Showing papers by "Norihan Md Arifin published in 2016"

Forced convection boundary layer stagnation-point flow in darcy-forchheimer porous medium past a shrinking sheet

Abstract: A mathematical model of forced convection boundary layer stagnation-point slip flow in Darcy-Forchheimer porous medium over a shrinking sheet is presentedin this paper. The governing partial differential equations are transformed into ordinary differential equation using self-similarity transformations which are then solved numerically with shooting method. A parametric study of the physical parameters involved in the problem is conducted and representative set of numerical results are presented through graphs and tables, and are discussed.

Boundary Layer Flow and Heat Transfer over a Permeable Exponentially Stretching/Shrinking Sheet with Generalized Slip Velocity

Abstract: In this paper, the steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is studied. The flow and heat transfer induced by stretching/shrinking sheets are important in the study of extrusion processes and is a subject of considerable interest in the contemporary literature. Appropriate similarity variables are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary (similarity) differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual (upper and lower branch) solutions are found for a certain range of the suction and stretching/shrinking parameters. Stability analysis is performed to determine which solutions are stable and physically realizable and which are not stable. The effects of suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed in detail. It is found that the introduction of the generalized slip boundary condition resulted in the reduction of the local skin friction coefficient and local Nusselt number. Finally, it is concluded from the stability analysis that the first (upper branch) solution is stable while the second (lower branch) solution is not stable.

Unsteady viscous MHD flow over a permeable curved stretching/shrinking sheet

Abstract: Purpose The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a uniform magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically. Design/methodology/approach The transformed system of ordinary differential equations was solved using a fourth-order Runge-Kutta integration scheme. Results for the reduced skin friction coefficient and velocity profiles are presented through graphs and tables for several sets of values of the governing parameters. The effects of these parameters on the flow characteristics are thoroughly examined. Findings Results show that for the both cases of stretching and shrinking surfaces, multiple solutions exist for a certain range of the curvature, mass suction, unsteadiness, stretching/shrinking parameters and magnetic field parameter. Originality/value The paper describes how multiple (dual) solutions for the flow reversals are obtained. It is shown that the solutions exist up to a critical value of the shrinking parameter, beyond which the boundary layer separates from the surface and the solution based upon the boundary layer approximations is not possible.

Synchronization of two different fractional-order chaotic systems with unknown parameters using a robust adaptive nonlinear controller

Abstract: In this paper, a robust adaptive nonlinear feedback controller scheme is proposed to realize the synchronization between two different fractional-order chaotic systems with fully unknown parameters, external disturbance and uncertainties. Bounds of the uncertainties and external disturbance assumed to be unknown. A new theorem is presented to satisfy Lyapunov stability condition in fractional-order systems when their parameters are fully unknown with external disturbance and uncertainties. Numerical simulations are applied using MATLAB software to show the effectiveness of the proposed schemes.

Boundary Layer Flow and Heat Transfer in Nanofluid over a Stretching Sheet using Buongiorno Model and Thermophysical Properties of Nanoliquids

Abstract: The boundary layer flow and heat transfer in nanofluid over a stretching sheet using Buongiorno model and thermophysical properties of nanoliquids is numerically studied. The governing partial differential equations are transformed into nonlinear ordinary differential equations by using the similarity variables and been solved numerically using shooting method for nanoparticles, namely silver Ag, copper Cu, alumina Al 2 O 3 and titania TiO 2 in water as based fluid with Prandtl number Pr = 6.2. The numerical results obtained for the local Nusselt number and the local Sherwood number as well as velocity, temperature and nanoparticle concentration profiles are presented graphically and discussed. The effects of Brownian motion Nb , thermophoresis Nt and nanoparticle volume fraction φ on the flow and heat transfer behaviours are discussed in detail. This study has shown that the stretching sheet is an unique solutions. Otherwise, when the nanoparticle volume fraction parameter increases, Brownian motion and thermophoresis parameters decrease, the local Nusselt number increases, but decreases the local Sherwood number.

Dynamics of Leslie-Gower model with simplified Holling type IV functional response

Abstract: In this paper a three-species of Leslie-Gower predatorprey food chain model with Holling type IV functional response is proposed. The dissipativeness of the solution of the model is discussed. Local and global stability analyses of the system are carried out. The dynamics of the predator-prey food chain model with simplified Holling type IV functional response is investigated theoretically and numerically.

Stability of dual solutions in boundary layer flow and heat transfer on a moving plate in a copper-water nanofluid with slip effect

Abstract: An analysis is performed to study the flow and heat transfer characteristics on a moving plate in a nanofluid. The governing nonlinear differential equations are transformed into a system of nonlinear ordinary equations using a similarity transformation which is then solved numerically using a shooting method. While, for the stability analysis, the unsteady problem has to be introduced by introducing new dimensionless time variable which is then solved numerically using solver bvp4c. The numerical results are presented in tables and graphs for the skin friction coefficient and the local Nusselt number as well as the velocity and the temperature profile for a range of various parameters such as nanoparticles volume fraction, first order slip parameter and velocity ratio parameter. It is observed that the skin friction coefficient and the local Nusselt number which represents the heat transfer rate at the surface are significantly influenced by these parameters. The results indicate that dual solutions (first and second solutions) exist when the plate and free stream move in the opposite direction. A stability analysis has been performed to show which solutions are stable and physically realizable. Based on the analysis, the results indicate that the first solution is linearly stable, while the second solution is linearly unstable.

