Moreover, 15 explicit equations, which were successfully performed in analyzing all sample networks with the closest results to that of the benchmark solution, were introduced as the most accurate ones. According to the obtained results, 15 explicit relations face the convergence problems which were identified as unreliable equations. In each scenario, one of these explicit relations was considered in the process of analyzing water networks. In the numerical experiment, these pipe networks were solved using three different h-based methods including h-based Newton–Raphson method, finite element method, and the gradient algorithm. In this study, 56 explicit relations available in the literature were implemented in the analysis of four water distribution networks while the benchmark solution is computed considering the implicit C–W formula. The mechanisms underlying the enhanced overall heat transfer are explored and presented.Īlthough many explicit correlations have already been presented as alternatives to implicit Colebrook–White (C–W) formula, performances of C–W-based relations in pipe network analysis have not been investigated. For a given pumping power, the new structure also provides better heat dissipation performance than the plate fin and the pyramidal lattice sandwich panels. Under certain Reynolds number, the introduction of the pyramidal lattice significantly enhances the overall Nusselt number of the plate fin sandwich panel by up to 150%, which is even higher than the sum of the overall Nusselt numbers for the bare plate fin and pyramidal lattice sandwich panels. Compared to the bare pyramidal lattice sandwich panel, flow acceleration is induced by the formation of the flow boundary layers on the fin surfaces. Results reveal that the insertion of the pyramidal lattice modifies the fluid flow in the plate fin sandwich panel. The flow and heat transfer characteristics of this new sandwich panel and those of the bare pyramidal lattice and the plate fin sandwich panels are compared. Forced convective heat transfer in this new structure is numerically investigated based on model validation. We propose a new sandwich panel by introducing the multifunctional pyramidal lattice into a plate fin sandwich panel.
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