Chapters authored
Unsteady Magnetohydrodynamic Convective Heat and Mass Transfer Past an Infinite Vertical Plate in a Porous Medium with Thermal Radiation, Heat Generation/Absorption and Chemical Reaction
Part of the book: Advanced Topics in Mass Transfer
Successive Linearisation Solution of Free Convection Non-Darcy Flow with Heat and Mass Transfer
Part of the book: Advanced Topics in Mass Transfer
Soret and Dufour Effects on Steady MHD Natural Convection Flow Past a Semi-Infinite Moving Vertical Plate in a Porous Medium with Viscous Dissipation in the Presence of a Chemical Reaction
Part of the book: Evaporation, Condensation and Heat transfer
On New High Order Iterative Schemes for Solving Initial Value Problems in Epidemiology
Part of the book: Numerical Simulation
Successive Linearization of Heat and Mass Transfer over an Unsteady Stretching Permeable Surface in the Presence of Thermal Radiation and a Variable Chemical Reaction
Part of the book: Mass Transfer
Numerical Analysis of Mixed Convection Magnetohydrodynamic Heat and Mass Transfer past a Stretching Surface in a Micro-Polar Fluid-Saturated Porous Medium Under the Influence of Ohmic Heating
Part of the book: Mass Transfer
On a New Numerical Approach on Micropolar Fluid, Heat and Mass Transfer Over an Unsteady Stretching Sheet Through Porous Media in the Presence of a Heat Source/Sink and Chemical Reaction
The problem of MHD micropolar fluid, heat and mass transfer over unsteady stretching sheet through porous medium in the presence of a heat source/sink and chemical reaction is presented in this chapter. By applying suitable similarity transformations, we transform the governing partial differential equations into a system of ordinary differential equations. We then apply the recently developed numerical technique known as the Spectral Quasi-Linearization Method. The validity of the accuracy of the technique is checked against the bvp4c routine method. Numerical results for the surface shear stresses, Nusselt number and the Sherwood number are presented in tabular form. Also numerical results for the velocity, temperature and concentration distribution are presented in graphical forms, illustrating the effects of varying values of different parameters.
Part of the book: Numerical Simulation
Solving Nonlinear Parabolic Partial Differential Equations Using Multidomain Bivariate Spectral Collocation Method
In this study we introduce the multidomain bivariate spectral collocation method for solving nonlinear parabolic partial differential equations (PDEs) that are defined over large time intervals. The main idea is to reduce the size of the computational domain at each subinterval to ensure that very accurate results are obtained within shorter computational time when the spectral collocation method is applied. The proposed method is based on applying the quasi-linearization technique to simplify the nonlinear partial differential equation (PDE) first. The time domain is decomposed into smaller nonoverlapping subintervals. Discretization is then performed on both time and space variables using spectral collocation. The approximate solution of the PDE is obtained by solving the resulting linear matrix system at each subinterval independently. When the solution in the first subinterval has been computed, the continuity condition is used to obtain the initial guess in subsequent subintervals. The solutions at different subintervals are matched together along a common boundary. The examples chosen for numerical experimentation include the Burger’s-Fisher equation, the Fitzhugh-Nagumo equation and the Burger’s-Huxley equation. To demonstrate the accuracy and the effectiveness of the proposed method, the computational time and the error analysis of the chosen illustrative examples are presented in the tables.
Part of the book: Nonlinear Systems
Numerical Analysis of Three‐Dimensional MHD Nanofluid Flow over a Stretching Sheet with Convective Boundary Conditions through a Porous Medium
Numerical analysis has been carried out on the problem of three‐dimensional magnetohydrodynamic boundary layer flow of a nanofluid over a stretching sheet with convictive boundary conditions through a porous medium. Suitable similarity transformations were used to transform the governing partial differential equations into a system of ordinary differential equations. We then solved the resultant ordinary differential equation by using the spectral relaxation method. Effects of the dimensionless parameters on velocity, temperature and concentration profiles together with the friction coefficients, Nusselt and Sherwood numbers were discussed with the assistance of graphs and tables. The velocity was found to decrease with increasing values of the magnetic, stretching and permeability parameters. The local temperature was observed to rise as the Brownian motion, thermophoresis and Biot numbers increased. The concentration profiles diminish with increasing values of the Lewis number and chemical reaction parameter.
Part of the book: Nanofluid Heat and Mass Transfer in Engineering Problems
Numerical Simulation of Wave (Shock Profile) Propagation of the Kuramoto-Sivashinsky Equation Using an Adaptive Mesh Method
View all chaptersIn this paper, the Kuramoto-Sivashinsky equation is solved using Hermite collocation method on an adaptive mesh. The method uses seventh order Hermite basis functions on a mesh that is adaptive in space. Numerical experiments are carried out to validate effectiveness of the method.
Part of the book: Finite Element Method