Boundedness and Stability of Leslie–Gower Model with Sokol–Howell Functional Response

Abstract: In this chapter, a three-species model of Leslie–Gower predator–prey food chain model with Sokol–Howell functional response is proposed. The boundedness of the solution of the model is discussed. Local and global stability analyses of the system are carried out. The dynamics of the predator–prey food chain model with Sokol–Howell functional response is investigated theoretically as well as numerically.

Stagnation-point flow and heat transfer over an exponentially shrinking sheet: A stability analysis

Abstract: Numerical solutions for the stagnation-point flow and heat transfer over an exponentially shrinking sheet have been investigated. The governing boundary layer equations are transformed into an ordinary differential equation using a non-similar transformation. By using the bvp4c solver in MATLAB, the results of the equations can be solved numerically. Numerical results indicate that in certain parameter, the non-unique solutions for the velocity and the temperature do exist. A linear stability analysis shows that only one solution is linearly stable otherwise is unstable. Then, the stability analysis is performed to identify which solution is stable between the two non-unique solutions.

Boundary layer flow and heat transfer on a moving plate in a copper-water nanofluid using Buongiorno model

Abstract: The study of the steady two dimensional boundary layer flow of a copper (Cu)-water nanofluid on a moving plate is investigated. The assumption is the plate moves in the same or opposite direction to the free stream. The nonlinear partial differential equations are transformed into nonlinear ordinary differential equations using a similarity variables,then a shooting technique is used to solved it numerically. The numerical results for skin friction coefficient, the local Nusselt number, the local Sherwood number as well as the velocity, temperature and concentration profiles are obtained. The effect of nanoparticle volume fraction, Brownian motion and thermophoresis parameters on heat transfer are examined. The results show that the local Nusselt number and the local Sherwood number increase with increasing in the Brownian motion parameter Nb and thermophoresis parameter Nt.

Slip effects on MHD non-darcy boundary layer flow over a stretching sheet in a porous medium with radiation and ohmic dissipation

Abstract: In this study, MHD boundary layer slip flow of an incompressible fluid over a stretching sheet in Darcy-Forchheimer porous medium are investigated numerically. Analysis has been carried out in the presence of thermal radiation and ohmic dissipation. Velocity and thermal slips are considered instead of no-slip conditions at the boundary. The governing boundary layer equations along with the boundary conditions are transformed into a dimensionless form by a similarity transformation and the resulting coupled ordinary differential equations are then solved by shooting method. The effects of governing parameters on the flow and thermal fields are examined. The skin friction and wall temperature gradient with effects of slip parameter are reported graphically for various parametric conditions to show interesting aspect of the numerical solution.

Stability analysis in stagnation-point flow towards a shrinking sheet with homogeneous - heterogeneous reactions and suction effects

Abstract: A numerical study is evaluate the problem of stagnation –point flow towards a shrinking sheet with homogeneous –heterogeneous reactions with suction effects. A developed model of homogeneous –heterogeneous reaction in boundary layer flow with similar diffusivities for reactant and auto catalysis was apply in this analysis. A stability analysis has been performed to determine which solution is stable and physically realizable by using the bvp4c solver in Matlab. The effects of the governing parameters on the skin friction coefficient, homogeneous –heterogeneous reactions and the velocity and concentration profiles are presented graphically and thoroughly discussed.

Flow and heat transfer on a moving flat plate in a parallel stream with constant surface heat flux: a stability analysis

Abstract: Numerical solutions for the moving flat plat in a parallel stream with constant heat flux have been studied. The governing equations which are continuity, momentum and energy are convert to an ordinary differential equation using a non-similar transformation. By using shooting method with Maple implementation, the results of the equations can be solved numerically. Numerical results indicate that the velocity ratio parameter λ < 0, the non-unique solutions do exist. Then, the analysis of stability is carried out into two non-unique solutions to determine which is more stable between both of the solution by bvp4c solver in Matlab. From the result of stability analysis, the eigenvalues for the upper branch is positive while the lower branch is negative. Therefore, the first solution is stable than second solution.

MHD Flow of a Nanofluid at the Forward Stagnation Point of an Infinite Permeable Wall with a Convective Boundary Condition

Abstract: The steady magnetohydrodynamic (MHD) flow of a nanofluid at the forward stagnation point of an infinite permeable wall is investigated in this study. A mathematical model has been constructed and the governing partial differential equations are converted into ordinary differential equations by similarity transformation. The similarity equations are solved numerically by a shooting technique. Results for the surface shear stresses, surface heat transfer, and velocity, nanoparticle fraction and temperature profiles are presented in tables and in some graphs. Effects of the magnetic parameter , constant mass flux Biot number , Brownion motion parameter thermophoresis parameter and Lewis number are examined. The present results are compared with previously available numerical results obtained using other methods of solution, and they are found to be in good agreement.