Hamid Bellout

Illinois State University, Worcester, Massachusetts, United States

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Publications (54)62.07 Total impact

  • Allen Montz · Hamid Bellout · Frederick Bloom
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    ABSTRACT: The existence and uniqueness of solutions to the boundary-value problem for steady Poiseuille flow of an isothermal, incompressible, nonlinear bipolar viscous fluid in a cylinder of arbitrary cross-section is established. Continuous dependence of solutions, in an appropriate norm, is also established with respect to the constitutive parameters of the bipolar fluid model, as these parameters converge to zero, under the additional assumption that the cylinder has a circular cross-section.
    No preview · Article · Sep 2015 · Discrete and Continuous Dynamical Systems - Series B
  • Hamid Bellout · Frederick Bloom
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    ABSTRACT: The higher-order boundary conditions associated with the flow of an incompressible, nonlinear, bipolar viscous fluid in a bounded domain are derived; these boundary conditions differ from the various ad hoc sets of higher-order boundary conditions that have been used in work involving fluid dynamics models employing higher-order gradients of the velocity field. The derivation presented is based on a principle of virtual work and some deep results of Heron on higher-order traces of divergence-free vector fields.
    No preview · Article · Oct 2013 · Quarterly of Applied Mathematics
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    Allen Montz · Kotamarthi · Bellout H

