Semi-infinite Vertical Flat Plate Research Articles

Hall and ion slip effects on Unsteady MHD Convective Rotating flow of Nanofluids\u2014Application in Biomedical Engineering

There is an intense worldwide activity in the development of instrumentation for medical diagnosis and bioscreening based on biological labeling and detection of nanoparticles. Based on this profound observation, Hall and ion slip effects on magnetohydrodynamic (MHD) free convective rotating flow of nanofluids in a porous medium past a moving vertical semi-infinite flat plate are investigated. The equations for governing flow are solved analytically by perturbation approximation. The effects of various parameters on the flow are discussed through graphs and tables. The velocity increases with Hall and ion slip parameters. An increase in the convective parameter led to amplify the thermal boundary layer thickness, but when the heat generation parameter is taken into consideration, an opposite effect occurs. The skin friction coefficient increases with an increase in nanoparticle volume fraction and it reduces with increase in Hall and ion slip parameters. Outcomes disclose that the impact of thermal convection of nanoparticles has increased the temperature distribution, which helps in destroying the cancer cells during the drug delivery process.

Chemically reactive species of time-dependent natural convection couple stress fluid flow past an isothermal vertical flat plate

The transient two-dimensional natural convective couple stress fluid flow past a semi-infinite vertical flat plate in the presence of first-order homogenous chemical reaction is investigated. The analysis has been carried out by considering the effects of skin-friction coefficient and Nusselt and Sherwood numbers. The unsteady coupled nonlinear governing flow equations have been solved by applying the Crank–Nicolson implicit finite difference scheme. For the different set physical parameters, graphs are shown and examined. A relevant study with existing results is made in a limiting sense. The transient and steady-state velocity profiles decrease as the chemical reaction parameter, Schmidt number, and couple stress parameter increase. The deviations of concentration, temperature, and velocity contours of the couple stress fluid flow are considerably varied in comparison with the Newtonian fluid flow.

Transient entropy analysis of the magnetohydrodynamics flow of a Jeffrey fluid past an isothermal vertical flat plate

This study presents the analysis of entropy generation concept for unsteady magnetohydrodynamics Jeffrey fluid flow over a semi-infinite vertical flat plate. This physical problem is constituted by transient coupled highly nonlinear equations and is evaluated numerically by using an implicit scheme. The average values of wall shear stress and Nusselt number, entropy generation number and Jeffrey fluid-flow variables are analysed for distinct values of physical parameters at both transient and steady states. The results show that the time needed for achieving a steady state pertaining to the temperature and velocity gets augmented with the increased values of Jeffrey fluid parameter. The results also specify that the entropy generation number increases with the increasing values of Jeffrey fluid parameter, group parameter and Grashof number while the opposite trend is seen for the magnetic parameter.

Two-phase natural convection flow of a dusty fluid

Purpose – The purpose of this paper is to conduct a detailed investigation of the two-dimensional natural convection flow of a dusty fluid. Therefore, the incompressible boundary layer flow of a two-phase particulate suspension is investigated numerically over a semi-infinite vertical flat plate. Comprehensive flow formations of the gas and particle phases are given in the boundary layer region. Primitive variable formulation is employed to convert the nondimensional governing equations into the non-conserved form. Three important two-phase mechanisms are discussed, namely, water-metal mixture, oil-metal mixture and air-metal mixture. Design/methodology/approach – The full coupled nonlinear system of equations is solved using implicit two point finite difference method along the whole length of the plate. Findings – The authors have presented numerical solution of the dusty boundary layer problem. Solutions obtained are depicted through the characteristic quantities, such as, wall shear stress coefficient, wall heat transfer coefficient, velocity distribution and temperature distribution for both phases. Results are interpreted for wide range of Prandtl number Pr (0.005-1,000.0). It is observed that thin boundary layer structures can be formed when mass concentration parameter or Prandtl number (e.g. oil-metal particle mixture) are high. Originality/value – The results of the study may be of some interest to the researchers of the field of chemical engineers.

Mixed convection boundary layer flow past vertical flat plate in nanofluid: case of prescribed wall heat flux

An analysis is carried out to investigate the steady mixed convection boundary layer flow of a water based nanofluid past a vertical semi-infinite flat plate. Using an appropriate similarity transformation, the governing partial differential equations are transformed into the coupled, nonlinear ordinary (similar) differential equations, which are then solved numerically for the Prandtl number Pr = 6.2. The skin friction coefficient, the local Nusselt number, and the velocity and temperature profiles are presented graphically and discussed. Effects of the solid volume fraction ϕ and the mixed convection parameter λ on the fluid flow and heat transfer characteristics are thoroughly examined. Different from an assisting flow, it is found that the solutions for an opposing flow are non-unique. In order to establish which solution branch is stable and physically realizable in practice, a stability analysis is performed.

Unsteady flow of nanofluids past a vertical flat plate with leading edge accretion or ablation

Unsteady flow of a nanofluid past a semi-infinite vertical flat plate is theoretically investigated. Unsteadiness is caused by steady rates of accretion or ablation at leading edge. Two types of nanofluids, namely, Cu-water and Ag-water are considered, with Prandtl number Pr = 6.2. Governing partial differential equations are transformed into ordinary differential equations, using a similarity transformation. The resulting ordinary differential equations are solved numerically. Results are compared with those of regular fluid (ϕ = 0) with Pr = 0.7 and comparison shows good agreement with previous results. Effects of nanoparticle volume fraction on flow and heat transfer characteristics, influence of buoyancy force and unsteady parameter, are presented and discussed in detail. It is found that effects of the volume fraction on skin friction and wall temperature gradient are more significantly influential in Ag-water solution than in Cu-water solution.

