Khairy Zaimi

Boundary layer flow and heat transfer over a nonlinearly permeable stretching/shrinking sheet in a nanofluid

The steady boundary layer flow and heat transfer of a nanofluid past a nonlinearly permeable stretching/shrinking sheet is numerically studied. The governing partial differential equations are reduced into a system of ordinary differential equations using a similarity transformation, which are then solved numerically using a shooting method. The local Nusselt number and the local Sherwood number and some samples of velocity, temperature and nanoparticle concentration profiles are graphically presented and discussed. Effects of the suction parameter, thermophoresis parameter, Brownian motion parameter and the stretching/shrinking parameter on the flow, concentration and heat transfer characteristics are thoroughly investigated. Dual solutions are found to exist in a certain range of the stretching/shrinking parameter for both shrinking and stretching cases. Results indicate that suction widens the range of the stretching/shrinking parameter for which the solution exists.

Flow Past a Permeable Stretching/Shrinking Sheet in a Nanofluid Using Two-Phase Model

The steady two-dimensional flow and heat transfer over a stretching/shrinking sheet in a nanofluid is investigated using Buongiorno’s nanofluid model. Different from the previously published papers, in the present study we consider the case when the nanofluid particle fraction on the boundary is passively rather than actively controlled, which make the model more physically realistic. The governing partial differential equations are transformed into nonlinear ordinary differential equations by a similarity transformation, before being solved numerically by a shooting method. The effects of some governing parameters on the fluid flow and heat transfer characteristics are graphically presented and discussed. Dual solutions are found to exist in a certain range of the suction and stretching/shrinking parameters. Results also indicate that both the skin friction coefficient and the local Nusselt number increase with increasing values of the suction parameter.

Stagnation-Point Flow Toward a Stretching/Shrinking Sheet in a Nanofluid Containing Both Nanoparticles and Gyrotactic Microorganisms

The stagnation-point flow and heat transfer toward a stretching/shrinking sheet in a nanofluid containing gyrotactic microorganisms with suction are investigated. Using a similarity transformation, the nonlinear system of partial differential equations is converted into nonlinear ordinary differential equations. These resulting equations are solved numerically using a shooting method. The skin friction coefficient, local Nusselt number, local Sherwood number, and the local density of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and the density of motile microorganisms profiles are analyzed subject to several parameters of interest, namely suction parameter, thermophoresis parameter, Brownian motion parameter, Lewis number, Schmidt number, bioconvection Peclet number, and the stretching/shrinking parameter. It is found that dual solutions exist for a certain range of the stretching/shrinking parameter for both shrinking and stretching cases. The results indicate that the skin friction coefficient, local Nusselt number, local Sherwood number, and the local density of the motile microorganisms increase with suction effect. It is also observed that suction widens the range of the stretching/shrinking parameter for which the solution exists.

Boundary Layer Flow and Heat Transfer past a Permeable Shrinking Sheet in a Nanofluid with Radiation Effect

The steady two-dimensional boundary layer flow of a nanofluid over a shrinking sheet with thermal radiation and suction effects is studied. The resulting system of ordinary differential equations is solved numerically using a shooting method for three different types of nanoparticles, namely, copper (Cu), alumina (Al2O3), and titania (TiO2). The results obtained for the velocity and temperature profiles as well as the skin friction coefficient and the local Nusselt number for some values of the governing parameters, namely, the nanoparticle volume fraction, shrinking, suction, and viscous dissipation parameters, are discussed. The numerical results show that dual solutions exist in a certain range of suction parameter.

Stagnation-Point Flow and Heat Transfer over a Nonlinearly Stretching/Shrinking Sheet in a Micropolar Fluid

This paper considers the problem of a steady two-dimensional stagnation-point flow and heat transfer of an incompressible micropolar fluid over a nonlinearly stretching/shrinking sheet. A similarity transformation is employed to convert the partial differential equations into nonlinear ordinary ones which are then solved numerically using a shooting method. Numerical results obtained are presented graphically, showing the effects of the micropolar or material parameter and the stretching/shrinking parameter on the flow field and heat transfer characteristics. The dual solutions are found to exist in a limited range of the stretching/shrinking parameter for the shrinking case, while unique solutions are possible for all positive values of the stretching/shrinking parameter (stretching case). It is also observed that the skin friction coefficient and the magnitude of the local Nusselt number increase as the material parameter increases.

Flow and heat transfer over a shrinking sheet in a nanofluid with suction at the boundary

The suction effect on two-dimensional boundary layer flow of a nanofluid over a shrinking sheet for three different types of nanoparticles, namely, copper (Cu), titanium oxide (TiO2), and alumina (Al2O3) is studied. Using an appropriate similarity transformation, the nonlinear system of partial differential equations is first transformed into nonlinear ordinary differential equations which are then solved numerically using a shooting method. The effects of the parameters involved namely the suction and shrinking parameters on the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented graphically and discussed. The numerical results indicate that dual solutions exist for a certain range of the suction parameter.

Unsteady viscous flow and heat transfer due to a permeable stretching/shrinking cylinder

An analysis is carried out to investigate the unsteady viscous flow and heat transfer due to a permeable stretching/shrinking cylinder. The unsteady Navier-Stokes equations are first transformed to nonlinear ordinary differential equations using a similarity transformation, before being solved numerically by a shooting method. The effects of the parameters involved namely the suction parameter, the stretching/shrinking parameter and the unsteadiness parameter on the velocity and temperature fields are analyzed and presented graphically. The numerical results indicate that dual solutions exist for a certain range of the stretching/shrinking parameter. The surface shear stress and the surface heat flux increase in the presence of suction at the boundary.