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Projects 2008/9 PDF Print E-mail

The following is a list of available projects for the academic year 2008/9. Students are urged to consult the supervisors for further details about the projects.

  1. Forest Model Simulation

    Suppose that we are interested in a forest that is composed of two species of trees, with x(t) and y(t) denoting the number of each species in the forest in year t. When a tree dies, a new tree grows in its place, but the new tree might be of either species. The changes in the populations of the trees in time may be modelled by a system of differential equations

    Solve the system of equations exactly using ordinary differentiation tech niques and numerically using the Runge-Kutta method (or any method of your choice) to illustrate what will happen to the populations over time.

    Supervisor: Dr. S.S. Motsa

  2. Mathematics Modeling of the SARS epidemic

    In this project we illustrate the use of mathematical modeling techniques in modeling the spread of Severe Acute Respiratory Syndrome (SARS) in a community. A simple SIR model, described by the differential equations given below, is used to study the dynamics of  the disease.

     eqn1

    The main tasks are as follows:

    • Solve the governing equations numerically using the Runge-Kutta method.
    •  Solve the governing equations using in-built MATLAB or MAPLE differential equations solvers.
    •  Present the results graphically, analyze and interpret the results.

    Supervisor: Dr. S.S. Motsa

  3. Analytical and Numerical solutions of a fluid flow over a moving surface

    This project is based on a paper that was published by Ali Chamkha in 2003. The problem under consideration is that of a fluid flowing over a permeable moving surface. The governing equations are given as

    The main aim of the project is to find an exact solution of the above equations and compare the solution with a finite difference numerical solution.

    Supervisor: Dr. S.S. Motsa

  4. Unsteady heat conduction in a semi-infinite slab with surface convection

    Prove that the transient temperature distribution in a semi-infnite solid that is initially at a uniform temperature Ti and that has convection at the boundary surface  is given by

     where erfc is the complementary error function.

    Supervisor: Dr. S.S. Motsa

  5. Heat transfer in a semi-in nite wall subject to periodically vary- ing surface conditions

    Solve the one dimensional heat equation

    subject to the boundary conditions

    and the initial condition

    using

    • Laplace Transforms (or any other method)
    • Finite Differences

    Supervisor: Dr. S.S. Motsa