    Full-text · Article · Aug 2013
  • Olga Terlyga · Hamid Bellout · Frederick Bloom
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    ABSTRACT: A mixed hyperbolic-parabolic system is derived for a lumped parameter continuum model of pulse combustion. For a regularized version of the initial-boundary value problem for an associated linear system, with time-dependent boundary conditions, Galerkin approximations are used to establish the existence of a suitable class of unique solutions. Standard parabolic theory is then employed to established higher regularity for the solutions of the regularized problem. Finally, a priori estimates are derived which allow for letting the artificial viscosity, in the regularized system, approach zero so as to obtain the existence of a unique solution for the original mixed hyperbolic-parabolic problem.
    No preview · Article · Feb 2013 · Electronic Journal of Differential Equations
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    ABSTRACT: We study a coupled nonlinear system of differential equation approximating the rotating MHD flow over a rotating sphere near the equator. In particular, using the Schauder fixed point theorem, we are able to establish existence of solutions. Other results on similar systems show that the question of existence in not obvious and, hence, that the present results are useful. Indeed, the work of McLeod in the 1970s shows some nonexistence results for similar problems. From here, we are also able to discuss some of the features of the obtained solutions. The observed behaviors of the solutions agree well with the numerical simulations present in the literature.
    No preview · Article · Feb 2013 · Zeitschrift für angewandte Mathematik und Physik ZAMP
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    ABSTRACT: In this brief paper, we consider the generalized equation of steady transonic gas flow with the addition of a singular source term. While the addition of a source term often destroys self-similarity of such flows, we demonstrate that a self-similar solution can still exist in the case of a singular source. We first reduce the governing nonlinear partial differential equation into an ordinary differential equation for a class of similarity solutions. Then, we study the existence of solutions for this similarity equation. After that, several explicit solution forms are given. In constructing exact solutions analytically, we demonstrate that dual solution branches may exist for some parameter regimes. For those parameter regimes where exact or analytical solutions are not possible, we obtain numerical solutions. The results demonstrate interesting properties of the solutions which warrant further study.
    Preview · Article · Jan 2013 · Quarterly of Applied Mathematics
  • Olga Terlyga · Hamid Bellout · Frederick Bloom
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    ABSTRACT: A global existence theorem is established for an initial-boundary value problem, with time-dependent boundary data, arising in a lumped parameter model of pulse combustion; the model in question gives rise to a nonlinear mixed hyperbolic-parabolic system. Using results previously established for the associated linear problem, a fixed point argument is employed to prove local existence for a regularized version of the nonlinear problem with artificial viscosity. Appropriate α-priori estimates are then derived which imply that the local existence result can be extended to a global existence theorem for the regularized problem. Finally, a different set of α priori estimates is generated which allows for taking the limit as the artificial viscosity parameter converges to zero; the corresponding solution of the regularized problem is then proven to converge to the unique solution of the initial-boundary value problem for the original, nonlinear, hyperbolic-parabolic system.
    No preview · Article · Jan 2012 · Acta Mathematica Scientia
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    ABSTRACT: Solutions for a class of degenerate, nonlinear, nonlocal boundary value problems, arising in nano boundary layer fluid flows over a stretching surface, are obtained. Viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface are considered. Using the Schauder fixed point theorem, existence and uniqueness results are established. The effects of the slip parameter k and the suction parameter a on the fluid velocity and on the tangential stress are investigated and discussed (through numerical results). We find that for fluid flows at nanoscales, the shear stress at the wall decreases (in an absolute sense) with an increase in the slip parameter k.
    No preview · Article · Dec 2011 · Nonlinear Analysis Real World Applications
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    Hamid Bellout · Qingkai Kong · Min Wang
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    ABSTRACT: In this paper, we study the dependence of the unique positive solution of the periodic boundary value problem-u″+ρ2u=w(t)us,0<s<1andρ≠0,u(0)=u(1),u′(0)=u′(1)on the parameter ρ as ρ → 0. We show that this solution u(t; ρ) is infinitely differentiable in ρ and has singularity in the order of ρ−α with α = 2/(1 − s) as ρ → 0. Furthermore, the graph of u(t; ρ) has fluctuation in t only of the order O(ρ−α+2). This will help us to determine the location of the solution in numerical computations to study the behavior of the solution when ρ is sufficiently close to 0.
    Full-text · Article · Jun 2011 · Applied Mathematics and Computation
  • Hamid Bellout · Frederick Bloom
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    ABSTRACT: An approach is described for constructing (using molecular dynamics simulations at the atomic scale) a mathematical model for the constitutive behavior of a carbon nanotube. The method is based on applying homogenization theory to a hexagonal array of carbon atoms with a specific chirality vector. The molecular dynamics simulations generate a set of periodic, rapidly varying, elastic constants for the nanotube. An example is presented to illustrate the technique for a specific array on a nanotube surface.
    No preview · Article · Jan 2011 · Mathematics and Mechanics of Solids
  • Patrick Penel · Jiří Neustupa · Hamid Bellout
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    ABSTRACT: Under assumptions on smoothness of the initial velocity and the external body force, we prove that there exists To > 0, ν* > 0 and a unique family of strong solutions uν of the Euler or Navier-Stokes initial-boundary value problem on the time interval (0, T0), depending continuously on the viscosity coefficient v for 0 < ν < ν*. The solutions of the Navier-Stokes problem satisfy a Navier-type boundary condition. We give the information on the rate of convergence of the solutions of the Navier-Stokes problem to the solution of the Euler problem for ν → 0+.
    No preview · Article · Aug 2010 · Discrete and Continuous Dynamical Systems
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    F. Talay Akyildiz · Hamid Bellout
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    ABSTRACT: This study numerically investigates the fully developed flow of a Newtonian fluid in a porous-saturated corrugated pipe, on the basis of a Brinkman model. The variable coefficient Helmholtz equation, which is obtained by means of an epitrochoid transformation, is solved using a spectral–Galerkin method. The effects of both the Darcy number and corrugation on the velocity field are discussed and presented graphically. The nature of these effects is documented for the first time.
