The stability of a vertical oblique magnetic field is investigated both theoretically and numerically, considering the effects internal heat chemical reaction under gravity modulation. experimental setup comprises two opposite plates held at different uniform temperatures solute concentrations, with other being permeable. A meticulous analysis porous medium influence executed using Darcy–Lapwood–Brinkman model. For linear analysis, normal mode techniques are employed to solve resulting...

This study investigates the stability of parallel buoyant magneto-convection in a rotating vertical porous medium filled with Casson fluid. The boundaries are considered isothermal rigid and kept at different uniform temperatures. Based on Darcy's law, Navier–Stokes equation is employed. In linear theory, an eigenvalue problem found using normal mode approach. original three-dimensional cast equivalent two-dimensional form Squire's transformations. Subsequently, solved numerically Chebyshev...

The stability of buoyant flow in an infinite extended vertical fluid layer bounded by impermeable conducting isothermal rigid walls, known as magnetic field influence on Casson rotating convection, is investigated. A system governing equations (Navier–Stokes, heat, and induction ones) solved with boundary conditions. When the majority electrically fluids are extremely small, can be simplified taking smallness Prandtl number into account. In linear stability, Chebyshev collocation method used...

The stability of thermally driven buoyant convection in a fluid-saturated, rotating horizontally porous layer with permeable boundaries is investigated by considering triple-diffusive system subjected to rotation modulation and influenced internal heating chemical reactions. momentum equation derived using Darcy's law for layers. A linear analysis conducted the standard normal mode technique. critical thermal Rayleigh number at onset stationary determined based on physical governing...

Inserting of anterior chamber phakic intraocular lenses are emerging as a transformative option for vision correction, offering individuals with high myopia and thin corneas safe effective solution without compromising the natural lens. Implantation Z-shaped lens fourth generation (ZSAL-4) can change typical flow patterns aqueous humor. To study this patterns, we utilized advanced computational fluid dynamics using Ansys Fluent. This method originated novel approach to measuring...

This study investigates the linear and weakly nonlinear convection driven by both thermal compositional buoyancy in a rotating horizontal porous layer, under influence of: (a) gravity modulation (b) rotation modulation. It is assumed that amplitude of minimal. In stability analysis, normal mode technique employed to calculate Rayleigh number at onset stationary convection. A perturbation analysis applied regime, focusing on small supercritical number. The Nusselt Sherwood numbers,...

In this paper, a numerical study uses linear and weakly nonlinear stability analyses to investigate the impact of internal heating on convection in couple-stress liquid porous slab heated from below cooled above. The density variation is modeled using Navier-Stokes equations under Boussinesq approximation. onset convective instability analyzed by linearizing governing for perturbations, considering only two-dimensional perturbation equations. eigenvalue problem solved establish principle...

Shock wave propagation in gases through turbulent flow has wide-reaching implications for both theoretical research and practical applications, including aerospace engineering, propulsion systems, industrial gas processes. The study of normal shock over non-ideal investigates the changes pressure, density, velocity across wave. Mach number is derived system explored various molecule quantities turbulence intensities. This analytically investigated adiabatic with modified Rankine–Hugoniot...

Abstract In this paper, we have presented a computational method for solving singularly perturbed delay differential equations with twin layers or oscillatory behaviour. method, the original second order equation is replaced by an asymptotically equivalent first neutral type equation. Then, employed numerical integration and linear interpolation to get tridiagonal system. This system solved efficiently using discrete invariant imbedding algorithm. Several model examples are solved, results...

This paper presents linear and weakly non analysis of magnetoconvection due to horizontal magnetic field vertical axis rotation thermal compositional buoyancy. For stability analysis, the normal mode is utilized find Rayleigh number which function Rosby number, Lewis Ekman number. Also, correlation between wave graphically analyzed. The Newell-Whitehead scheme employed derive two dimensional amplitude equation. conditions for Eckhaus Zigzag instabilities are determined. system coupled...

The Darcy-Lapwood-Brinkman model with the Boussinesq approximation is used to study linear and nonlinear stability analysis obtain conditions for occurrence of various types bifurcations, viz., Pitchfork bifurcation, Hopf Takens-Bogdanov bifurcation points. We have stress-free boundary derived a two-dimensional Landau-Ginzburg equation real coefficients at supercritical pitchfork discussed effect Nusselt number on heat transport by convection. shown secondary instabilities such as Eckhaus...

Abstract Magnetoconvection in a rotating fluid due to thermal and compositional buoyancy with anisotropic diffusivities is investigated by both linear weakly nonlinear analyses. By stability analysis, the threshold values of physical parameters give conditions for occurrence various types bifurcations. using multiple scale two‐dimensional amplitude equation derived secondary instabilities investigated. Nusselt number used study heat transport. Furthermore, effect stratification anisotropy...

Soret-driven convection in a two-component fluid layer subject to vertical temperature and concentration gradients is investigated analytically numerically. The Darcy-Lapwood-Brinkman model for the momentum equation Boussinesq approximation used study linear weakly nonlinear properties of sparsely packed porous medium due compositional thermal buoyancy. We have derived twodimensional Landau-Ginzburg with real coefficients near onset stationary at supercritical pitchfork bifurcation. studied...

Linear and weakly nonlinear properties of magnetoconvection in a sparsely packed porous medium are investigated. We have obtained the values Takens-Bogdanov bifurcation points codimension two by plotting graphs neutral curves corresponding to stationary oscillatory convection for different physical parameters relevant near supercritical pitchfork bifurcation. derived two-dimensional Ginzburg-Landau equation with real coefficients using Newell-Whitehead (1969) method. The effect parameter on...

Abstract We studied linear and nonlinear instabilities of horizontal magnetoconvection with rotating fluid in a sparsely packed porous media. the critical Rayleigh number traced marginal stability curves at different parameters , . obtained Takens‐Bogdanov co‐dimension two bifurcation points. The Newell‐Whitehead multiple scheme was employed to derive amplitude equations Pitchfork Hopf bifurcation. At onset we identified Eckhaus Zigzag instability regions Nusselt number. system coupled...

Nonlinear enhancement of convective instability in a sparsely packed porous medium due to the horizontal magnetic field is studied. The Boussinesq approximation applied Darcy Lapwood Brinkman (DLB) model. In linear and nonlinear stability analysis, normal mode method employed find critical modes occurrence distinct instabilities. A two-dimensional Landau-Ginzburg (LG) equation derived discussed Nusselt number primary Two coupled one-dimensional LG equations near onset oscillatory convection...