The steady Navier-Stokes/energy system with temperature-dependent viscosity - Part 1: Analysis of the continuous problem

International Journal for Numerical Methods in Fluids

Volumn 56, Issue 1, 2008, Pages 63-89

  Pérez, Carlos E ^a   Thomas, Jean Marie ^b   Blancher, Serge ^b,c   Creff, René ^b,c  

^a UNIVERSITY OF CONCEPCIÓN   (Chile)

^b UNIVERSITÉ DE PAU ET DES PAYS DE L'ADOUR   (France)

^c Hélioparc ^*  (France)

Author keywords

Couples equations; Navier Stokes; Variables viscosity

Indexed keywords

INCOMPRESSIBLE FLOW; MIXED CONVECTION; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; STEADY FLOW; THERMAL EFFECTS; VISCOSITY;

COUPLES EQUATION; ENERGY EQUATION; VARIABLE VISCOSITY;

COMPUTATIONAL FLUID DYNAMICS;

COMPUTATIONAL FLUID DYNAMICS; INCOMPRESSIBLE FLOW; MIXED CONVECTION; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; STEADY FLOW; THERMAL EFFECTS; VISCOSITY;

EID: 37549055782     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1509     Document Type: Article

References (34)

1. Lide DR (ed.). CRC Handbook of Chemistry and Physics (82nd edn). CRC Press: Boca Raton, FL, 1998.
2. Galdi G. An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Vol. 1: Linearized Steady Problems. Springer Tracts in Natural Philosophy, vol. 38. Springer: Berlin, 1994.
3. Girault V, Raviart PA. Finite Element Methods for Navier-Stokes Equations(2nd edn). Springer: Berlin, 1986.
4. Lions J-L. Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires. Dunod: Gauthier-Villars, 1969.
5. Temam R. Navier-Stokes Equations. North-Holland: Amsterdam, 1996.
6. Diaz JI, Galiano G. On the Boussinesq system with nonlinear thermal diffussion. Nonlinear Analysis - Theory Methods and Applications 1997; 30(6):3255-3263.
7. Goncharova ON. Unique solvability of a two-dimensional nonstationary problem for the convection equations with temperature-dependent viscosity. Differential Equations 2002; 38(2):249-258.
8. Alekseev GV, Smishliaev AB. Solvability of the boundary-value problems for the Boussinesq equations with inhomogeneous boundary conditions. Journal of Mathematical Fluid Mechanics 2001; 3:18-39.
9. Conca C, Murat F, Pironneau O. The Stokes and Navier-Stokes equations with boundary conditions involving the pressure. Japanese Journal of Mathematics 1994; 20(2):279-318.
10. Heywood JF, Rannacher R, Turek S. Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids 1996; 22:325-352.
11. Bruneau GH, Fabrie P. New efficient boundary conditions for incompressible Navier-Stokes equations: a well-posedness result. Mathematical Modelling and Numerical Analysis 1996; 30(7):815-840.
12. Duvaut G, Lions J-L. Transfert de chaleur dans un fluide de Bingham dont la viscosité dépend de la température. Journal of Functional Analysis 1972; 11:93-110.
13. Bruneau C-H, Fabrie P. Effective downstream boundary conditions for incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids 1994; 19:693-705.
14. Bui An Ton B. On the initial boundary-value problem for non-homogeneous incompressible heat-conducting fluids. Rocky Mountain Journal of Mathematics 1981; 11(1):99-112.
15. Lions P-L. Mathematical Topics in Fluid Dynamics, Vol. 1: Incompressible Models. Clarendon Press: Oxford, 1996.
16. Wardi S. A convergence result for an iterative method for the equations of a quasi-Newtonian flow with temperature-dependent viscosity. Mathematical Modelling and Numerical Analysis 1998; 32(4):391-404.
17. Bernardi C, Métivet B, Pernaud-Thomas B. Couplage des équations de Navier-Stokes et de la chaleur: le modèle et son approximation par Eléments Finis. Mathematical Modelling and Numerical Analysis 1995; 29(7):871-921.
18. Farhloul M, Nicaise S, Paquet L. A mixed formulation of Boussinesq equations: analysis of nonsingular solutions. Mathematics of Computation 2000; 69(231):965-986.
19. Gaultier M, Lezaun M. Equations de Navier-Stokes couplées à des équations de la chaleur: résolution par une méthode de point fixe en dimension infinie. Annales des Sciences Mathématiques du Québec 1989; 13(1):1-17.
20. Ern A, Guermond J-L. Eléments Finis: Théorie Applications, Mise en Oeuvre. Mathématiques & Applications, vol. 36. Springer: Berlin, 2002.
21. Gresho PM, Sani RL. Résumé and remarks on the open boundary condition minisymposium. International Journal for Numerical Methods in Fluids 1994; 18:983-1008.
22. Fletcher CA. Computational Techniques for Fluid Dynamics. Springer: Berlin, 1988.
23. Schlichting H. Boundary Layer Theory. McGraw-Hill: New York, 1955.
24. Kundu P, Cohen IM. Fluid Mechanics (3rd edn). Elsevier: Amsterdam, 2004.
25. Pérez CE. Analyse numérique de phéomènes de couplage liés aux transferts thermiques. Ph.D. Thesis, Thèse, Université de Pau et des Pays de l'Adour, 2003.
26. Herwig H, Schäfer P. Influence of variable properties on the stability of two-dimensional boundary layers. Journal of Fluid Mechanics 1992; 243:1-14.
27. Leal MA, Machado HA, Cotta RM. Integral transform solutions of transient natural convection in enclosures with variable fluid properties. International Journal of Heat and Mass Transfer 2000; 43:3977-3990.
28. Pinarbasi A, Liakopoulos A. The role of variable viscosity in the stability of channel flow. International Communications in Heat and Mass Transfer 1995; 22(6):837-847.
29. Taine J, Petit J-P. Transferts Thermiques, Mécanique des Fluides Anisothermes. Dunod: Paris, 1998.
30. Blancher S, Creff R, Pérez CE. Unsteady forced convection on a flat plate periodically heated in a periodic section channel. In Proceedings of the Twelfth International Heat Transfer Conference, Grenoble, France, August 2002, Taine J (ed.). Elsevier: Amsterdam, 2002; 1-10.
31. Ciarlet PG. Mathematical Elasticity, Volume I: Three-dimensional Elasticity. Studies in Mathematics and its Applications, vol. 20. North Holland: Amsterdam, 1988.
32. Gresho PM, Sani RL. Incompressible Flow and the Finite Element Method, volume two: Isothermal Laminar Flow (1st edn). Wiley: New York, 1999.
33. Gagneux G, Madaune-Tort M. Analyse Mathématique de Modèles Non Linéaires de L'ingénierie Pétrolière, vol. 22. Springer: Berlin, 1996.
34. Stampacchia G. Equations Elliptiques du Second Ordre à Coefficients Discontinus. Les Presses de l'Université de Montréal: Montreal, 1966.