Zuhaila Ismail

Effects of slip and convective conditions on MHD flow of nanofluid over a porous nonlinear stretching/shrinking sheet

Abstract The purpose of this paper is to theoretically investigate the steady two-dimensional electrical magnetohydrodynamic (MHD) nanofluid flow over a stretching/shrinking sheet. The effects of stretching and shrinking parameter, as well as electric and magnetic fields, thermal radiation, viscous and Joule heating in the presence of slip, heat and mass convection boundary conditions at the surface, are imposed and studied. The mathematical model governing the flow has been constructed which are partial differential equations and then rehabilitated for a system of ordinary differential equations involving the momentum, energy and concentration equations via suitable similarity transformations. Though various conjectures have been put forward to explain the concept of boundary layer flow, the current investigation employed implicit finite difference scheme indicates good agreement with those of the previously published investigation in the limiting sense. Numerical results of the dual solutions for the velocity, temperature, and concentration as well as heat transfer are elucidated through graphs and tables. The velocity, thermal and solutal boundary layer thickness in the first solutions is smaller than that of the second solutions, the first solution is more stable compared to the second solution. Temperature and nanoparticle concentration fields are augmented by the heat and mass convective boundary conditions.

Thermal stratification effects on MHD radiative flow of nanofluid over nonlinear stretching sheet with variable thickness

The combined effects of thermal stratification, applied electric and magnetic fields, thermal radiation, viscous dissipation and Joules heating are numerically studied on a boundary layer flow of electrical conducting nanofluid over a nonlinearly stretching sheet with variable thickness. The governing equations which are partial differential equations are converted to a couple of ordinary differential equations with suitable similarity transformation techniques and are solved using implicit finite difference scheme. The electrical conducting nanofluid particle fraction on the boundary is passively rather than actively controlled. The effects of the emerging parameters on the electrical conducting nanofluid velocity, temperature, and nanoparticles concentration volume fraction with skin friction, heat transfer characteristics are examined with the aids of graphs and tabular form. It is observed that the variable thickness enhances the fluid velocity, temperature, and nanoparticle concentration volume fraction. The heat and mass transfer rate at the surface increases with thermal stratification resulting to a reduction in the fluid temperature. Electric field enhances the nanofluid velocity which resolved the sticking effects caused by a magnetic field which suppressed the profiles. Radiative heat transfer and viscous dissipation are sensitive to an increase in the fluid temperature and thicker thermal boundary layer thickness. Comparison with published results is examined and presented.

A fluid mechanical explanation of the spontaneous reattachment of a previously detached Descemet membrane

Descemet membrane detachment (DMD) is a rare but potentially serious surgical complication that arises most often during cataract surgery. A recent study (Couch, S. M. & Baratz, K. H. (2009) Cornea, 28, 1160-1163) cited the case of a patient with DMDs in both eyes, noting that though one detachment was surgically repaired, the other spontaneously reattached and needed no further treatment. A fluid mechanical model of buoyancy-driven aqueous humour flow in the anterior chamber around a DMD is developed to explain this phenomenon. The analytical model is based on the lubrication theory limit of the Navier-Stokes equations. The flow is determined for a fixed geometry and the possible motion of the DMD is then analysed. Numerical calculations are also carried out (using COMSOL© Multiphysics) to confirm the lubrication theory results. The analytical and numerical results both show that, under the correct conditions, either spontaneous reattachment or worsening of the tear may occur. We conclude that it is possible that clinical outcomes for DMDs may be controlled by adjusting the temperature difference across the eye and/or the orientation of the patient.

Numerical Computational of Fluid Flow through a Detached Retina

In this paper, a phenomenon of fluid flow through a detached retina is studied. Rhegmatogeneous retinal detachment happens when vitreous humour flow through a detached retina. The exact mechanism of Rhegmatogeneous retinal detachment is complex and remains incomplete. To understand the fluid flow, a paradigm mathematical model is developed and is approximated by the lubrication theory. The numerical results of the velocity profile and pressure distribution are computed by using Finite Element Method. The effects of fluid mechanical on the retinal detachment is discussed and analyzed. Based on the analysis, it is found that the retinal detachment deformation affects the pressure distribution. It is important to comprehend the development of the retinal detachment so that a new treatment method can be developed.

