Stanford Shateyi

The Effects of Thermal Radiation, Hall Currents, Soret, and Dufour on MHD Flow by Mixed Convection over a Vertical Surface in Porous Media

The study sought to investigate the influence of a magnetic field on heat and mass transfer by mixed convection from vertical surfaces in the presence of Hall, radiation, Soret (thermal-diffusion), and Dufour (diffusion-thermo) effects. The similarity solutions were obtained using suitable transformations. The similarity ordinary differential equations were then solved by MATLAB routine bvp4c. The numerical results for some special cases were compared with the exact solution and those obtained by Elgazery (2009) and were found to be in good agreement. A parametric study illustrating the influence of the magnetic strength, Hall current, Dufour, and Soret, Eckert number, thermal radiation, and permeability parameter on the velocity, temperature, and concentration was investigated.

Thermal Radiation and Buoyancy Effects on Heat and Mass Transfer over a Semi-Infinite Stretching Surface with Suction and Blowing

This study sought to investigate thermal radiation and buoyancy effects on heat and mass transfer over a semi-infinite stretching surface with suction and blowing. Appropriate transformations were employed to transform the governing differential equations to nonsimilar form. The transformed equations were solved numerically by an efficient implicit, iterative finite-difference scheme. A parametric study illustrating the influence of wall suction or injection, radiation, Schmidt number and Grashof number on the fluid velocity, temperature and concentration is conducted. We conclude from the study that the flow is appreciably influenced by thermal radiation, Schmidt number, as well as fluid injection or suction.

Thermal Radiation Effects on Heat and Mass Transfer over an Unsteady Stretching Surface

The unsteady heat, mass, and fluid transfer over a horizontal stretching sheet has been numerically investigated. Using a similarity transformation the governing time-dependent boundary layer equations for the momentum, heat, and mass transfer were reduced to a sets of ordinary differential equations. These set of ordinary differential equations were then solved using the Chebyshev pseudo-spectral collocation method, and a parametric analysis was carried out. The study observed, among other observations that the local Sherwood number increases as the values of the stretching parameter 𝐴 and the Schmidt number 𝑆𝑐 increase. Also the fluid temperature was found to be significantly reduced by increases in the values of the Prandtl number 𝑃𝑟, the unsteadiness parameter 𝐴, and the radiation parameter 𝑅. The velocity and concentration profiles were found to be reduced by increasing values of the unsteadiness parameter 𝐴.

Variable Viscosity on Magnetohydrodynamic Fluid Flow and Heat Transfer over an Unsteady Stretching Surface with Hall Effect

The problem of magnetohydrodynamic flow and heat transfer of a viscous, incompressible, and electrically conducting fluid past a semi-infinite unsteady stretching sheet is analyzed numerically. The problem was studied under the effects of Hall currents, variable viscosity, and variable thermal diffusivity. Using a similarity transformation, the governing fundamental equations are approximated by a system of nonlinear ordinary differential equations. The resultant system of ordinary differential equations is then solved numerically by the successive linearization method together with the Chebyshev pseudospectral method. Details of the velocity and temperature fields as well as the local skin friction and the local Nusselt number for various values of the parameters of the problem are presented. It is noted that the axial velocity decreases with increasing the values of the unsteadiness parameter, variable viscosity parameter, or the Hartmann number, while the transverse velocity increases as the Hartmann number increases. Due to increases in thermal diffusivity parameter, temperature is found to increase.

Hydromagnetic Stagnation-Point Flow towards a Radially Stretching Convectively Heated Disk

The steady stagnation-point flow and heat transfer of an electrically conducted incompressible viscous fluid are extended to the case where the disk surface is convectively heated and radially stretching. The fluid is subjected to an external uniform magnetic field perpendicular to the plane of the disk. The governing momentum and energy balance equations give rise to nonlinear boundary value problem. Using a spectral relaxation method with a Chebyshev spectral collocation method, the numerical solutions are obtained over the entire range of the physical parameters. Emphasis has been laid to study the effects of viscous dissipation and Joule heating on the thermal boundary layer. Pertinent results on the effects of various thermophysical parameters on the velocity and temperature fields as well as local skin friction and local Nusselt number are discussed in detail and shown graphically and/or in tabular form.

On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations

We consider a system of nonlinear equations . A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.

A new numerical approach to MHD flow of a Maxwell fluid past a vertical stretching sheet in the presence of thermophoresis and chemical reaction

In this study we consider steady MHD flow of a Maxwell fluid past a vertical stretching sheet in a Darcian porous medium. The motion of the fluid is caused by the stretched sheet. The governing boundary layer equations for momentum, thermal energy and concentration are reduced using a similarity transformation to a set of coupled ordinary differential equations. The similarity ordinary differential equations are then solved numerically by a recently developed spectral relaxation method together with the Chebyshev pseudo-spectral collocation method. Effects of the physical parameters on the velocity, temperature and concentration profiles as well as the local skin friction coefficient and the heat and mass transfer rates are depicted graphically and/or in tabular form.MSC: 65Pxx, 76-XX.

Magnetohydrodynamic Flow Past a Vertical Plate With Radiative Heat Transfer

The problem of steady, laminar, magnetohydrodynamic flow past a semi-infinite vertical plate is studied. The primary purpose of this study was to characterize the effects of thermal radiative heat transfer, magnetic field strength, and Hall currents on the flow properties. The governing nonlinear coupled differential equations comprising the laws of mass, linear momentum, and energy modified to include magnetic and radiative effects were solved numerically. The effects of the Hall current, the Hartmann number, and the radiative parameter on the velocity and temperature profiles are presented graphically. Large Hall currents and radiation effects cause the fluid to heat up and the velocity to increase in the lateral direction but decrease in the tangential direction. This study showed inter alia that reducing Hall currents and increasing the strength of the magnetic field lead to a reduction in the temperature and, consequently, in the thermal boundary layer, and so confirming that heat transfer mitigation through magnetic control is possible.

A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain

This paper contributes a new matrix method for the solution of high-order linear complex differential equations with variable coefficients in rectangular domains under the considered initial conditions. On the basis of the presented approach, the matrix forms of the Bernoulli polynomials and their derivatives are constructed, and then by substituting the collocation points into the matrix forms, the fundamental matrix equation is formed. This matrix equation corresponds to a system of linear algebraic equations. By solving this system, the unknown Bernoulli coefficients are determined and thus the approximate solutions are obtained. Also, an error analysis based on the use of the Bernoulli polynomials is provided under several mild conditions. To illustrate the efficiency of our method, some numerical examples are given.

Basins of Attraction for Various Steffensen-Type Methods

The dynamical behavior of different Steffensen-type methods is analyzed. We check the chaotic behaviors alongside the convergence radii (understood as the wideness of the basin of attraction) needed by Steffensen-type methods, that is, derivative-free iteration functions, to converge to a root and compare the results using different numerical tests. We will conclude that the convergence radii (and the stability) of Steffensen-type methods are improved by increasing the convergence order. The computer programming package MATHEMATICA provides a powerful but easy environment for all aspects of numerics. This paper puts on show one of the application of this computer algebra system in finding fixed points of iteration functions.