Precious Sibanda

Magnetohydrodynamic Mixed-Convective Flow and Heat and Mass Transfer Past a Vertical Plate in a Porous Medium With Constant Wall Suction

The problem of steady laminar hydromagnetic heat transfer by mixed convection flow over a vertical plate embedded in a uniform porous medium in the presence of a uniform normal magnetic field is studied. Convective heat transfer through porous media has wide applications in engineering problems such as in high temperature heat exchangers and in insulation problems. We construct solutions for the free convection boundary-layer flow equations using an Adomian–Pade approximation method that in the recent past has proven to be an able alternative to the traditional numerical techniques. The effects of the various flow parameters such as the Eckert, Hartmann, and Schmidt numbers on the skin friction coefficient and the concentration, velocity, and temperature profiles are discussed and presented graphically. A comparison of our results with those obtained using traditional numerical methods in earlier studies is made, and the results show an excellent agreement. The results demonstrate the reliability and the efficiency of the Adomian–Pade method in an unbounded domain.

Homogeneous-heterogeneous reactions in micropolar fluid flow from a permeable stretching or shrinking sheet in a porous medium

The effects of a homogeneous-heterogeneous reaction on steady micropolar fluid flow from a permeable stretching or shrinking sheet in a porous medium are numerically investigated in this paper. The model developed by Chaudhary and Merkin (Fluid Dyn. Res. 16:311-333, 1995) for a homogeneous-heterogeneous reaction in boundary layer flow with equal diffusivities for reactant and autocatalysis is used and extended in this study. The uniqueness of this problem lies in the fact that the solutions are possible for all values of the stretching parameter λ>0, while for λ<0 (shrinking surface), solutions are possible only for a limited range of values. The effects of physical and fluid parameters such as the stretching parameter, micropolar parameter, permeability parameter, Schmidt number, strength of homogeneous and heterogeneous reaction parameter on the skin friction, velocity and concentration are analyzed, and these results are presented through graphs. The solute concentration at the surface is found to decrease with the strength of the homogeneous reaction, and to increase with heterogeneous reactions, the permeability parameter and stretching or shrinking parameters. The velocity at the surface was found to increase with the micropolar parameter.

Convection from an inverted cone in a porous medium with cross-diffusion effects

In this study convection from an inverted cone in a porous medium with cross-diffusion is studied numerically. Diffusion-thermo and thermo-diffusion effects are assumed to be significant. The governing equations are transformed into nonlinear ordinary differential equations and then solved numerically using a shooting method together with a sixth order Runge-Kutta method. Verification of the accuracy and correctness of the results is achieved by solving the equations using an independent linearisation method. The effects of the Dufour and the Soret parameters are investigated. The results for the skin friction, Nusselt number and the Sherwood number are presented graphically and in tabular form.

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.

A Novel Numerical Technique for Two-Dimensional Laminar Flow between Two Moving Porous Walls

We investigate the steady two-dimensional flow of a viscous incompressible fluid in a rectangular domain that is bounded by two permeable surfaces. The governing fourth-order nonlinear differential equation is solved by applying the spectral-homotopy analysis method and a novel successive linearisation method. Semianalytical results are obtained and the convergence rate of the solution series was compared with numerical approximations and with earlier results where the homotopy analysis and homotopy perturbation methods were used. We show that both the spectral-homotopy analysis method and successive linearisation method are computationally efficient and accurate in finding solutions of nonlinear boundary value problems.

On steady MHD flow and heat transfer past a rotating disk in a porous medium with ohmic heating and viscous dissipation

Purpose – The purpose of this paper is to investigate the hydromagnetic steady flow and heat transfer characteristics of an incompressible viscous electrically conducting fluid past a rotating disk in a porous medium with ohmic heating, Hall current and viscous dissipation are also investigated.Design/methodology/approach – Using appropriate similarity variables and boundary‐layer approximations, the fluid equations for continuity, momentum and energy balance governing the problem are formulated. These equations are solved numerically by using the most effective Newton‐Raphson shooting method along with fourth‐order Runge‐Kutta integration algorithm.Findings – It was found that magnetic field retards the fluid motion due to the opposing Lorentz force generated by the magnetic field. Both the magnetic field and the Eckert number tend to enhance the heat transfer efficiency. The Hall parameter however reduces the heat transfer rate. In terms of the friction coefficient, the magnetic interaction parameter, t...

A Note on the Solution of the Von Kármán Equations Using Series and Chebyshev Spectral Methods

The classical von Kármán equations governing the boundary layer flow induced by a rotating disk are solved using the spectral homotopy analysis method and a novel successive linearisation method. The methods combine nonperturbation techniques with the Chebyshev spectral collocation method, and this study seeks to show the accuracy and reliability of the two methods in finding solutions of nonlinear systems of equations. The rapid convergence of the methods is determined by comparing the current results with numerical results and previous results in the literature.

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.

Effects of chemical reaction on boundary layer flow past a vertical stretching surface in the presence of internal heat generation

Purpose – The purpose of this paper is to investigate the effects of first‐order homogeneous chemical reaction on a two‐dimensional boundary layer flow past a vertical stretching surface in the presence of internal heat generation.Design/methodology/approach – Using the Boussinesq and boundary‐layer approximations, the fluid equations for momentum, energy balance and concentration governing the problem are formulated. The governing partial differential equations are transformed using similarity transformations into a set of coupled ordinary differential equations that are solved numerically using a shooting technique and a sixth‐order Runge‐Kutta scheme.Findings – It was found that for positive values of the buoyancy parameters, the local skin friction and mass transfer coefficients increase with increasing Eckert and Schmidt numbers while the heat transfer coefficient decreases with both Eckert and Schmidt numbers. Both the velocity and temperature profiles increase significantly when the heat generation...

A spectral‐homotopy analysis method for heat transfer flow of a third grade fluid between parallel plates

Purpose – The purpose of this paper is to study the steady laminar flow of a pressure driven third‐grade fluid with heat transfer in a horizontal channel. The study serves two purposes: to correct the inaccurate results presented in Siddiqui et al., where the homotopy perturbation method was used, and to demonstrate the computational efficiency and accuracy of the spectral‐homotopy analysis methods (SHAM and MSHAM) in solving problems that arise in fluid mechanics.Design/methodology/approach – Exact and approximate analytical series solutions of the non‐linear equations that govern the flow of a steady laminar flow of a third grade fluid through a horizontal channel are constructed using the homotopy analysis method and two new modifications of this method. These solutions are compared to the full numerical results. A new method for calculating the optimum value of the embedded auxiliary parameter ∼ is proposed.Findings – The “standard” HAM and the two modifications of the HAM (the SHAM and the MSHAM) lea...