Application of two spectral methods to a problem of convection with uniform internal heat source

• Autorzy: Dragomirescu I. , Georgescu A.
• Języki publikacji: EN

Abstrakty

EN

Two methods based on Fourier series expansions (a Chandrasekhar functions - based method and a shifted Legendre polynomials - based method) are used to study analytically the eigenvalue problem governing the linear convection problem with an uniform internal heat source in a horizontal fluid layer bounded by two rigid walls. For each method some theoretical reraarks are made. Numerical results are given and they are compared with some existing ones. Good agrement is found.

Słowa kluczowe

EN

eigenvalue problem; convection; internal heat source

PL

wartość własna; wartość charakterystyczna; pierwiastek charakterystyczny; zagadnienie znajdowania wartości własnych; konwekcja; rozkład Fouriera; szereg Fouriera; funkcja Chandrasekhara

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2008
• Tom: Vol. 30
• Strony: 43--52
• Opis fizyczny: Bibliogr. 9 poz., tab.

Twórcy

autor

Dragomirescu I.

autor

Georgescu A.

• University "Politechnica" of Timisoara, Department of Mathematics Timisoara, Romania,

Bibliografia

• [1] Chandrasekar, S., Hydrodynamic and hydromagnetic stability, Oxford University Press, 1961.
• [2] Dragomirescu I., Georgescu, A., Stability bounds in a problem of convection with uniform internal heat source, Proceedings of the 6th ICNPAA, Ed. by Seenith Sivasundaram, Cambridge Scientific Publishers Ltd, 2007, 163-170.
• [3] Dragomirescu, I., On the Chandrasekhar - Galerkin method in a convection problem for a micropolar fluid, Univ. "Politehnica" of Timisoara, St. Bull. Math. Phys., 50(64), 2 (2005), 53-61.
• [4] Georgescu, A., Mansutti, Coincidence of the linear and non-linear stability bounds in a horizontal thermal convection problem, Int. J. of Non-linear Mechanics, 34 (1999), 603-613.
• [5] Hill, A.A., Straughan, B., A Legendre spectral element method for eigenvalues in hydromagnetic stability, J. of Computational and Applied Mathematics, 193 (2003), 363-381.
• [6] Ming-I Char, Chiang, Ko-Ta, Stability analysis of Bénard-Marangoni convection in fluids with internal heat generation, J. Phys D: Appl Phys, 27, 4 (1994), 748-755.
• [7] Roberts, P.H., Convection in horizontal layers with internal heat generation. Theory, J. Fluid Mech, 30 (1967) 33-49.
• [8] Tritton, D.J., Zarraga, M.N., Convection in horizontal layers with internal heat generation. Experiments, J. Fluid Mech, 30 (1967), 21-31.
• [9] Vel'tishchev, N.F., Convection in a horizontal fluid layer with a uniform heat source, Fluid Dynamics, 39, 2 (2004), 189-197.