Ahmad Izani Md. Ismail

A Fourier Pseudospectral Method for Solving Coupled Viscous Burgers Equations

Abstract The Fourier pseudo-spectral method has been studied for a one- dimensional coupled system of viscous Burgers equations. Two test problems with known exact solutions have been selected for this study. In this paper, the rate of con- vergence in time and error analysis of the solution of the first problem has been studied, while the numerical results of the second problem obtained by the present method are compared to those obtained by using the Chebyshev spectral collocation method. The numerical results show that the proposed method outperforms the conventional one in terms of accuracy and convergence rate.

The application of cubic trigonometric B-spline to the numerical solution of the hyperbolic problems

In this paper, a collocation finite difference scheme based on new cubic trigonometric B-spline is developed and analyzed for the numerical solution of a one-dimensional hyperbolic equation (wave equation) with non-local conservation condition. The usual finite difference scheme is used to discretize the time derivative while a cubic trigonometric B-spline is utilized as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann (Fourier) method. The accuracy of the proposed scheme is tested by using it for several test problems. The numerical results are found to be in good agreement with known exact solutions and with existing schemes in literature.

Radiative Convective Nanofluid Flow Past a Stretching/Shrinking Sheet with Slip Effects

Steady two-dimensional laminar mixed convective boundary-layer slip nanofluid flow in a Darcian porous medium due to a stretching/shrinking sheet is studied theoretically and numerically. A thermal radiative effect is incorporated in the model. The governing transport, partial differential equations, along with the boundary conditions, are transformed into a dimensionless form and then, via a linear group of transformation, a system of coupled similarity differential equations is derived. The transformed equations are solved numerically using the Runge–Kutta–Fehlberg fourth–fifth-order numerical quadrature method from Maple symbolic software. The effects of the controlling parameters (namely, stretching/shrinking, velocity slip, thermal slip, mass slip, Darcy number, radiation conduction, buoyancy ratio parameter, and Lewis number) on the dimensionless velocity, temperature, nanoparticle volume fraction, velocity gradient, temperature gradient, and nanoparticle volume fraction gradient are shown in graphi...

Group Analysis of Free Convection Flow of a Magnetic Nanofluid with Chemical Reaction

A theoretical study of two-dimensional magnetohydrodynamics viscous incompressible free convective boundary layer flow of an electrically conducting, chemically reacting nanofluid from a convectively heated permeable vertical surface is presented. Scaling group of transformations is used in the governing equations and the boundary conditions to determine absolute invariants. A third-order ordinary differential equation which corresponds to momentum conservation and two second-order ordinary differential equations which correspond to energy and nanoparticle volume fraction (species) conservation are derived. Our (group) analysis indicates that, for the similarity solution, the convective heat transfer coefficient and mass transfer velocity are proportional to whilst the reaction rate is proportional to , where is the axial distance from the leading edge of the plate. The effects of the relevant controlling parameters on the dimensionless velocity, temperature, and nanoparticle volume fraction are examined. The accuracy of the technique we have used was tested by performing comparisons with the results of published work and the results were found to be in good agreement. The present computations indicate that the flow is accelerated and temperature enhanced whereas nanoparticle volume fractions are decreased with increasing order of chemical reaction. Furthermore the flow is strongly decelerated, whereas the nanoparticle volume fraction and temperature are enhanced with increasing magnetic field parameter. Increasing convection-conduction parameter increases velocity and temperatures but has a weak influence on nanoparticle volume fraction distribution. The present study demonstrates the thermal enhancement achieved with nanofluids and also magnetic fields and is of relevance to nanomaterials processing.

Scaling Group Transformation for MHD Boundary Layer Slip Flow of a Nanofluid over a Convectively Heated Stretching Sheet with Heat Generation

Steady viscous incompressible MHD laminar boundary layer slip flow of an electrically conducting nanofluid over a convectively heated permeable moving linearly stretching sheet has been investigated numerically. The effects of Brownian motion, thermophoresis, magnetic field, and heat generation/absorption are included in the nanofluid model. The similarity transformations for the governing equations are developed. The effects of the pertinent parameters, Lewis number, magnetic field, Brownian motion, heat generation, thermophoretic, momentum slip and Biot number on the flow field, temperature, skin friction factor, heat transfer rate, and nanoparticle, volume fraction rate are displayed in both graphical and tabular forms. Comparisons of analytical (for special cases) and numerical solutions with the existing results in the literature are made and is found a close agreement, that supports the validity of the present analysis and the accuracy of our numerical computations. Results for the reduced Nusselt and Sherwood numbers are provided in tabular and graphical forms for various values of the flow controlling parameters which govern the momentum, energy, and the nanoparticle volume fraction transport in the MHD boundary layer.

