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Hybrid integral transforms for flow development in ducts partially filled with porous media
Kleber Marques Lisboa1, Renato Machado Cotta1
1Laboratory of Nano- and Microfluidics and Microsystems, LabMEMS, Mechanical Engineering Department, POLI & COPPE and Interdisciplinary Nucleus for Social Development-NIDES/CT, Universidade Federal do Rio de Janeiro, Cidade Universitária Cx. Postal 68503, Rio de Janeiro, RJ CEP 21945-970, Brazil.
Abstract:
A hybrid numerical-analytical solution is developed for laminar flow development in a parallel plate duct partially filled with porous media. The integral transform method is employed in combination with a single domain reformulation strategy for representing the heterogeneous media within the channel. A novel eigenfunction expansion basis is proposed, including abrupt spatial variations of physical properties due to the domain transitions. The introduction of the new basis allows for a solution with similar convergence rates as in previous applications with simpler formulations, as demonstrated through a careful convergence analysis of the expansions. The inherent automatic error control characteristic of the integral transforms approach then provides benchmark results for the developing velocity profile. Moreover, a physical analysis further verifies the consistency of both the proposed expansion and the mixed symbolic-numerical code developed. A detailed verification with a finite-element commercial code is also performed.
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