Buoyancy Effects on Thermal Boundary Layer Over a Vertical Plate With a Convective Surface Boundary Condition

This study aims to analyze the effects of thermal buoyancy on the laminar boundary layer about a vertical plate in a uniform stream of fluid under a convective surface boundary condition. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by applying shooting iteration technique together with fourth-order Runge–Kutta integration scheme. The variations in dimensionless surface temperature and fluid-solid interface characteristics for different values of Prandtl number (Pr), local Grashof number Grx, and local convective heat transfer parameter Bix are graphed and tabulated. A comparison with previously published results on special case of the problem shows excellent agreement

MHD transient flows and heat transfer of dusty fluid in a channel with variable physical properties and Navier slip condition

AbstractIn this paper, we study the unsteady flow and heat transfer of a dusty fluid between two parallel plates with variable viscosity and electric conductivity. The fluid is driven by a constant pressure gradient and an external uniform magnetic field is applied perpendicular to the plates with a Navier slip boundary condition. The governing non-linear partial differential equations are solved numerically using a semi-implicit finite difference scheme. The effect of the wall slip parameter, viscosity and electric conductivity variation and the uniform magnetic field on the velocity and temperature fields for both the fluid and dust particles is discussed

Transmission dynamics of HIV/AIDS with screening and non-linear incidence

This paper examines the transmission dynamics of HIV/AIDS with screening using non-linear incidence. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium is not stable due existence of forward bifurcation at threshold parameter equal to unity. However numerical results suggest that screening of unaware infectives has the effect of reducing the transmission dynamics of HIV/AIDS. Also, the effect of non-linear incidence parameters showed that transmission dynamics of HIV/AIDS will be lowered when infectives after becoming aware of their infection, do not take part in sexual interaction or use preventive measures to prevent the spreading of the infection. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the transmission dynamics of HIV/AIDS with screening using non-linear incidence.Keywords: HIV/AIDS, Screening, Non-linear incidence, Reproduction number, Stabilit

Unsteady flow of a reactive variable viscosity non-Newtonian fluid through a porous saturated medium with asymmetric convective boundary conditions

AbstractThis article examines the thermal effects in an unsteady flow of a pressure driven, reactive, variable viscosity, third-grade fluid through a porous saturated medium with asymmetrical convective boundary conditions. We assume that exothermic chemical reactions take place within the flow system and that the asymmetric convective heat exchange with the ambient at the surfaces follow Newton’s law of cooling. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using a semi-implicit finite difference scheme. Graphical results are presented and discussed qualitatively and quantitatively with respect to various parameters embedded in the problem

Blood perfusion flow of an electro-kinetic fluid through a porous medium with viscous dissipation

Paper presented at the 4th Strathmore International Mathematics Conference (SIMC 2017), 19 - 23 June 2017, Strathmore University, Nairobi, Kenya.In this work, we considered a mathematical model of an electro-kinetic fluid flow through a porous medium with blood perfusion and viscous dissipation. The fluid is assumed to poses temperature-dependent variable viscosity and thermal conductivity. The nonlinear governing partial differential equations were obtained and solved numerically using Garlekin weighted residue method coupled with fourth order Runge-Kutta technique. The results obtained were presented graphically and discussed

Laminar flow in channels and tubes of varying cross-section (an exploitation of perturbation theory)

SIGLEAvailable from British Library Document Supply Centre-DSC:DX199060 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Fluid dynamics of parallel plates Viscometer: A case study of methods of series summation

The fluid dynamics of parallel plates viscometer is investigated mathematically using both the Navier-Stokes and continuity equations for an incompressible viscous fluid. The problem admits similarity solutions, thereby reducing the unsteady Navier-Stokes equations to a parameter dependent fourth order nonlinear ordinary differential equation. Analytical solutions are constructed for the problem using perturbation technique together with a special type of Hermite-Padé approximants. Mathematics Subject Classification (2000): 76E25. Key words: Squeezing flow, perturbation theory, Hermoite-Padé approximants. Quaestiones Mathematicae 26(2003), 405–41

Laminar flow in channels and tubes of varying cross-sections (an exploration of perturbation theory)

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN007771 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Entropy-generation analysis for variable-viscosity channel flow with non-uniform wall temperature

This paper is an analytical study of inherent irreversibility in the flow of a variable-viscosity fluid through a channel with a non-uniform wall temperature. It is assumed that the channel is narrow and the fluid viscosity varies linearly with temperature. Analytical expressions for fluid velocity and temperature are derived and employed to obtain expressions for volumetric entropy-generation numbers, irreversibility distribution ratio and the Bejan number in the flow field.Channel flow Variable-viscosity Non-uniform wall temperature Irreversibility analysis

A new derivative-free method for solving nonlinear equations

This paper presents a new method for solving nonlinear equations. The method is free of derivatives and easy to implement. Although its convergence is linear, numerical experiments conducted indicate that its performance compares well not only with Newton-based methods of higher order but with other derivative-free methods as well