Resolving a heat exchanger coil, a filter or a tower fill cell by cell is neither possible nor necessary. These are represented as porous regions that apply a defined resistance to the flow. The method is sound; the weak link is always the coefficients.
Two resistance terms
Pressure loss is related to velocity through a linear and a quadratic term: the viscous term dominates at low velocity, the inertial term at high. For packed beds, Ergun's correlation gives both terms in terms of porosity and particle diameter and is the classical source for the coefficients [1].
Where to get the coefficients
Manufacturer data. If a published pressure loss versus flow curve exists for the coil or filter, this is the most reliable source. Fitting a second-order polynomial to the curve is sufficient.
From experiment. The same, if you have measured your own sample.
From a detailed sub-model. Solving a small periodic model of the repeating unit (a single fin cell, a single pore) and extracting the resistance. This is the right route for new geometries and follows the same approach as in the heat exchanger note.
By guessing. This is where the porous media model is most often abused. A fabricated coefficient puts the solution into a physical-looking but entirely wrong distribution.
Watch the orientation
Most real porous structures are anisotropic: in a coil the flow moves easily along the channels and hardly at all across them. If the cross-direction resistance is not made realistically high, the solution diverts flow sideways through the coil and shows the distribution as far more uniform than it is.
Heat transfer is defined separately
A porous region only supplies momentum resistance; heat transfer has to be defined in addition. Where solid and fluid temperatures can separate (fast transients, high power density), the single-temperature equilibrium assumption misleads.
Its limit
A porous model gives an average resistance; it does not show the local flow inside the region. If what you want is the distribution inside the packing, the model is the wrong tool.
References
- Ergun, S. (1952). Fluid flow through packed columns. Chemical Engineering Progress, 48(2), 89–94.
- Shah, R. K. & Sekulić, D. P. (2003). Fundamentals of Heat Exchanger Design. John Wiley & Sons. DOI: 10.1002/9780470172605