|
| Titre : |
Study Of The Stationary Solution Of Non-Isothermal Bingham Flow |
| Type de document : |
document électronique |
| Auteurs : |
Oumaima Dames, Auteur ; Saadallah ,Abdelkader, Directeur de thèse |
| Editeur : |
Sétif:UFS |
| Année de publication : |
2024 |
| Importance : |
1 vol (32 f.) |
| Format : |
29 cm |
| Langues : |
Anglais (eng) |
| Catégories : |
Thèses & Mémoires:Mathématique
|
| Mots-clés : |
Asymptotic approach, Bingham fluid, Temperature, Reynolds equation, Variational inequality,
Tresca friction. |
| Index. décimale : |
510-Mathématique |
| Résumé : |
This research investigates the asymptotic behavior of a stationary, non-isothermal Bingham fluid
flow in a three-dimensional thin domain Ωε associated with nonlinear Tresca friction conditions. By
applying a scaling technique, the problem is transformed from the thin domain depending on the
parameter ε into a fixed reference domain Ω independent of this parameter (which represents the
layer thickness tending to zero). Uniform a priori estimates are established, and the convergence of
the unknowns—namely velocity, pressure, and temperature—is analyzed. Finally, the limit problem
is proven, and the general two-dimensional Reynolds equation is derived as a simplified and accurate
model for industrial applications.
|
| Note de contenu : |
Sommaire
Dedication 2
Acknowledgement 3
General introduction 5
1 Preliminaries 6
1.1 Some reminders of functional analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.1 Lebesgue spaces: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.2 Sobolev space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.3 Vector-valued function spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 Lower semi-continuity properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3 Gronwall's lemma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Asymptotic convergence of a viscoelastic problems with short memory in a thin
domain with tresca boundry conditions 15
2.1 Introduction and position of the problem . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Variational formulation of the problem . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Existence and uniqueness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Asymptotic analysis of the problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.1 A priori estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.2 Convergence theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4.3 The main results concerning the limit problem . . . . . . . . . . . . . . . . . 30
2.4.4 Reynolds equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.5 Uniqueness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Conclusion 41 |
| Côte titre : |
MAM/0877 |
Study Of The Stationary Solution Of Non-Isothermal Bingham Flow [document électronique] / Oumaima Dames, Auteur ; Saadallah ,Abdelkader, Directeur de thèse . - [S.l.] : Sétif:UFS, 2024 . - 1 vol (32 f.) ; 29 cm. Langues : Anglais ( eng)
| Catégories : |
Thèses & Mémoires:Mathématique
|
| Mots-clés : |
Asymptotic approach, Bingham fluid, Temperature, Reynolds equation, Variational inequality,
Tresca friction. |
| Index. décimale : |
510-Mathématique |
| Résumé : |
This research investigates the asymptotic behavior of a stationary, non-isothermal Bingham fluid
flow in a three-dimensional thin domain Ωε associated with nonlinear Tresca friction conditions. By
applying a scaling technique, the problem is transformed from the thin domain depending on the
parameter ε into a fixed reference domain Ω independent of this parameter (which represents the
layer thickness tending to zero). Uniform a priori estimates are established, and the convergence of
the unknowns—namely velocity, pressure, and temperature—is analyzed. Finally, the limit problem
is proven, and the general two-dimensional Reynolds equation is derived as a simplified and accurate
model for industrial applications.
|
| Note de contenu : |
Sommaire
Dedication 2
Acknowledgement 3
General introduction 5
1 Preliminaries 6
1.1 Some reminders of functional analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.1 Lebesgue spaces: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.2 Sobolev space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.3 Vector-valued function spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 Lower semi-continuity properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3 Gronwall's lemma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Asymptotic convergence of a viscoelastic problems with short memory in a thin
domain with tresca boundry conditions 15
2.1 Introduction and position of the problem . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Variational formulation of the problem . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Existence and uniqueness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Asymptotic analysis of the problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.1 A priori estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.2 Convergence theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4.3 The main results concerning the limit problem . . . . . . . . . . . . . . . . . 30
2.4.4 Reynolds equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.5 Uniqueness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Conclusion 41 |
| Côte titre : |
MAM/0877 |
|
Study Of The Stationary Solution Of Non-Isothermal Bingham Flow
