Sandile Motsa

By Sandile Motsa and Stanford Shateyi

Part of the book: Advanced Topics in Mass Transfer

By Sandile Motsa and Stanford Shateyi

Part of the book: Evaporation, Condensation and Heat transfer

By Sandile Motsa and Stanford Shateyi

Part of the book: Numerical Simulation

By Stanford Shateyi and Sandile S. Motsa

Part of the book: Mass Transfer

By Sandile S. Motsa and Stanford Shateyi

Part of the book: Mass Transfer

By Sandile Motsa

This work presents a new numerical approach for solving unsteady two-dimensional boundary layer flow with heat and mass transfer. The flow model is described in terms of a highly coupled and nonlinear system of partial differential equations that models the problem of unsteady mixed convection flow over a vertical cone due to impulsive motion. The proposed method of solution uses a local linearisation approach to decouple the original system of PDEs to form a sequence of equations that can be solved in a computationally efficient manner. Approximate functions defined in terms of bivariate Lagrange interpolation polynomials are used with spectral collocation to approximate the solutions of the decoupled linearised equations. To test the accuracy and to validate the results of the proposed method, numerical error analysis and convergence tests are conducted. The present results are also compared with results from published literature for some special cases. The proposed algorithm is shown to be very accurate, convergent and very effective in generating numerical results in a computationally efficient manner.

Part of the book: Mass Transfer

By Motsa Sandile Sydney, Magagula Vusi Mpendulo, Goqo Sicelo Praisegod, Oyelakin Ibukun Sarah and Sibanda Precious

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

By Motsa Sandile Sydney, Samuel Felix Mutua and Shateyi Stanford

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