Browsing by Author "Cengizci, Suleyman"

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SUPS-Based Computational Investigation of Heat Transfer in a Nanofluid-Filled Cubic Enclosure With a Spherical Obstacle
(Springer, 2025) Cengizci, Suleyman; Oztop, Hakan F.; Atay, M. Tarik
This study investigates natural convection heat transfer through numerical simulations. The computational domain consists of a cubic enclosure filled with an Al2O3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Al}_2\hbox {O}_3$$\end{document}-H2O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {H}_2\hbox {O}$$\end{document} nanofluid, containing a concentric sphere that may be either heated or cooled. Various configurations are analyzed by varying the Rayleigh number (103 <= Ra <= 105\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10<^>3 \le \text {Ra} \le 10<^>5$$\end{document}) and the nanoparticle volume fraction (0.01 <=phi <= 0.1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.01 \le \phi \le 0.1$$\end{document}). The governing equations comprise the unsteady incompressible Navier-Stokes equations coupled with the heat transport equation. The Boussinesq approximation is employed, treating the density as constant except in the buoyancy term. To mitigate numerical instabilities inherent in the classical Galerkin finite element method (GFEM), a stabilized finite element formulation, known as the SUPS, is implemented. This formulation incorporates the streamline-upwind and pressure-stabilizing mechanisms. The proposed computational framework and in-house parallel incompressible flow solvers are validated against established benchmark cases, demonstrating good agreement despite using unstructured tetrahedral meshes without adaptive refinement. For the considered flow domain, the stabilized method ensures accurate solution profiles without significant spurious oscillations while substantially reducing computational cost, as linear interpolation functions are sufficient. Findings indicate that increasing the nanoparticle volume fraction enhances velocity magnitudes and the overall heat transfer rate around the sphere. Additionally, a slight reduction in the average number of nonlinear iterations is observed, suggesting improved computational efficiency. These results emphasize the effectiveness of stabilized finite element formulations in accurately and efficiently simulating convection-driven flow phenomena.
Citation - WoS: 2
Citation - Scopus: 3
An Asymptotic-Numerical Hybrid Method for Singularly Perturbed System of Two-Point Reaction-Diffusion Boundary-Value Problems
(Tubitak Scientific & Technological Research Council Turkey, 2019) Cengizci, Suleyman; Natesan, Srinivasan; Atay, Mehmet Tank
This article focuses on the numerical approximate solution of singularly perturbed systems of second-order reaction-diffusion two-point boundary-value problems for ordinary differential equations. To handle these types of problems, a numerical-asymptotic hybrid method has been used. In this hybrid approach, an efficient asymptotic method, the so-called successive complementary expansion method (SCEM) is employed first, and then a numerical method based on finite differences is applied to approximate the solution of corresponding singularly perturbed reaction-diffusion systems. Two illustrative examples are provided to demonstrate the efficiency, robustness, and easy applicability of the present method with convergence properties.
Citation - Scopus: 1
A Semi-Analytic Method for Solving Singularly Perturbed Twin-Layer Problems With a Turning Point
(Vilnius Gediminas Tech Univ, 2023) Cengizci, Suleyman; Kumar, Devendra; Atay, Mehmet Tarik
This computational study investigates a class of singularly perturbed second-order boundary-value problems having dual (twin) boundary layers and simple turning points. It is well-known that the classical discretization methods fail to resolve sharp gradients arising in solving singularly perturbed differential equations as the perturbation (diffusion) parameter decreases, i.e., epsilon -> 0(+). To this end, this paper proposes a semi-analytic hybrid method consisting of a numerical procedure based on finite differences and an asymptotic method called the Successive Complementary Expansion Method (SCEM) to approximate the solution of such problems. Two numerical experiments are provided to demonstrate the method's implementation and to evaluate its computational performance. Several comparisons with the numerical results existing in the literature are also made. The numerical observations reveal that the hybrid method leads to good solution profiles and achieves this in only a few iterations.
Citation - WoS: 3
Citation - Scopus: 3
A Uniformly Valid Approximation Algorithm for Nonlinear Ordinary Singular Perturbation Problems With Boundary Layer Solutions
(Springer int Publ Ag, 2016) Cengizci, Suleyman; Atay, Mehmet Tarik; Eryilmaz, Aytekin
This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.