Unsteady forced bioconvection slip flow of a micropolar nanofluid from a stretching/shrinking sheet

The unsteady forced bioconvection boundary layer flow of a viscous incompressible micropolar nanofluid containing microorganisms over a stretching/shrinking sheet is studied numerically. A mathematical model, with the aid of appropriate transformations, is presented. The transformed non-linear ordinary differential equations are solved numerically by the Runge–Kutta–Fehlberg fourth- to fifth-order numerical method. The effect of the governing parameters on the dimensionless velocity, micro-rotation, temperature, nanoparticle volume fraction and microorganism as well as the local skin friction coefficient, the heat transfer rate and microorganisms transfer rate is thoroughly examined. The findings show that the value of skin friction and Nusselt number are decreased and microorganism number is increased as velocity slip, thermal slip and microorganism slip parameter are increased, respectively. Results from this investigation were compared with previous investigations demonstrating very good correlation. The present results are relevant to improving the performance of microbial fuel cells deploying nanofluids.

Optimal Homotopy Asymptotic Method for Flow and Heat Transfer of a Viscoelastic Fluid in an Axisymmetric Channel with a Porous Wall

In this article, an approximate analytical solution of flow and heat transfer for a viscoelastic fluid in an axisymmetric channel with porous wall is presented. The solution is obtained through the use of a powerful method known as Optimal Homotopy Asymptotic Method (OHAM). We obtained the approximate analytical solution for dimensionless velocity and temperature for various parameters. The influence and effect of different parameters on dimensionless velocity, temperature, friction factor, and rate of heat transfer are presented graphically. We also compared our solution with those obtained by other methods and it is found that OHAM solution is better than the other methods considered. This shows that OHAM is reliable for use to solve strongly nonlinear problems in heat transfer phenomena.

Mathematical Modelling of Radiative Hydromagnetic Thermosolutal Nanofluid Convection Slip Flow in Saturated Porous Media

High temperature thermal processing of nanomaterials is an active area of research. Many techniques are being investigated to manipulate properties of nanomaterials for medical implementation. In this paper, we investigate thermal radiation processing of a nanomaterial fluid sheet extruded in porous media. A mathematical model is developed using a Darcy drag force model. Instead of using linear radiative heat flux, the nonlinear radiative heat flux in the Rosseland approximation is taken into account which makes the present study more meaningful and practically useful. Velocity slip and thermal and mass convective boundary conditions are incorporated in the model. The Buongiornio nanofluid model is adopted wherein Brownian motion and thermophoresis effects are present. The boundary layer conservation equations are transformed using appropriate similarity variables and the resulting nonlinear boundary value problem is solved using Maple 14 which uses the Runge-Kutta-Fehlberg fourth fifth order numerical method. Solutions are validated with previous nonmagnetic and nonradiative computations from the literature, demonstrating excellent agreement. The influence of Darcy number, magnetic field parameter, hydrodynamic slip parameter, convection-conduction parameter, convection-diffusion parameter, and conduction-radiation parameter on the dimensionless velocity, temperature, and nanoparticle concentration fields is examined in detail. Interesting patterns of relevance are observed to improve manufacturing of nanofluids.

Well-balanced scheme for shallow water equations with arbitrary topography

We study the one-dimensional shallow water equations with arbitrary topography. We first verify that traditional discretisations of the right-hand side of the equation of the balance of momentum give unsatisfactory results. We then show that the equations can be written in the divergence form for stationary waves. Motivated by the encouraging results for the well-balanced scheme for fluid flows in a nozzle with variable cross-section in Kroner and Thanh (2005), we construct a numerical scheme based on stationary waves. This scheme is constructed so that it maintains equilibrium states. Tests show that our scheme is both stable and fast.

Numerical modeling of tracer transport in a contact tank

Abstract Chlorine is extensively used to disinfect the drinking water supply. However, the inefficient use of chlorine as a disinfectant can result in the formation of chemical compounds which can have adverse health effects. Numerical models are increasingly being used in the design of efficient chlorine contact tanks. In this paper, details are given of the application of a two-dimensional semi-time-centred implicit QUICK scheme to model the transport of a tracer in a scaled physical model of a serpentine chlorine contact disinfection tank. The model is shown to give good agreement with laboratory measurements in the compartments of the tank where the flow is relatively uniform over the depth.