Norihan Md. Arifin

Stagnation-point flow past a shrinking sheet in a nanofluid

In this paper, the stagnation-point flow and heat transfer towards a shrinking sheet in a nanofluid is considered. The nonlinear system of coupled partial differential equations was transformed and reduced to a nonlinear system of coupled ordinary differential equations, which was solved numerically using the shooting method. Numerical results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ, the shrinking parameter λand the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It was found that nanoparticles of low thermal conductivity, TiO2, have better enhancement on heat transfer compared to nanoparticles Al2O3 and Cu. For a particular nanoparticle, increasing the volume fraction φ results in an increase of the skin friction coefficient and the heat transfer rate at the surface. It is also found that solutions do not exist for larger shrinking rates and dual solutions exist when λ < −1.0.

Dual solutions in magnetohydrodynamic mixed convection flow near a stagnation-point on a vertical surface

The steady magnetohydrodynamic (MHD) mixed convection stagnation-point flow toward a vertical heated surface is investigated in this study. The external velocity impinges normal to the vertical surface and the surface temperature are assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions also exist for the assisting flow, besides that usually reported in the literature for the opposing flow.

MHD Mixed Convection Boundary Layer Flow Toward a Stagnation Point on a Vertical Surface With Induced Magnetic Field

In this paper, the steady magnetohydrodynamic (MHD) mixed convection stagnation point flow of an incompressible, viscous, and electrically conducting fluid over a vertical flat plate is investigated. The effect of induced magnetic field is taken into account. Numerical results are obtained using an implicit finite-difference scheme. Both assisting and opposing flows are considered. The results for skin friction, heat transfer, and induced magnetic field coefficients are obtained and discussed for various parameters. The velocity, temperature, and induced magnetic field profiles are also presented. For the case of the opposing flow, it is found that dual solutions exist for a certain range of the buoyancy parameter. Dual solutions are also obtained for the assisting flow.

Stagnation Point Flow and Mass Transfer with Chemical Reaction past a Stretching/Shrinking Cylinder

This paper is about the stagnation point flow and mass transfer with chemical reaction past a stretching/shrinking cylinder. The governing partial differential equations in cylindrical form are transformed into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically using a shooting method. Results for the skin friction coefficient, Schmidt number, velocity profiles as well as concentration profiles are presented for different values of the governing parameters. Effects of the curvature parameter, stretching/shrinking parameter and Schmidt number on the flow and mass transfer characteristics are examined. The study indicates that dual solutions exist for the shrinking cylinder but for the stretching cylinder, the solution is unique. It is observed that the surface shear stress and the mass transfer rate at the surface increase as the curvature parameter increases.

Dual solutions in MHD flow on a nonlinear porous shrinking sheet in a viscous fluid

In this paper, the problem of magnetohydrodynamic (MHD) flow of a viscous fluid on a nonlinear porous shrinking sheet is studied. The boundary layer partial differential equations are first transformed into an ordinary differential equation, which is then solved numerically by the shooting method. The features of the flow for various governing parameters are presented and discussed in detail. It is found that dual solutions only exist for positive values of the controlling parameter.MSC: 34B15, 76D10.

Mixed Convection Boundary Layer Flow Embedded in a Thermally Stratified Porous Medium Saturated by a Nanofluid

We present the numerical investigation of the steady mixed convection boundary layer flow over a vertical surface embedded in a thermally stratified porous medium saturated by a nanofluid. The governing partial differential equations are reduced to the ordinary differential equations, using the similarity transformations. The similarity equations are solved numerically for three types of metallic or nonmetallic nanoparticles, namely, copper (Cu), alumina (Al2O3), and titania (TiO2), in a water-based fluid to investigate the effect of the solid volume fraction or nanoparticle volume fraction parameter φ of the nanofluid on the flow and heat transfer characteristics. The skin friction coefficient and the velocity and temperature profiles are presented and discussed.

Radiation effect on Marangoni convection boundary layer flow of a nanofluid

PurposeIn this paper, we present a mathematical model for Marangoni convection boundary layer flow with radiation and different types of nanoparticles, namely, Cu, Al2O3, and TiO2 in a water-based fluid.MethodThe governing equations in the form of partial differential equations have been reduced to a set of ordinary differential equations by applying suitable similarity transformations, which is then solved numerically using the shooting method.ResultsNumerical results are obtained for the surface-temperature gradient or the heat transfer rate as well as the temperature profiles for some values of the governing parameters, namely, the nanoparticle volume fraction φ, the constant exponent β, and thermal radiation parameter Nr.ConclusionThe results indicate that the heat transfer rate at the surface decreases as the thermal radiation parameter Nr increases.MSC: 76N20, fluid mechanics.

Feedback Control of the Marangoni–Bénard Instability in a Fluid Layer with a Free-Slip Bottom

Feedback control was applied to the steady Marangoni–Benard convection in a horizontal layer of fluid with a free-slip bottom heated from below and cooled from above. The critical values of the Marangoni numbers for the onset of steady convection are calculated and the latter is found to be critically dependent on the Crispation and Bond numbers. It is shown that the onset of instability can be delayed and the critical Marangoni number can be increased through the use of feedback control.

DUAL SOLUTIONS ON THERMOSOLUTAL MARANGONI FORCED CONVECTION BOUNDARY LAYER WITH SUCTION AND INJECTION

This paper considers the extended problem of the thermosolutal Marangoni forced convection boundary layer by Pop et al. (2001) when the wall is permeable, namely, there is a suction or injection effect. The governing system of partial differential equations is transformed into a system of ordinary differential equations, and the transformed equations are solved numerically using the shooting method. The effects of suction or injection parameter 𝑓0 on the velocity, temperature, and concentration profiles are illustrated and presented in tables and figures. It is shown that dual solutions exist for the similarity parameter 𝛽 less than 0.5.

Uniform Solution on the Combined Effect of Magnetic Field and Internal Heat Generation on Rayleigh–Bénard Convection in Micropolar Fluid

Combined effect of magnetic field and internal heat generation on the onset of Rayleigh― Benard convection in a horizontal micropolar fluid layer is studied. The bounding surfaces of the liquids are considered to be rigid-free, rigid-rigid, and free-free with combination isothermal on the spin-vanishing boundaries. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. The influence of various parameters on the onset of convection has been analyzed. It is shown that the presence of magnetic field always has a stability effect on the Rayleigh―Benard convection in micropolar fluid.