    Full-text · Article · Apr 2010 · Computers & Mathematics with Applications
  • Hamid Bellout · Jiří Neustupa · Patrick Penel
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    ABSTRACT: Provided the initial velocity and the external body force are sufficiently smooth, there exist T(0) > 0, nu* > 0 and a unique continuous family of strong solutions u(v) (0 <= nu <= nu*) of the Euler or Navier-Stokes initial-boundary value problem on the time interval (0, T(0)). The solutions of the Navier-Stokes problem satisfy a Navier-type boundary condition. To cite this article: H. Bellout et al., C R. Acad. Sci. Paris, Ser. 1347 (2009). (C) 2009 Published by Elsevier Masson SAS on behalf of Academie des sciences.
    No preview · Article · Oct 2009 · Comptes Rendus Mathematique
  • Hamid Bellout · Jiří Neustupa
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    ABSTRACT: Under assumptions on smoothness of the initial velocity and the external body force, we prove that there exists T 0 > 0, ν 0 > 0 and a unique continuous family of strong solutions u ν (0 ≤ ν < ν 0) of the Euler or Navier–Stokes initial-boundary value problem on the time interval (0, T 0). In addition to the condition of the zero flux, the solutions of the Navier–Stokes equation satisfy certain natural boundary conditions imposed on curl u ν and curl 2 u ν .
    No preview · Article · Oct 2008 · Journal of Mathematical Fluid Mechanics
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    F. Talay Akyildiz · Hamid Bellout · K. Vajravelu
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    ABSTRACT: Solutions for a class of nonlinear second-order differential equations, arising in diffusion of chemically reactive species of a non-Newtonian fluid immersed in a porous medium over a stretching sheet, are obtained. Furthermore, using the Brouwer fixed point theorem, existence results are established. Moreover, the exact analytical solutions (for some special cases) are obtained. The results obtained for the diffusion characteristics reveal many interesting behaviors that warrant further study of the effects of reaction rate on the transfer of chemically reactive species.
    Full-text · Article · Aug 2006 · Journal of Mathematical Analysis and Applications
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    Guy Bayada · Hamid Bellout
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    ABSTRACT: In this paper a two-dimensional quasi-variational inequality arising in elastohydrodynamic lubrication is studied for non-constant viscosity. So far, existence results for such piezo–viscous problems require an L∞L∞ property for an auxiliary problem. For the usual pressure–viscosity relations, this property needs small data assumptions which are not observed in experimental conditions. In the present work, such small data assumptions are proved unnecessary for existence results. Besides well-established monotonicity behavior for the viscosity–pressure relation, the only condition used here is on the asymptotic behavior for this law as the pressure tends to infinity. If the procedure used here, namely the introduction of a reduced pressure by Grubin transform followed by a regularization procedure, appears somewhat classical, the way in which an upper bound is obtained is completely new.
    Preview · Article · Sep 2005 · Journal of Differential Equations
  • F. Talay Akyildiz · Hamid Bellout
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    ABSTRACT: The onset of chaotic motion in Newtonian fluid with a temperature dependent viscosity is explored in the context of the Rayleigh–Bénard thermal convection setup. Galerkin truncation is used to derive a low-order dynamical system (generalized Lorenz system) from the governing equations which reduces to the classical Lorenz system for a Newtonian fluid with a constant viscosity. The effect of the temperature dependent viscosity on the nonlinear solutions is analyzed by considering projections in the phase-space. Also, time signature of the solutions is investigated. The onset of chaotic motion is also discussed in detail for different values of temperature dependent viscosity in this paper.
    No preview · Article · Mar 2005 · Applied Mathematics and Computation
  • F.Talay Akyildiz · Hamid Bellout · K Vajravelu
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    ABSTRACT: Exact solutions for a class of non-linear second-order differential equations arising in a third grade fluid flow, at a rotating cylinder (unbounded domain case) and between rotating cylinders (bounded domain case), are obtained. Furthermore, the exact solutions are compared with the numerical ones. It is observed that the difference between the exact and the numerical solutions is about 1% for small R (the non-dimensional distance between the cylinders) and is about 3% when R=100. This difference increases with an increasing R. Moreover, for large R it is not easy to obtain meaningful results numerically. Hence, these exact solutions for various values of the parameters R and ω (rotation parameter) are useful for experimental and numerical studies, and warrant further study.
    No preview · Article · Dec 2004 · International Journal of Non-Linear Mechanics
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    Hamid Bellout · Jiří Neustupa · Patrick Penel
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    ABSTRACT: We treat the Stokes and the Navier-Stokes equation with the conditions curlku · n = 0 (k = 0, 1, 2) on the boundary of the flow field. The approach is based on a spectral analysis and properties of operator curl. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Preview · Article · Jun 2004 · Mathematische Nachrichten
  • Fahir Talay Akyildiz · Hamid Bellout
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    ABSTRACT: Thermally developing laminar flow of a dipolar fluid in a duct (pipe or channel) including axial conduction (Graetz problem extended) is investigated. The solutions are based on a self-adjoint formalism resulting from a decomposition of the convective diffusion equation for laminar flow into a pair of first-order partial differential equations. This approach, which is based on the solution method of Paputsakis et al. for a laminar pipe flow of a Newtonian fluid, is not plagued by any uncertainties arising from expansions in terms of eigenfunctions belonging to a non-self-adjoint operator. Then the eigenvalue problem is solved by means of the method of the weighted residual. Following this, the effect of the dipolar constant on the Nusselt number and temperature field are discussed in detail. Finally, it is shown that the Newtonian solution is a special case of the present result.
    No preview · Article · Jun 2004 · International Journal of Heat and Mass Transfer

Publication Stats

659 Citations
62.07 Total Impact Points

Institutions

  • 2013-2015
    • Illinois State University
      Worcester, Massachusetts, United States
  • 1988-2013
    • Northern Illinois University
      • Department of Mathematical Sciences
      DeKalb, Illinois, United States
  • 1993-2002
    • Charles University in Prague
      Praha, Praha, Czech Republic
  • 1992
    • Wichita State University
      Wichita, Kansas, United States
  • 1987
    • Purdue University
      • Department of Mathematics
      West Lafayette, Indiana, United States