Computer-assisted successive linearization solution of the Darcy-Forchheimer-Brinkman flow through a rectangular channel
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Mahesha Narayana
Abstract
Numerical solution of nonlinear differential equations forms an integral part of modeling and simulation in recent times. The nonlinear Darcy-Forchheimer- Brinkman (DFB) model has been extensively used in frontier areas like petroleum engineering, hydrogeology, reactor engineering, biology, medicine, and so on. This well-celebrated model has been chosen as a representative problem to highlight the utility and significance of the computer-assisted successive linearization method (SLM) that in general can be applied to nonlinear boundary value problems (BVPs). The study aims to solve the BVP of the fully developed DFB flow through the sparsely packed porous medium using computer-assisted SLM and investigate its accuracy and robustness. The SLM involves successively linearizing the nonlinear differential equations and starting with an initial solution solve the resultant iterative system of linearized BVPs using the spectral collocation method. The present method, in general, has a quadratic rate of convergence and not sensitive to the initial solution unlike other numerical methods like the shooting method. It is found that the governing parameters have the least effect on the method which means that method convergences even for large values of parameters. Further, SLM is successful in capturing boundary and inertia effects in DFB flow.
Abstract
Numerical solution of nonlinear differential equations forms an integral part of modeling and simulation in recent times. The nonlinear Darcy-Forchheimer- Brinkman (DFB) model has been extensively used in frontier areas like petroleum engineering, hydrogeology, reactor engineering, biology, medicine, and so on. This well-celebrated model has been chosen as a representative problem to highlight the utility and significance of the computer-assisted successive linearization method (SLM) that in general can be applied to nonlinear boundary value problems (BVPs). The study aims to solve the BVP of the fully developed DFB flow through the sparsely packed porous medium using computer-assisted SLM and investigate its accuracy and robustness. The SLM involves successively linearizing the nonlinear differential equations and starting with an initial solution solve the resultant iterative system of linearized BVPs using the spectral collocation method. The present method, in general, has a quadratic rate of convergence and not sensitive to the initial solution unlike other numerical methods like the shooting method. It is found that the governing parameters have the least effect on the method which means that method convergences even for large values of parameters. Further, SLM is successful in capturing boundary and inertia effects in DFB flow.
Chapters in this book
- Frontmatter I
- Contents V
- Foreword VII
- Editor X
- Analytical study of Küppers-Lortz instability in a Newtonian-Boussinesq liquid with rigidisothermal boundaries 1
- Quadratic radiation and quadratic Boussinesq approximation on hybrid nanoliquid flow 13
- Convective heat transfer of magneto flow of Fe3O4-MWCNT/H2O hybrid nanofluid in a porous space between two concentric cylinders 55
- Computational analysis of bioconvection in magnetized flow of thixotropic nanofluid with gyrotactic microorganisms 75
- On the features of Stefan blowing magnetized flow of bioconvected nanofluid through slip conditions 103
- Computer-assisted successive linearization solution of the Darcy-Forchheimer-Brinkman flow through a rectangular channel 121
- Linear and non-linear instability analysis of the onset of magnetoconvection in couplestress fluids with thermorheological effect 143
- Two-component convection in micropolar fluid under time-dependent boundary concentration 163
- A numerical study of metal hydride reactor embedded with helical coil heat exchanger 201
- Dynamics of non-Newtonian nanoliquid with quadratic thermal convection 223
- List of contributors 249
Chapters in this book
- Frontmatter I
- Contents V
- Foreword VII
- Editor X
- Analytical study of Küppers-Lortz instability in a Newtonian-Boussinesq liquid with rigidisothermal boundaries 1
- Quadratic radiation and quadratic Boussinesq approximation on hybrid nanoliquid flow 13
- Convective heat transfer of magneto flow of Fe3O4-MWCNT/H2O hybrid nanofluid in a porous space between two concentric cylinders 55
- Computational analysis of bioconvection in magnetized flow of thixotropic nanofluid with gyrotactic microorganisms 75
- On the features of Stefan blowing magnetized flow of bioconvected nanofluid through slip conditions 103
- Computer-assisted successive linearization solution of the Darcy-Forchheimer-Brinkman flow through a rectangular channel 121
- Linear and non-linear instability analysis of the onset of magnetoconvection in couplestress fluids with thermorheological effect 143
- Two-component convection in micropolar fluid under time-dependent boundary concentration 163
- A numerical study of metal hydride reactor embedded with helical coil heat exchanger 201
- Dynamics of non-Newtonian nanoliquid with quadratic thermal convection 223
- List of contributors 249
