Numerical studies for solving a free convection boundary-layer flow over a vertical plate

• Autorzy: Othman M. I. A. , Mahdy A. M. S.
• Języki publikacji: EN

Abstrakty

EN

In this paper, the aim of this study is to present a reliable combination of the shifted Legendre collocation method to approximate of the problem of free convection boundarylayer flow over a vertical plate as produced by a body force about a flat plate in the direction of the generating body force. The proposed method is based on replacement of the unknown function by truncated series of well known shifted Legendre expansion of functions. An approximate formula of the integer derivative is introduced. Special attention is given to study the convergence analysis and derive an upper bound of the error of the presented approximate formula. The introduced method converts the proposed equation by means of collocation points to a system of algebraic equations with shift Legendre coefficients. Thus, by solving this system of equations, the shifted Legendre coefficients are obtained. Boundary conditions in an unbounded domain, i.e. boundary condition at infinity, pose a problem in general for the numerical solution methods. The obtained results are in good agreement with those provided previously by the iterative numerical method. As a result, without taking or estimating missing boundary conditions, the shifted Legendre collocation method provides a simple, non-iterative and effective way for determining the solutions of nonlinear free convection boundary layer problems possessing the boundary conditions at infinity.

Słowa kluczowe

EN

nonlinear differential equations; free convection boundary-layer flow; heat transfer; shifted Legendre collocation method

PL

nieliniowe równania różniczkowe; opływ konwencyjnej warstwy przyściennej; przepływ ciepła; metoda kolokacji Legendre'a

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2018
• Tom: Vol. 22, nr 1
• Strony: 41--48
• Opis fizyczny: Bibliogr. 8 poz., 1 rys.

Twórcy

autor

Othman M. I. A.

• Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Egypt

autor

Mahdy A. M. S.

• Department of Mathematics, Faculty of Science, Taif University 888, Saudi Arabia

Bibliografia

• [1] Schmidt, E., Beckmann, W.: Das Temperatur-und Geschwindigkeitsfeld vor einer Wärme abgebenden senkrechter Platte bei natürlicher Konvektion, Tech. Mech. u. Thermodynamik, 1, 10, 391–406, 1, 11, 341–349, 1930.
• [2] Ostrach, S.: An analysis of laminar free-convection flow and heat transfer about a flat plate parallel to the direction of the generating body force, NACA Report, 1111, 1953.
• [3] Na, T. Y., Habib, I. S.: Solution of the natural convection problem by parameter differentiation, Int. J. Heat Mass Transfer, 17, 457–459, 1974.
• [4] Kuo, B. L.: Application of the differential transformation method to the solutions of the free convection problem, Appl. Math. and Comp., 165, 63–79, 2005.
• [5] Bell, W. W.: Special Functions for Scientists and Engineers, Butler and Tanner Ltd, Frome and London, 1968.
• [6] Khader, M. M., Sweilam, N. H., Mahdy, A. M. S.: An efficient numerical method for solving the fractional diffusion equation, J. Appl. Math. and Bioinformatics, 1, 1–12, 2011.
• [7] Khader, M. M., Hendy, A. S.: The approximate and exact solutions of the fractional-order delay differential equations using Legendre pseudospectral method, Int. J. Pure and Applied Mathematics, 74, 3, 287–297, 2012.
• [8] Sweilam, N. H., Khader, M. M., Mahdy, A. M. S.: Numerical studies for solving fractional-order Logistic equation, Int. J. Pure and Applied Mathematics, 78, 8, 1199–1210, 2012.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).