Hydromagnetic slip flow of nanofluid with thermal stratification and convective heating

Abstract A numerical study of combined effects of thermal stratification and convective heating for the two-dimensional unsteady flow of hydromagnetic natural convection of nanofluid with buoyancy effects against permeable stretching sheet in presence of electric field is presented. Viscous dissipation and Ohmic heating, as well as radiative heat transfer, are taken into account in the heat convection field. The impact of the chemical reaction due to zero flux of nanoparticle concentration is adopted. The model associated with Brownian motion and thermophoretic diffusion is controlled with slip flow as well as the convective boundary conditions with effects of thermal stratification are employed. Suitable similarity transformations are utilised to transform the governing equations into a couple of ordinary differential equations. The transformed equations systems are then solved numerically using Keller box method. The effects of the pertinent parameters on dimensionless nanofluid velocity, temperature and concentration as well as the skin friction, and Nusselt number are examined. The numerical data obtained in the present investigation are validated and are in good agreement with the previously published data. The numerical computations reveal that that electric and magnetic fields exhibit opposite’s flow behaviour due to fluid motion and both enhance the fluid temperature field. The consequence of convective heating intensifies the nanofluid temperature for higher values as thermal stratification reduces the profiles and its associate’s thermal boundary layer thickness.

The effect of body acceleration on the generalized power law model of blood flow in a stenosed artery

Unsteady blood flow characterized by the generalized power law model in a stenosed artery subject to external body acceleration is considered numerically using the Marker and Cell finite difference discretization on staggered grid, where the pressure is calculated iteratively using the successive-over-relaxation method. The codes have been developed and the results analysed using Matlab. The focus of discussion is on the effects of body acceleration on the flow characteristics, in particular its effects on the wall pressure, pressure drop and the streamlines as these results have not yet been presented and discussed in previous works.

Aqueous humour dynamics in anterior chamber with the Descemet’s membrane detachment

Descemet membrane detachment (DMD) develops in the human eye once the aqueous humour (AH) enters the Descemet membrane (DM) space through a break and causes the membrane to separate from the stroma (the main layer of the cornea which is responsible in giving the cornea its strength). A mathematical model of AH flow through the DMD has been developed. The mathematical model is set up to analyze the fluid mechanics concerning the progression of DMD. This model is based on the Naiver-Stokes equations that govern the flow of AH in the anterior chamber (AC). Specifically, fluid flow in the AC is described as a flow driven by buoyancy effects due to the existing temperature different between the cornea and the pupil. A thin flap (DMD) which is kept in contact with a dome shape (cornea) is considered in the flow in order to show how the type of the DMD affect the fluid flow behave in the AC. The relevant fluid flow equations have been solved numerically using finite element method with the aiding of COMSOL Multi...

Numerical computational of fluid flow through a sclera buckling

In this paper, the implementation of the finite element analysis on the investigation of a phenomenon of fluid flow through a detached retina with sclera buckling treatment is elaborated. To analyze the fluid flow, a paradigm mathematical model is developed. The velocity profile and pressure distribution are simulated. Based on the analysis, it is found that the scale effects which arises from difference in size of the sclera buckling do affects the velocity profile in the human eye. It is important to comprehend the effect of the sclera buckling on the dynamics of the vitreous humour in order to improve the sclera buckling treatment on curing retinal detachment.

The Deformation of Human Eyeball when Undergoing Scleral Buckling

Scleral buckling is a surgical technique to treat rhegmatogenous retinal detachment (RRD). Vision may be affected by the scleral buckle. Since the buckle is pushed into the sclera towards the detached retina, it may change the shape and the focal length of the eyeball. A paradigm mathematical model of human eyeball is set up to examine how the focal length of the eye is affected under the action of the external force. In particular, this model has been developed using the membrane equations of equilibrium for axisymmetric spherical shells. Using numerical analysis the resulting displacements of the eyeball will be examined. The results of the scleral buckle may prove useful to predict changes in focal length.