Weakly Nonlinear Stability Analysis of a Nanofluid in a Horizontal Porous Layer Using a Multidomain Spectral Collocation Method

Abstract

In this chapter, we present a weakly nonlinear stability analysis of the flow of a nanofluid in a porous medium with stress-free boundary conditions. Some previous studies have investigated cross-diffusion in a nanofluid layer although in most cases these studies mostly deal with linear stability analysis. It is important to study the nonlinear stability in flows subject to cross-diffusion due to the wide range of applications where such flows arise such as in hydrothermal growth, compact heat exchanges, the solidification of binary mixtures, geophysical systems, solar pond, etc. Here we consider flow between parallel plates with an applied magnetic field and zero nanoparticle flux at the boundaries. A truncated Fourier series is introduced reducing the flow equations to a Lorenz-type system of nonlinear evolution equations. The multidomain spectral method is used to solve the equations that describe the growth of the convection amplitudes. The solutions are obtained as sets of trajectories in the phase space. Some interesting spiral trajectories and their sensitivity to the Rayleigh number are given.

A numerical study of heat and mass transport by double‐diffusive magnetoconvection in an electrically conducting fluid under sinusoidal/non‐sinusoidal rotational modulation

“…Generally, the method is ideal for chaotic systems of first‐order IVPs. Many studies 53,63–65 provide in‐depth explanations and validation of the MSRM, as well as a detailed verification of the method. The time interval $$[0,T]$$ is subdivided into small subintervals $${\rm{\Omega }}=[{t}_{i-1},{t}_{i}]$$, where $$i=1,2,3,\ldots p$$.…”

“…Generally, the method is ideal for chaotic systems of first-order IVPs. Many studies 53,[63][64][65] provide in-depth explanations and validation of the MSRM, as well as a detailed verification of the method. The time interval…”

On trigonometric cosine, square, sawtooth, and triangular wave‐type rotational modulations on triple‐diffusive convection in salted water

“…Literature shows that the method is accurate, efficient, and reliable as compared with other methods, like, the Runge-Kutta, Adams-Bashforth-Moulton, and finite difference methods. 57,58 For a system of nonlinear equations, the interval…”

Cross‐diffusion effects on the onset of double‐diffusive convection in a rotating vertical heterogeneous porous cylinder with vertical throughflow

“…Relevant literature on double-diffusive convection is documented in many studies. [1][2][3][4][5] Double-diffusive convection may occur in porous media, such as in geological formations or in industrial processes where porous media are used in heat and mass transfer processes. In porous media, the flow is affected by the pore structure, which may create additional transport mechanisms, such as advection and dispersion, that interact with thermal and diffusive buoyancy.…”

“…This phenomenon is also known as thermohaline convection or salt‐finger convection, depending on the nature of the two salt components involved. Relevant literature on double‐diffusive convection is documented in many studies 1–5 …”