Effect of variable permeability porous medium inter-connectors on the thermo-hydraulics of heat exchanger modelled as porous media

Using numerical methods, the effect of spatially variable permeability of porous medium tube-to-tube inter-connectors on the thermo-hydraulics of near-compact heat exchangers (NCHX, surface to volume ratio, α = 100–300 m2/m3), is studied. The porous medium connects the tubes (D = 2 mm) of the NCHX kept in in-line arrangement along the flow direction having a square pitch of XT=XL=2.25XT=XL=2.25. This novel study further treats the NCHX itself as a global porous medium characterized with global permeability (Kg) and form coefficient (Cg), which is being influenced by the local tube-to-tube inter-connector porous medium, characterized with a local permeability (Ki). The cooling fluid with Pr = 0.7 is under laminar flow (10 < Re < 100) through the NCHX with and without local PM inter-connectors of uniform permeability (UP, PMC1 and PMC2 with Ki = 10−5 and 10−10 m2, respectively) and variable permeability (VP, PMC3 and PMC4 with Ki varying along the flow direction from 10−5 to 10−10 m2 and 10−10 to 10−05 m2, respectively). At higher flow rates (Re > 70) it is shown that PMC4 registers less pressure-drop compared to PMC1, the UP case with highest Ki. Nusselt number variation for Re for VP cases (PMC3 and PMC4) is bounded by the two limiting UP cases PMC1 and PMC2, for identical porosity. Comparisons between NCHX tube bank in the UP and VP cases are done using an overall enhancement ratio (ER), which was found to increase with increasing Ki of the PM inter-connectors. Treating the NCHX models as a global porous medium, two useful engineering correlations are presented to predict the ξ and Nu as a function of Re and the non-dimensional global porous medium drag coefficients Dag and Dug (which are functions of local Ki). Both correlations predict the numerical data with ±6% accuracy within the range of Re tested.