Raseelo Joel Moitsheki

Stokes’ first problem for Sisko fluid over a porous wall

We investigate the time-dependent flow of an incompressible Sisko fluid over a wall with suction or blowing. The flow is caused by sudden motion of the wall in its own plane. The magnetodynamic nature of the fluid is taken into account by applying a variable magnetic field. The resulting nonlinear problem is solved by invoking a symmetry approach and numerical techniques. The essential features of the embedded key parameters are described. Particularly the significance of the rheological effects is studied.

Systematic construction of hidden nonlocal symmetries for the inhomogeneous nonlinear diffusion equation

We consider a class of inhomogeneous nonlinear diffusion equations (INDE) that arise in solute transport theory. Hidden nonlocal symmetries that seem not to be recorded in the literature are systematically determined by considering an integrated equation, obtained using the general integral variable, rather than a system of first-order partial differential equations (PDEs) associated with the concentration and flux of a conservation law. Reductions for the INDE to ordinary differential equations (ODEs) are performed and some invariant solutions are constructed.

On Nonperturbative Techniques for Thermal Radiation Effect on Natural Convection past a Vertical Plate Embedded in a Saturated Porous Medium

In this article, the heat transfer characteristics of natural convection about a vertical permeable flat surface embedded in a saturated porous medium are studied by taking into account the thermal radiation effect. The plate is assumed to have a power-law temperature distribution. Similarity variables are employed in order to transform the governing partial differential equations into a nonlinear ordinary differential equation. Both Adomian decomposition method (ADM) and Hes variational iteration method (VIM) coupled with Pade approximation technique are implemented to solve the reduced system. Comparisons with previously published works are performed, and excellent agreement between the results is obtained.

Analytical Solutions for Steady Heat Transfer in Longitudinal Fins with Temperature-Dependent Properties

Explicit analytical expressions for the temperature profile, fin efficiency, and heat flux in a longitudinal fin are derived. Here, thermal conductivity and heat transfer coefficient depend on the temperature. The differential transform method (DTM) is employed to construct the analytical (series) solutions. Thermal conductivity is considered to be given by the power law in one case and by the linear function of temperature in the other, whereas heat transfer coefficient is only given by the power law. The analytical solutions constructed by the DTM agree very well with the exact solutions even when both the thermal conductivity and the heat transfer coefficient are given by the power law. The analytical solutions are obtained for the problems which cannot be solved exactly. The effects of some physical parameters such as the thermogeometric fin parameter and thermal conductivity gradient on temperature distribution are illustrated and explained.

Transient Heat Diffusion with Temperature-Dependent Conductivity and Time-Dependent Heat Transfer Coefficient

Lie point symmetry analysis is performed for an unsteady nonlinear heat diffusion problem modeling thermal energy storage in a medium with a temperature-dependent power law thermal conductivity and subjected to a convective heat transfer to the surrounding environment at the boundary through a variable heat transfer coefficient. Large symmetry groups are admitted even for special choices of the constants appearing in the governing equation. We construct one-dimensional optimal systems for the admitted Lie algebras. Following symmetry reductions, we construct invariant solutions.

Similarity reductions of equations for river pollution

We consider a system of coupled partial differential equations describing pollutant transport in a river system. Symmetry analysis of this system resulted in admitted large Lie algebras for a some special cases of the arbitrary constants and the source term. Furthermore, we construct the one-dimensional optimal systems of the admitted symmetries. However, similarity (invariant) solutions for the system are constructed for some more realistic source term.

Classical Lie point symmetry analysis of nonlinear diffusion equations describing thermal energy storage

In this paper, we employed the linear transformation group approach to time dependent nonlinear diffusion equations describing thermal energy storage problem. Symmetry analysis of the governing equation resulted in admitted large Lie symmetry algebras for some special cases of the arbitrary constants and the source term. Some transformations that lead to equations with fewer arbitrary parameters are applied and classical Lie point symmetry methods are employed to analyze the transformed equations. Some symmetry reductions are performed and wherever possible the reduced ordinary differential equations are completely solved subject to realistic boundary conditions.

Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem

We consider the one-dimensional steady fin problem with the Dirichlet boundary condition at one end and the Neumann boundary condition at the other. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for which the principal Lie algebra is extended. Some invariant solutions are constructed. The effects of thermogeometric fin parameter and the exponent on temperature are studied. Also, the fin efficiency is analyzed.

Steady Heat Transfer through a Two-Dimensional Rectangular Straight Fin

Exact solutions for models describing heat transfer in a two-dimensional rectangular fin are constructed. Thermal conductivity, internal energy generation function, and heat transfer coefficient are assumed to be dependent on temperature. We apply the Kirchoff transformation on the governing equation. Exact solutions satisfying the realistic boundary conditions are constructed for the resulting linear equation. Symmetry analysis is carried out to classify the internal heat generation function, and some reductions are performed. Furthermore, the effects of physical parameters such as extension factor (the purely geometric fin parameter) and Biot number on temperature are analyzed. Heat flux and fin efficiency are studied.

Some invariant solutions for a microwave heating model

In this paper, we apply the classical Lie point symmetry techniques to time dependent nonlinear reaction-diffusion equations with source term that arise in modelling microwave heating. In particular, we obtained invariant solutions for the case were the source term decreases spatially and increases with temperature.