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Journal of Porous Media
IF: 1.752 5-Year IF: 1.487 SJR: 0.43 SNIP: 0.762 CiteScore™: 2.3

ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v16.i7.60
pages 647-661

POWER-LAW FLUID FLOWS IN CHANNELS WITH A PERMEABLE WALL

Maria Laura Martins-Costa
Universidade Federal Fluminense
Jesus Alfonso Puente Angulo
Laboratory of Theoretical and Applied Mechanics, Graduate Program in Mechanical Engineering, Universidade Federal Fluminense, 24210-240, Niterói, RJ, Brazil; Department of Mechanical Engineering, Federal Center of Technological Education of Rio de Janeiro, Angra dos Reis, RJ, Brazil
Heraldo da Costa Mattos
UNIVERSIDADE FEDERAL FLUMINENSE

ABSTRACT

The flow of an incompressible non-Newtonian fluid limited by two impermeable flat plates is studied by considering two distinct flow regions: one with the fluid only (without a porous matrix) and the second one with this fluid flowing through a porous medium. A mixture theory model is employed to describe these two adjacent flow regions in which the fluid has a power-law behavior. Adequate compatibility conditions at the interface between the two regions are considered. Numerical simulations have been performed employing a Runge-Kutta methodology coupled with a shooting strategy. Such problem is interesting in order to verify the coupled influence of material parameters and compatibility conditions. Employing this numerical strategy, the solution of the problem is essentially reduced to finding the root of a real function. The flow behavior for distinct values of the power-law index, characterizing what is usually referred as shear-thinning and shear-thickening fluids, was investigated. Comparison with some limit cases has validated the numerical procedure.


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