Linear Stability of Convection in an Inclined Porous Channel Filled with Nanofluid, Casson Fluid, and Dusty Fluid

Abstract

In recent years, the study of convective transport through porous media has emerged as an intriguing and significant subject, owing to its relevance in various industrial and engineering applications. Additionally, the exploration of convective instability in fluid-saturated porous layers, heated from below, has long captivated the attention of researchers across different physical conditions. This field finds extensive utility in geophysics, food processing, oil reservoir modeling, thermal insulation construction, and nuclear reactors. Understanding the mechanism of instability in incompressible nanofluid, Casson fluid, and dusty fluid flows through porous media is of utmost importance due to its practical implications in engineering. Nanofluids, which are created by uniformly dispersing and suspending metallic particles on a nanometer scale in conventional heat transfer fluids like water, oil, or ethylene glycol, are particularly relevant and Casson fluid refers to a type of non-Newtonian fluid that exhibits a non-linear relationship between shear stress and shear rate. The primary objective of this thesis is to conduct a linear stability analysis of incompressible nanofluid, Casson fluid and dusty fluid flows in an inclined channel filled with a porous medium. This thesis is organized into four parts and fourteen chapters. Part- I is composed of a single chapter, Chapter 1. This chapter serves as an introduction and covers several concepts, including nanofluid, Casson fluid, dusty Casson fluid, and porous medium. Additionally, it includes a review of relevant literature related to these topics. Part-II contains six chapters, namely Chapters 2, 3, 4, 5, 6 and 7. Chapter- 2 investi gates convective stability of nanofluid flow in inclined porous channel, considering Brownian motion, thermophoresis, and Brinkman’s equation. In Chapter- 3, deals the impact of local thermal non-equilibrium (LTNE) on nanofluid flow stability in an inclined channel filled with a porous medium. Chapter- 4 considers the effects of double diffusion and a magnetic field on the stability of nanofluid flow in an inclined porous channel. Chapter 5 investigates the effect of variable viscosity on the stability of nanofluid flow in an inclined porous channel. Chapter- 6 investigates numerically the local thermal non-equilibrium state of the fluid, par ticle, and solid-matrix phases for the stability of nanofluid flow in an inclined channel with variable viscosity filled with a porous medium. In Chapter- 7, the effects of double diffu sion and variable viscosity on the stability of a nanofluid-saturated Darcy-Brinkman porous medium in an inclined channel are investigated. Part III comprises three chapters, namely Chapters 8, 9, and 10. Chapter 8 delves into the examination of the stability of Casson fluid flow in an inclined channel with a highly permeable porous medium. The analysis takes into account the presence of a heat source or vi sink. In Chapter 9, the investigation shifts towards exploring the stability of Casson fluid f low in an inclined porous channel, considering the effects of chemical reaction and radiation. Chapter 10 is dedicated to investigating the impact of variable viscosity on the stability of Casson fluid flow in an inclined porous channel. Part-IV contains three chapters, namely Chapters 11, 12, and 13. In Chapter 11, the focus shifts to the investigation of the impact on the stability of two-phase dusty Casson f luid flow in an inclined porous channel. In Chapter 12, the emphasis is placed on studying the impact of variable viscosity on the stability of two-phase dusty Casson fluid flow in an inclined porous channel. Chapter 13 discusses the impact of heat source/sink and radiation on the stability of two-phase dusty Casson fluid flow in an inclined porous channel. In each of the preceding chapters, the non-linear governing equations and their associated boundary conditions are initially cast into dimensionless form through a suitable set of non-dimensional transformations and then converted into a system of linear ordinary differential equations by linear stability analysis and the normal mode technique. Chebyshev’s spectral collocation method is used to solve the resultant system of ordinary differential equations. The impact of relevant parameters on the onset of convection is depicted in graphs and tables. In addi tion, for some problems, the pattern of streamlines, isotherms, and isonanoconcentrations is plotted at a critical level over a single period. Part V is comprised of a solitary chapter, namely Chapter 14, which serves the purpose of summarizing the research findings, presenting overall conclusions, and future work scope