Shirley Abelman

Two-Phase Simulation of Nanofluid Flow and Heat Transfer in an Annulus in the Presence of an Axial Magnetic Field

In this study, the effects of magnetic field on nanofluid flow, heat, and mass transfer between two horizontal coaxial cylinders are studied using a two-phase model. The effect of viscous dissipation is also taken into account. By using the appropriate transformation for the velocity, temperature, and concentration, the basic equations governing the flow, heat, and mass transfer are reduced to a set of ordinary differential equations. These equations subject to the associated boundary conditions are solved numerically using the fourth-order Runge-Kutta method. The effects of Hartmann number, Reynolds number, Schmidt number, Brownian parameter, thermophoresis parameter, Eckert number, and aspect ratio on flow, heat, and mass transfer are examined. Results show that the Nusselt number has a direct relationship with the aspect ratio and Hartmann number but it has a reverse relationship with the Reynolds number, Schmidt number, Brownian parameter, thermophoresis parameter, and Eckert number.

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.

On the Rayleigh problem for a Sisko fluid in a rotating frame

The unsteady rotating flow of a Sisko fluid bounded by a suddenly moved infinite flat plate is investigated. The fluid is electrically conducting in the presence of a transverse applied time-dependent magnetic field. A highly non-linear differential equation resulting from the balance of momentum and mass, coupled with appropriate boundary and initial conditions is solved numerically. The numerical solutions for different values of the parameters are compared and discussed.

Comparison of some recent numerical methods for initial-value problems for stiff ordinary differential equations

We consider the combustion equation as one of the candidates from the class of stiff ordinary differential equations. A solution over a length of time that is inversely proportional to @d>0 (where @d>0 is a small disturbance of the pre-ignition state) is sought. This problem has a transient at the midpoint of the integration interval. The solution changes from being non-stiff to stiff, and afterwards becomes non-stiff again. We provide its asymptotic and numerical solution obtained via a variety of methods. Comparisons are made for the numerical results which we obtain with the MATLAB ode solvers (ode45, ode15s and ode23s) and some nonstandard finite difference methods. Results corresponding to standard finite difference method are also presented. Furthermore, the discussion on these approaches along with the others, provides several open problems for new and young researchers.

A numerical study of the influence of slip boundary condition on rotating flow

A numerical solution is obtained for the steady flow of an electrically conducting non-Newtonian incompressible fluid past a plate. The flow is analysed under condition where the no-slip assumption between the plate and the fluid is no longer valid. The fluid under consideration obeys the rheological equations of state due to a third-grade fluid. The fluid is conducting in the presence of a uniform magnetic field under a small magnetic Reynolds number. The solution of the nonlinear equations of motion is obtained using MATLAB®. The effects of the slip, third-grade parameter and magnetic field on the velocity distribution are presented graphically and discussed.

Stability, bifurcation and chaos analysis of vector-borne disease model with application to Rift Valley fever.

This paper investigates a RVF epidemic model by qualitative analysis and numerical simulations. Qualitative analysis have been used to explore the stability dynamics of the equilibrium points while visualization techniques such as bifurcation diagrams, Poincaré maps, maxima return maps and largest Lyapunov exponents are numerically computed to confirm further complexity of these dynamics induced by the seasonal forcing on the mosquitoes oviposition rates. The obtained results show that ordinary differential equation models with external forcing can have rich dynamic behaviour, ranging from bifurcation to strange attractors which may explain the observed fluctuations found in RVF empiric outbreak data, as well as the non deterministic nature of RVF inter-epidemic activities. Furthermore, the coexistence of the endemic equilibrium is subjected to existence of certain number of infected Aedes mosquitoes, suggesting that Aedes have potential to initiate RVF epidemics through transovarial transmission and to sustain low levels of the disease during post epidemic periods. Therefore we argue that locations that may serve as RVF virus reservoirs should be eliminated or kept under control to prevent multi-periodic outbreaks and consequent chains of infections. The epidemiological significance of this study is: (1) low levels of birth rate (in both Aedes and Culex) can trigger unpredictable outbreaks; (2) Aedes mosquitoes are more likely capable of inducing unpredictable behaviour compared to the Culex; (3) higher oviposition rates on mosquitoes do not in general imply manifestation of irregular behaviour on the dynamics of the disease. Finally, our model with external seasonal forcing on vector oviposition rates is able to mimic the linear increase in livestock seroprevalence during inter-epidemic period showing a constant exposure and presence of active transmission foci. This suggests that RVF outbreaks partly build upon RVF inter-epidemic activities. Therefore, active RVF surveillance in livestock is recommended.

MHD Natural Convection with Convective Surface Boundary Condition over a Flat Plate

We apply the one parameter continuous group method to investigate similarity solutions of magnetohydrodynamic (MHD) heat and mass transfer flow of a steady viscous incompressible fluid over a flat plate. By using the one parameter group method, similarity transformations and corresponding similarity representations are presented. A convective boundary condition is applied instead of the usual boundary conditions of constant surface temperature or constant heat flux. In addition it is assumed that viscosity, thermal conductivity, and concentration diffusivity vary linearly. Our study indicates that a similarity solution is possible if the convective heat transfer related to the hot fluid on the lower surface of the plate is directly proportional to where is the distance from the leading edge of the solid surface. Numerical solutions of the ordinary differential equations are obtained by the Keller Box method for different values of the controlling parameters associated with the problem.

A computational algorithm for solving nearly penta-diagonal linear systems

An efficient computational algorithm for solving nearly penta-diagonal linear systems is presented. A problem arising from the spreading of a thin power-law fluid, subject to periodic boundary conditions, illustrates the algorithm.

Double diffusive magnetohydrodynamic (MHD) mixed convective slip flow along a radiating moving vertical flat plate with convective boundary condition.

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables.

Analytical Modeling of MHD Flow over a Permeable Rotating Disk in the Presence of Soret and Dufour Effects: Entropy Analysis

The main concern of the present article is to study steady magnetohydrodynamics (MHD) flow, heat transfer and entropy generation past a permeable rotating disk using a semi numerical/analytical method named Homotopy Analysis Method (HAM). The results of the present study are compared with numerical quadrature solutions employing a shooting technique with excellent correlation in special cases. The entropy generation equation is derived as a function of velocity, temperature and concentration gradients. Effects of flow physical parameters including magnetic interaction parameter, suction parameter, Prandtl number, Schmidt number, Soret and Dufour number on the fluid velocity, temperature and concentration distributions as well as entropy generation number are analysed and discussed in detail. Results show that increasing the Soret number or decreasing the Dufour number tends to decrease the temperature distribution while the concentration distribution is enhanced. The averaged entropy generation number increases with increasing magnetic interaction parameter, suction parameter, Prandtl number, and Schmidt number.