N. Bachok

Publications

3 Zero-Dissipative Explicit Runge-Kutta Method for Periodic Initial Value Problems

Authors: N. Bachok, N. Senu, F. Ismail, I. A. Kasim

Abstract:

In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge- Kutta methods

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2 Flow and Heat Transfer of a Nanofluid over a Shrinking Sheet

Authors: N. Bachok, N. L. Aleng, N. M. Arifin, A. Ishak, N. Senu

Abstract:

The problem of laminar fluid flow which results from the shrinking of a permeable surface in a nanofluid has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented which depends on the mass suction parameter S, Prandtl number Pr, Lewis number Le, Brownian motion number Nb and thermophoresis number Nt. It was found that the reduced Nusselt number is decreasing function of each dimensionless number.

Keywords: Nanofluid, boundary layer, shrinking sheet, thermophoresis, similarity solution, Brownian motion

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1 Effect of Magnetic Field on Mixed Convection Boundary Layer Flow over an Exponentially Shrinking Vertical Sheet with Suction

Authors: N. Bachok, N. M. Arifin, F. M. Ali, R. Nazar, I. Pop, S. S. P. M. Isa

Abstract:

A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and tables for several sets of values of the parameters. The effects of the governing parameters on the flow and heat transfer characteristics are thoroughly examined.

Keywords: Magnetic Field, mixed convection, exponentially shrinking sheet, suction

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Abstracts

4 Zero-Dissipative Explicit Runge-Kutta Method for Periodic Initial Value Problems

Authors: N. Bachok, N. Senu, F. Ismail, I. A. Kasim

Abstract:

In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: Runge-Kutta methods, dissipation, oscillatory solutions, phase-lag

Procedia PDF Downloads 264
3 Effect of Magnetic Field on Mixed Convection Boundary Layer Flow over an Exponentially Shrinking Vertical Sheet with Suction

Authors: N. Bachok, N. M. Arifin, F. M. Ali, R. Nazar, I. Pop, S. S. P. M. Isa

Abstract:

A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and tables for several sets of values of the parameters. The effects of the governing parameters on the flow and heat transfer characteristics are thoroughly examined.

Keywords: Magnetic Field, mixed convection, exponentially shrinking sheet, suction

Procedia PDF Downloads 187
2 Flow and Heat Transfer of a Nanofluid over a Shrinking Sheet

Authors: N. Bachok, N. L. Aleng, N. M. Arifin, A. Ishak, N. Senu

Abstract:

The problem of laminar fluid flow which results from the shrinking of a permeable surface in a nanofluid has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented which depends on the mass suction parameter S, Prandtl number Pr, Lewis number Le, Brownian motion number Nb and thermophoresis number Nt. It was found that the reduced Nusselt number is decreasing function of each dimensionless number.

Keywords: Nanofluid, boundary layer, shrinking sheet, thermophoresis, similarity solution, Brownian motion

Procedia PDF Downloads 249
1 Forced Convection Boundary Layer Flow of a Casson Fluid over a Moving Permeable Flat Plate beneath a Uniform Free Stream

Authors: N. Bachok, N. M. Arifin, F. M. Ali, R. Nazar, I. Pop, S. P. M. Isa

Abstract:

In this paper, the steady forced convection boundary layer flow of a Casson fluid past a moving permeable semi-infinite flat plate beneath a uniform free stream is investigated. The mathematical problem reduces to a pair of noncoupled ordinary differential equations by similarity transformation, which is then solved numerically using the shooting method. Both the cases when the plate moves into or out of the origin are considered. Effects of the non-Newtonian (Casson) parameter, moving parameter, suction or injection parameter and Eckert number on the flow and heat transfer characteristics are thoroughly examined. Dual solutions are found to exist for each value of the governing parameters.

Keywords: forced convection, boundary layer, Casson fluids, moving flat plate

Procedia PDF Downloads 307