 2001), we derive the
scaling relation for $Nu$ as a function of $Ra$ and provide a robust
theoretical explanation to the empirical relations proposed in previous
studies. Specifically, by incorporating the length scale of the flow structure
into the theory, we demonstrate why heat or mass transport differs between
two-dimensional and three-dimensional porous media convection. Our model is in
excellent agreement with the data obtained from numerical simulations,
affirming its validity and predictive capabilities.
