Author
José M.C. Pereira
Other affiliations: Technical University of Lisbon
Bio: José M.C. Pereira is an academic researcher from Instituto Superior Técnico. The author has contributed to research in topics: Porous medium & Partial oxidation. The author has an hindex of 10, co-authored 20 publications receiving 339 citations. Previous affiliations of José M.C. Pereira include Technical University of Lisbon.
Papers
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TL;DR: In this article, the authors used the variable order calculus to determine the region of validity of Tchen's equation for oscillatory flow, where the order of the derivative is fractional but constant, and where the strong non-linearity of the flow requires a variable order derivative.
Abstract: This work advances our understanding of the drag force acting on a particle due to the oscillatory flow of a viscous fluid with finite Reynolds and Strouhal numbers. The drag force is is determined using the novel concept of variable order (VO) calculus, where the order of derivative can vary with the parameters and variables, according to the dynamics of the flow. Using the VO formulation we determine: (i) The region of validity of Tchen's equation for oscillatory flow, (ii) the region where the order of the derivative is fractional but constant, and (iii) the region where the strong non-linearity of the flow requires a variable order derivative to account for the increased complexity of the flow.
107 citations
01 Jan 2013
TL;DR: In this article, the authors investigated the lean premixed combustion of hydrogen and carbon monoxide (H2/CO) mixtures within a porous inert media model-burner.
Abstract: The lean premixed combustion of hydrogen and carbon monoxide (H2/CO) mixtures within a porous inert media model-burner was investigated for ranges of H2/CO volumetric ratios from 2 to 4, inert volumetric concentrations in the fuel stream from 85% to 90%, thermal loads of 400 kW/m2 (2 kW) and 1000 kW/m2 (5 kW), constant reactants temperature of 673 K and an equivalence ratio of ϕ = 05 Experimental measurements and numerical predictions of temperature profiles and temperature gradients along the axial center-line of the combustion zone are presented and the thermal flame thickness is estimated and analyzed for the effect of thermal load, inert components in the fuel stream and H2/CO ratios The adopted numerical model uses a volume-averaged approach and solves both the gas- and solid-phase energy balances explicitly and accounts for the radiative heat transport in the solid-phase The thermal flame thickness results are compared with the respective laminar free flame values and differences between the flame thickness of free flames and flames inside a porous inert media are discussed
61 citations
TL;DR: In this paper, a non-intrusive Spectral Projection Method (NISP) is used to analyze the uncertainty of high temperature ceramic microwave heating with uncertain operating frequency and dielectric constants, and the results indicate that the uncertainty in the material's imaginary part of permittivity has only a significant impact for high temperatures of the material.
31 citations
TL;DR: In this paper, a non-catalytic partial oxidation within a small-scale porous media based reformer, intended for application in Solid Oxide Fuel Cell (SOFC) based systems, is investigated.
28 citations
TL;DR: In this article, the impact of the catalyst internal structure on the conversion rates of CO oxidation is investigated using a 3D multi-scale bottom-up approach for transport and reaction modeling in isothermal porous catalyst layers.
23 citations
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TL;DR: In this article, a new fractional derivative with non-local and no-singular kernel was proposed and applied to solve the fractional heat transfer model, and some useful properties of the new derivative were presented.
Abstract: In this manuscript we proposed a new fractional derivative with non-local and
no-singular kernel. We presented some useful properties of the new derivative
and applied it to solve the fractional heat transfer model.
2,364 citations
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TL;DR: In this paper, a new fractional derivative with non-local and no-singular kernel was proposed and applied to solve the fractional heat transfer model, and some useful properties of the new derivative were presented.
Abstract: In this manuscript we proposed a new fractional derivative with non-local and no-singular kernel. We presented some useful properties of the new derivative and applied it to solve the fractional heat transfer model.
1,372 citations
TL;DR: In this article, a classification of variable-order fractional diffusion models based on the possible physical origins which prompt the variable order is presented. But the characteristics of the new models change with time, space, concentration or other independent quantities.
Abstract: The purpose of this paper is to offer a unified discussion of variable-order differential operators in anomalous diffusion modeling. The characteristics of the new models, in contrast to constant-order fractional diffusion models, change with time, space, concentration or other independent quantities. We introduced a classification of variable-order fractional diffusion models based on the possible physical origins which prompt the variable-order. Some potential applications of the variable-order fractional diffusion models are also discussed.
479 citations
TL;DR: The authors presents a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and engineering, and presents a discussion of the relationship between fractional derivatives and integral derivatives.
Abstract: This paper presents a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and engineering.
387 citations
01 Jan 2001
TL;DR: This work constructs a simple and efficient adaptive FEM for elliptic partial differential equations and proves that this algorithm converges with linear rate without any preliminary mesh adaptation nor explicit knowledge of constants.
Abstract: Adaptive finite element methods (FEM) have been widely used in applications for over 20 years now. In practice, they converge starting from coarse grids, although no mathematical theory has been able to prove this assertion. Ensuring an error reduction rate based on a posteriori error estimators, together with a reduction rate of data oscillation (information missed by the underlying averaging process), we construct a simple and efficient adaptive FEM for elliptic partial differential equations. We prove that this algorithm converges with linear rate without any preliminary mesh adaptation nor explicit knowledge of constants. Any prescribed error tolerance is thus achieved in a finite number of steps. A number of numerical experiments in two and three dimensions yield quasi-optimal meshes along with a competitive performance. Extensions to higher order elements and applications to saddle point problems are discussed as well.
Keywords: A posteriori error estimators, data oscillation, adaptive mesh refinement, convergence, Stokes, Uzawa
AMS Subject Classifications: 65N12, 65N15, 65N30, 65N50, 65Y20
Published: SIAM Review, 44 (2002) 631--658.
337 citations