Chapters authored
Heat and Mass Transfer from an Inverted Cone in a Porous Medium with Cross-Diffusion Effects
Part of the book: Mass Transfer
Cross-Diffusion, Viscous Dissipation and Radiation Effects on an Exponentially Stretching Surface in Porous Media
Part of the book: Mass Transfer
A Multi-Domain Spectral Collocation Approach for Solving Lane-Emden Type Equations
In this work, we explore the application of a novel multi-domain spectral collocation method for solving general non-linear singular initial value differential equations of the Lane-Emden type. The proposed solution approach is a simple iterative approach that does not employ linearisation of the differential equations. Spectral collocation is used to discretise the iterative scheme to form matrix equations that are solved over a sequence of non-overlapping sub-intervals of the domain. Continuity conditions are used to advance the solution across the non-overlapping sub-intervals. Different Lane-Emden equations that have been reported in the literature have been used for numerical experimentation. The results indicate that the method is very effective in solving Lane-Emden type equations. Computational error analysis is presented to demonstrate the fast convergence and high accuracy of the method of solution.
Part of the book: Numerical Simulation
Weakly Nonlinear Stability Analysis of a Nanofluid in a Horizontal Porous Layer Using a Multidomain Spectral Collocation Method
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.
Part of the book: Complexity in Biological and Physical Systems