Haliza Rosali

Stokes’ First Problem in Nanofluids

This paper discusses numerically the unsteady flow and heat transfer of a viscous fluid driven by an impulsively started infinite flat plate in a nanofluid. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically by a shooting method. Results are presented graphically and the effects of the Brownian motion parameter Nb and the thermophoresis parameter Nt on the dimensionless heat transfer rate are discussed. It is found that the heat transfer rate is a decreasing function of both Nb and Nt.

Soret and Dufour Effects on Unsteady Boundary Layer Flow and HeatTransfer of Nanofluid Over a Stretching/Shrinking Sheet: A StabilityAnalysis

The effects of Soret and Dufour parameters on the boundary layer flow in nanofluid over stretching/ shrinking with time dependent is studied using Buongiorno model. The system of partial differential equations is transformed to the system of ordinary differential equations by applying similarity transformation. The results are obtained numerically using bvp4c in Matlab. The reduced skin friction coefficient reduced Nusselt number, velocity, temperature and concentration profiles are shown graphically with different values of Soret effect, Dufour effect, mass flux parameter, unsteadiness parameter, thermophoresis as well as Brownian motion parameter where the dual solutions are obtained. The unsteadiness parameter and mass flux parameter expand the range of solution for stretching/ shrinking parameter. Meanwhile, the Soret and Dufour parameters are found to affect the heat transfer rate at the surface. In order to determine the stability of the solutions, stability analysis is performed.

Stagnation-point flow over a stretching/shrinking sheet in a porous medium

An analysis is performed for the stagnation-point flow over a stretching/shrinking sheet in a porous medium. By using similarity variables, the governing system of partial differential equations are reduced to the coupled ordinary differential equations before being solved numerically using a Maple software. Numerical results are obtained for the skin friction coefficient, local Nusselt number, velocity and temperature profiles. Both stretching and shrinking sheets are considered. The influence of the governing parameters on the fluid flow and heat transfer characteristics are analyzed and discussed. Dual solutions are found to exist for the shrinking case, while only unique solutions are found for the stretching case.

Unsteady boundary layer flow of nanofluid over a moving surface with partial slip

This study discussed on the unsteady boundary layer over a moving surface with partial slip in nanofluid using Buongiorno’s model. The system of partial differential equations is transformed to ordinary differential equations using similarity transformation and has been solved by bvp4c in Matlab to obtain the numerical solutions. The numerical solutions are obtained for skin friction coefficient, local Nusselt number as well as local Sherwood number for various moving parameter for different slip parameter. The velocity, temperature and nanoparticle volume fraction profiles are presented in order to support the findings. The results revealed that increasing slip parameter increases the shear stress, heat and mass transfer at the surface.This study discussed on the unsteady boundary layer over a moving surface with partial slip in nanofluid using Buongiorno’s model. The system of partial differential equations is transformed to ordinary differential equations using similarity transformation and has been solved by bvp4c in Matlab to obtain the numerical solutions. The numerical solutions are obtained for skin friction coefficient, local Nusselt number as well as local Sherwood number for various moving parameter for different slip parameter. The velocity, temperature and nanoparticle volume fraction profiles are presented in order to support the findings. The results revealed that increasing slip parameter increases the shear stress, heat and mass transfer at the surface.

Unsteady boundary layer rotating flow and heat transfer in a copper-water nanofluid over a shrinking sheet

The study of unsteady three-dimensional boundary layer rotating flow with heat transfer in Copper-water nanofluid over a shrinking sheet is discussed. The governing equations in terms of partial differential equations are transformed to ordinary differential equations by introducing the appropriate similarity variables which are then solved numerically by a shooting method with Maple software. The numerical results of velocity gradient in x and y directions, skin friction coefficient and local Nusselt number as well as dual velocity and temperature profiles are shown graphically. The study revealed that dual solutions exist in certain range of s > 0.

Stagnation-point flow towards a vertical plate embedded in a porous medium

The steady stagnation-point flow towards a heated vertical surface embedded in a porous medium is investigated. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations using a similarity transformation. The shooting method is used to solve the similarity equations for different values of the mixed convection parameter. The features of the flow and heat transfer characteristics are analyzed and discussed. It is found that dual solutions exist for both assisting and opposing flows. The skin friction coefficient and the local Nusselt number increase as the mixed convection parameter increases.

On competition between modes of the onset of Marangoni convection with free-slip bottom under magnetic field

In this paper we use a numerical technique to analyze the onset of Marangoni convection in a horizontal layer of electrically-conducting fluid heated from below and cooled from above in the presence of a uniform vertical magnetic field. The top surface of a fluid is deformably free and the bottom boundary are rigid and free-slip. The critical values of the Marangoni numbers for the onset of Marangoni convection are calculated and the latter is found to be critically dependent on the Hartmann, Crispation and Bond numbers. In particular we present an example of a situation in which there is competition between modes at the onset of convection.