Showing papers by "Oluwole Daniel Makinde published in 2009"

On MHD boundary‐layer flow and mass transfer past a vertical plate in a porous medium with constant heat flux

Abstract: Purpose – The hydromagnetic mixed convection flow of an incompressible viscous electrically conducting fluid and mass transfer over a vertical porous plate with constant heat flux embedded in a porous medium is investigated.Design/methodology/approach – Using the Boussinesq and boundary‐layer approximations, the fluid equations for momentum, energy balance and concentration 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 for positive values of the buoyancy parameters, the skin friction increased with increasing values of both the Eckert number (Ec) and the magnetic field intensity parameter (M) and decreased with increasing values of both the Schmidt number (Sc) and the permeability parameter (K).Practical implications – A very useful source of information for researchers on the subject of hydromagnetic flow in porous media.Originali...

Thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined plane

Abstract: This study is devoted to the investigation of thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined isothermal plane. It is assumed that the reaction is exothermic under Arrhenius kinetics, neglecting the consumption of the material. The governing non-linear equations for conservation of momentum and energy are obtained and solved by using a new computational approach based on a special type of Hermite-Pade approximation technique implemented in MAPLE. This semi-numerical scheme offers some advantages over solutions obtained with traditional methods such as finite differences, spectral method, and shooting method. It reveals the analytical structure of the solution function. Important properties of overall flow structure including velocity field, temperature field, thermal criticality, and bifurcations are discussed.

On the Chebyshev collocation spectral approach to stability of fluid flow in a porous medium

Abstract: In this paper, the temporal development of small disturbances in a pressure-driven fluid flow through a channel filled with a saturated porous medium is investigated. The Brinkman flow model is employed in order to obtain the basic flow velocity distribution. Under normal mode assumption, the linearized governing equations for disturbances yield a fourth-order eigenvalue problem, which reduces to the well-known Orr–Sommerfeld equation in some limiting cases solved numerically by a spectral collocation technique with expansions in Chebyshev polynomials. The critical Reynolds number Rec, the critical wave number αc, and the critical wave speed cc are obtained for a wide range of the porous medium shape factor parameter S. It is found that a decrease in porous medium permeability has a stabilizing effect on the fluid flow. Copyright © 2008 John Wiley & Sons, Ltd.

On Temporal Stability Analysis for Hydromagnetic Flow in a Channel Filled with a Saturated Porous Medium

Abstract: In this paper, a linear stability analysis is presented to trace the time evolution of an infinitesimal, two-dimensional disturbance imposed on the base flow of an electrically conducting fluid in a channel filled with a saturated porous medium under the influence of a transversely imposed magnetic field. An eigenvalue problem is obtained and solved numerically using the Chebyshev collocation spectral method. The critical Reynolds number Re c, the critical wave number α c and the critical wave speed c c are obtained for a wide range of the porous medium shape factor parameter S and Hartmann number H. It is found that an increase in the magnetic field intensity and a decrease in porous medium permeability have a stabilizing effect on the fluid flow.

Hermite-Padé approach to thermal radiation effect on inherent irreversibility in a variable viscosity channel flow

Abstract: This present work examines the effect of thermal radiation on inherent irreversibility in the flow of a variable viscosity optically thin fluid through a channel with isothermal walls. First and Second Laws of thermodynamics are employed in order to analyze the problem. The simplified governing non-linear equations are solved analytically using a perturbation method coupled with a special type of Hermite-Pade semi-analytical technique. Expressions for dimensionless velocity and temperature, thermal criticality conditions and entropy generation number are obtained. Both numerical and graphical results are presented and discussed quantitatively with respect to various parameters embedded in the problem.

On Non-perturbative Approach to Transmission Dynamics of Infectious Diseases with Waning Immunity

Abstract: Abstract In this paper, a mathematical model that describes the dynamics of re-infection under the assumption that the vaccine induced immune protection may wane over time is presented. The qualitative analysis reveals that the disease eradication depends on vaccination coverage as well as on vaccine efficacy. Using an appropriate Lyapunov function, we establish that the disease free equilibrium is globally asymptotically stable if the vaccination coverage level exceeds a certain threshold value. Numerical algorithm based on Adomian decomposition method (ADM) coupled with Fade approximation technique and He's variational iteration method (VIM) are developed and implemented in MAPLE to approximate the solution of the governing non-linear systems. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.

Symmetry reductions and solutions for pollutant diffusion in a cylindrical system

Abstract: This study is devoted to investigating transient coupled fluid flow and mass transfer partial differential equations (PDEs) describing pollutant transport in cylindrical coordinates. Symmetry analysis of the system of coupled PDEs is performed and some large Lie algebras are obtained for some special cases of the arbitrary and special choices of constants, and the source term. Optimal systems are constructed for all the admitted symmetries. We perform reductions for different choices of the source term. In some cases invariant solution is sought, however some cases resulted in coupled systems of highly nonlinear ordinary differential equations (ODEs). Imposing realistic boundary conditions and considering a constant source term, we then use the Adomain decomposition techniques to solve the boundary value problem.

Analysis of Non-Newtonian Reactive Flow in a Cylindrical Pipe

Abstract: In this paper, a mathematical investigation on the effect of convective cooling on a reactive third-grade fluid flowing steadily through a cylindrical pipe is performed. It is assumed that the system exchange heat, with the ambient following Newton’s cooling law and the reaction, is exothermic under Arrhenius kinetics, neglecting the consumption of the material. The simplified governing nonlinear equations of momentum and energy are obtained and solved using a special type of the Hermite–Pade approximation technique. The important properties of the overall flow structure including velocity field, temperature field, bifurcations, and thermal criticality conditions are discussed.

Modelling the long term impact of existing products on perceived value of new products

Abstract: Innovation, continuous improvement, and changes forced by economics factors and marketing conditions are essential elements for bringing new products successfully in the marketplace; however, market competition with the existing products may have along term impact on the perceived value of the new products. Moreover, whether introducing new products/services or upgrades of existing products/services, better profit can be achieved by applying Lean product development technique and evaluating the long term impact of existing products on perceived value of new products will contribute in maintaining the desired profit margin. In this study, a two compartmental deterministic mathematical model for assessing the long term impact of existing products on perceived value of new products is proposed and analysed qualitatively. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.

Modeling Laminar Flow between a Fixed Impermeable Disk and a Porous Rotating Disk

Abstract: We formulate a mathematical model that governs operations of many engineering systems particularly the ceiling fan to explain the fluid flow between the fixed impermeable and the porous rotating disks. The model is based on the continuity and the Navier-Stokes equations which are reduced into a set of coupled ordinary differential equations through transformation by similarity variables. The coupled ordinary differential equations are solved using perturbation techniques and the series solution obtained is improved by Pate’s approximation. Our results meet the supposition that, with laminar flow regime, suction increases with increasing speed of rotation of the rotating porous disk and these are shown on the graphical representations. Key words: Impermeable disk, laminar flow, porous rotating disk, shear stress, Pade approximation.

Pebble bed: reflector treatment and pressure velocity coupling

Abstract: In this report, we describe some models and numerical methods used to simulate the flow and temperature in a pebble bed modular nuclear reactor. The reactor core is filled with around 450000 spheres containing low enriched uranium and helium is forced through these hot pebbles to cool the system down. The group first investigated the flow model in the pebbles. Numerical aspects were then considered to tackle difficulties encountered with the flow simulation and the temperature inside the pebbles. Numerical schemes are presented that can significantly improve the accuracy of the computed results.