Simulations of flow and heat transfer in a serpentine heat exchanger having dispersed resistance with porous-continuum and continuum models

A numerical study of fluid flow and heat transfer is conducted using the example of a serpentine section that is representative of a shell and tube heat exchanger utilizing two different approaches. In the first approach, a porous-continuum, homogeneous model (PCM) or macroscopic model is utilized based on the assumption that solid and fluid phases are observed as a single medium with anisotropic effective properties, over which local volume-averaged transport equations apply. In the second approach, a continuum, heterogeneous model (CM) or microscopic model is considered to solve the momentum equations for the fluid phase resulting in a conjugate heat transfer problem in both the solid and fluid volume. In the continuum model, the solid phase is composed of square rods in a spatially periodic pattern. A database of effective properties which includes the permeabilities, the Forchheimer coefficients, the thermal dispersion, and the heat transfer coefficients is constructed utilizing a periodic unit cell scale model. The data base is constructed from a representative elementary volume (REV) unit cell consisting of a fluid phase and heat generating solid phase; it is analyzed it by imposing a flow having various angles of approach relative to the unit cell and a range of Reynolds numbers spanning the Darcian and the inertial flow regimes. In all three models, the governing transport equations are numerically solved using the finite volume method (FVM). In the porous-continuum model analysis, the velocity and temperature distributions in the serpentine heat exchanger are obtained by solving the equations supplemented with the porous medium properties. The results from the direct continuum model computations were volume averaged on the REV in order to compare it to the porous-continuum model results. Profiles at various locations within the serpentine section show agreement between the porous-continuum, and continuum models. Further, comparison is discussed in terms of the local and global residuals from the porous-continuum and continuum computations. It is found that the local residuals correlate well with the radius of curvature of the streamlines and the unit cell scale. Global residuals are local residuals considered over a region of REV'S and are correlated to the packing density or number of unit cells within the serpentine section. The unit cell scale, streamline curvature and packing number become input parameters, and the local and global residual parameter can be used to estimate the error in using the porous-continuum model.