Modeling of unsteady and steady fluid flow, heat transfer and dispersion in porous media using unit cell scale

A unit cell scale computation of laminar steady and unsteady fluid flow and heat transfer is presented for a spatially periodic array of square rods representing two-dimensional isotropic or anisotropic porous media. In the model, a unit cell is taken as a representative elementary control volume and uniform heat flux boundary conditions are imposed on the solid-fluid interface. The governing equations are discretized by means of the finite volume approach; boundaries between adjacent cells are taken to be spatially periodic. Computations obtained using the SIMPLER algorithm, are made by varying the macroscopic flow direction from 0° to 90° relative to the unit cell, and varying the Reynolds number over the range 1-10³ spanning the Darcian and the inertial flow regimes to construct a database of local flow and heat transfer resistances in terms of permeabilities, inertial coefficients, Nusselt numbers, and thermal dispersion coefficients. The resulting database is utilized in a system scale analysis of a serpentine heat exchanger, where these directional terms from the microscale analysis provide closure to the porous-continuum model.