Chapter 9 Nonlinear and linear analyses of partially ionized plasma
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Sunil
Abstract
This study examines thermal convectionthermal convection in a layer of partially ionized plasma (PIPpartially ionized plasma (PIP)) heated from below, considering three boundary configurations: free-free, rigid-rigid, and rigid-free. Linear analysis, performed using the normal modenormal mode method, and nonlinear analysis, conducted via the energy methodenergy method, provided comprehensive insights. Exact solutions were derived for free-free boundariesfree-free boundaries, while the Galerkin-weighted residual methodGalerkin-weighted residual method was applied to rigid-rigid and rigid-free boundariesrigid-free boundaries for numerical results. A notable outcome is the agreement between the critical Rayleigh numbers obtained from linear and nonlinear analyses, highlighting global stabilityglobal stability and the absence of subcritical regions. The study quantified the role of collisional frequencycollisional frequency, demonstrating its significant influence on energy dissipationdissipation rates without altering the critical Rayleigh numberRayleigh number. Compressibility was found to delay the onset of convectiononset of convection by increasing the Rayleigh number.
In addition to the fundamental investigation of thermal convectionthermal convection in PIPpartially ionized plasma (PIP), the effects of rotation and magnetic fields have been separately studied in this chapter. This separation enables a focused exploration of their individual contributions to stabilizing the system. Detailed investigations revealed that at low rotation ratesrotation rates, rigid-rigid boundaries offer the highest stability for PIPpartially ionized plasma (PIP), whereas, at high rotation rates, free-free boundariesfree-free boundaries emerge as the most stable configuration. These findings provide valuable insights into the interplay of compressibilitycompressibility, rotation, magnetic fields, and boundary conditions in governing the thermal convection behavior of PIPpartially ionized plasma (PIP).
Abstract
This study examines thermal convectionthermal convection in a layer of partially ionized plasma (PIPpartially ionized plasma (PIP)) heated from below, considering three boundary configurations: free-free, rigid-rigid, and rigid-free. Linear analysis, performed using the normal modenormal mode method, and nonlinear analysis, conducted via the energy methodenergy method, provided comprehensive insights. Exact solutions were derived for free-free boundariesfree-free boundaries, while the Galerkin-weighted residual methodGalerkin-weighted residual method was applied to rigid-rigid and rigid-free boundariesrigid-free boundaries for numerical results. A notable outcome is the agreement between the critical Rayleigh numbers obtained from linear and nonlinear analyses, highlighting global stabilityglobal stability and the absence of subcritical regions. The study quantified the role of collisional frequencycollisional frequency, demonstrating its significant influence on energy dissipationdissipation rates without altering the critical Rayleigh numberRayleigh number. Compressibility was found to delay the onset of convectiononset of convection by increasing the Rayleigh number.
In addition to the fundamental investigation of thermal convectionthermal convection in PIPpartially ionized plasma (PIP), the effects of rotation and magnetic fields have been separately studied in this chapter. This separation enables a focused exploration of their individual contributions to stabilizing the system. Detailed investigations revealed that at low rotation ratesrotation rates, rigid-rigid boundaries offer the highest stability for PIPpartially ionized plasma (PIP), whereas, at high rotation rates, free-free boundariesfree-free boundaries emerge as the most stable configuration. These findings provide valuable insights into the interplay of compressibilitycompressibility, rotation, magnetic fields, and boundary conditions in governing the thermal convection behavior of PIPpartially ionized plasma (PIP).
Chapters in this book
- Frontmatter I
- Contents V
- Aim and scope VII
- Preface IX
- Acknowledgments
- About editors XIII
- List of contributing authors XV
- Chapter 1 Introduction to flow dynamics and heat transfer 1
- Chapter 2 Compressible fluid flow and heat transfer 29
- Chapter 3 Non-Newtonian fluid flow and heat transfer 59
- Chapter 4 Heat transfer in forced and natural convection 81
- Chapter 5 Numerical study of coupled partial differential equations in heat transfer problems with imprecisely defined parameters 91
- Chapter 6 Numerical approach to study the effect of uncertain spectrum of field variables in a porous cavity 107
- Chapter 7 Investigation of the thermal fluid system using direct numerical simulation 123
- Chapter 8 Dynamics of shock-accelerated V-shaped gas interface 139
- Chapter 9 Nonlinear and linear analyses of partially ionized plasma 155
- Chapter 10 Thermo-fluid behavior of electroosmotic flow in a hydrophobic microchannel under Joule heating and external fields 185
- Chapter 11 The study of oscillating water column energy device in a two-layer fluid system of finite impermeable depth 219
- Chapter 12 Data-driven prediction of thermal conductivity ratio in nanoparticle-enhanced 60:40 EG/water nanofluids 239
- Chapter 13 Industrial applications of flow dynamics and heat transfer 261
- Chapter 14 Optimization techniques in flow dynamics and heat transfer 301
- Chapter 15 Advanced optimization methods in flow dynamics 335
- Index 353
- De Gruyter Series in Advanced Mechanical Engineering
Chapters in this book
- Frontmatter I
- Contents V
- Aim and scope VII
- Preface IX
- Acknowledgments
- About editors XIII
- List of contributing authors XV
- Chapter 1 Introduction to flow dynamics and heat transfer 1
- Chapter 2 Compressible fluid flow and heat transfer 29
- Chapter 3 Non-Newtonian fluid flow and heat transfer 59
- Chapter 4 Heat transfer in forced and natural convection 81
- Chapter 5 Numerical study of coupled partial differential equations in heat transfer problems with imprecisely defined parameters 91
- Chapter 6 Numerical approach to study the effect of uncertain spectrum of field variables in a porous cavity 107
- Chapter 7 Investigation of the thermal fluid system using direct numerical simulation 123
- Chapter 8 Dynamics of shock-accelerated V-shaped gas interface 139
- Chapter 9 Nonlinear and linear analyses of partially ionized plasma 155
- Chapter 10 Thermo-fluid behavior of electroosmotic flow in a hydrophobic microchannel under Joule heating and external fields 185
- Chapter 11 The study of oscillating water column energy device in a two-layer fluid system of finite impermeable depth 219
- Chapter 12 Data-driven prediction of thermal conductivity ratio in nanoparticle-enhanced 60:40 EG/water nanofluids 239
- Chapter 13 Industrial applications of flow dynamics and heat transfer 261
- Chapter 14 Optimization techniques in flow dynamics and heat transfer 301
- Chapter 15 Advanced optimization methods in flow dynamics 335
- Index 353
- De Gruyter Series in Advanced Mechanical Engineering