Soret effect on mixed convection flow in a nanofluid under convective boundary condition

In this investigation, we intend to present the influence of the prominent Soret effect on mixed convection heat and mass transfer in the boundary layer region of a semi-infinite vertical flat plate in a nanofluid under the convective boundary conditions. The transformed boundary layer ordinary differential equations are solved numerically using the implicit iterative finite difference method. Consideration of the nanofluid and the convective boundary conditions enhanced the number of non-dimensional parameters considerably thereby increasing the complexity of the present problem. A wide range of parameter values is chosen to bring out the effect of Soret parameter on the mixed convection process with the convective boundary condition. The effect of mixed convection, Soret and Biot parameters on the flow, heat and mass transfer coefficients is analyzed. The numerical results obtained for the velocity, temperature, volume fraction, and concentration profiles, as well as the local skin-friction coefficient, local wall temperature, local nanoparticle concentration and local wall concentration reveal interesting phenomenon, some of these qualitative results are presented through plots and tables.

Mixed Convective Heat Transfer Flow of Nanofluid past a Permeable Vertical Flat Plate with Magnetic Effects: A Finite Element Study

Steady, two dimensional mixed convection laminar boundary layer flow of incompressible nanofluid along a permeable vertical semi-infinite flat plate with magnetic field effects has been investigated numerically. The resulting govering equations (obtained from the boussinesq) with associated boundary conditions are solved, using a robust, extensively validated, Galerkin Finite Element Method for different types of spherical shaped metal oxide nanoparticles with two different ratios of the nanolayer thickness to the original particle radius (0.02 or 0.1). The effects of the parameters governing the problems are discussed and shown graphically. The present study is of immediate interest in next-generation solar film collectors, heat exchangers technology, material processing exploiting vertical surfaces and all those processes which are highly affected with heat transfer.

Influence of fluctuating thermal and mass diffusion on unsteady MHD buoyancy-driven convection past a vertical surface with chemical reaction and Soret effects

The influence of thermal radiation and first-order chemical reaction on unsteady MHD convective flow, heat and mass transfer of a viscous incompressible electrically conducting fluid past a semi-infinite vertical flat plate in the presence of transverse magnetic field under oscillatory suction and heat source in slip-flow regime is studied. The dimensionless governing equations for this investigation are formulated and solved analytically using two-term harmonic and non-harmonic functions. Comparisons with previously published work on special cases of the problem are performed and results are found to be in excellent agreement. A parametric study illustrating the effects of various physical parameters on the fluid velocity, temperature and concentration fields as well as skin-friction coefficient, the Nusselt and Sherwood numbers in terms of amplitude and phase is conducted. The numerical results of this parametric study are presented graphically and in tabular form to highlight the physical aspects of the problem.

An integral treatment for combined heat and mass transfer by mixed convection along vertical surface in a saturated porous medium

Combined free and forced convection heat and mass transfer over an impermeable vertical surface embedded in a saturated porous medium is considered. A similarity transformation has been used to study the mixed convection boundary-layer flow over a semi-infinite vertical flat plate. Integral solutions are derived for the coupled nonlinear similarity equations of coupled heat and mass transfer in porous media for the case where the free stream velocity and temperature and concentration near the wall are kept constant. The governing parameters for the problem under consideration are the Lewis number Le, the buoyancy ratio N and mixed convection parameter (). The results for the heat and mass transfer coefficients in terms of Nusselt and Sherwood numbers are represented graphically for the various values of governing parameters of the problem. The heat and mass transfer in the boundary layer region has been analyzed for aiding and opposing flows. Key words: Convection in porous media, heat and mass transfer, integral method, boundary layer.

Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate

In this paper, we discuss similarity reductions for problems of magnetic field effects on free convection flow of a nanofluid past a semi-infinite vertical flat plate. The application of a one-parameter group reduces the number of independent variables by 1, and consequently the governing partial differential equation with the auxiliary conditions to an ordinary differential equation with the appropriate corresponding conditions. The differential equations obtained are solved numerically and the effects of the parameters governing the problem are discussed. Different kinds of nanoparticles were tested.

MHD free convection flow along a vertical flat plate with thermal conductivity and viscosity depending on temperature

In this present work the effects of temperature dependent viscosity and thermal conductivity on the coupling of conduction and Joule heating with MHD free convection flow along a semi-infinite vertical flat plate have been analyzed. The governing boundary layer equations with associated boundary conditions for this phenomenon are transformed to non-dimensional form using the appropriate variables. By the help of the implicit finite difference method with Keller–box scheme, the resulting non-linear system of partial differential equation is then solved numerically. The purpose of this paper is to study the skin friction coefficient, the surface temperature, the velocity and the temperature profiles over the whole boundary layer for different values of the Prandtl number Pr, the magnetic parameter M, the thermal conductivity variation parameter, the viscosity variation parameter and the Joule heating parameter J. The results indicate that the flow pattern, temperature field and rate of heat transfer are significantly dependent on the above mentioned parameters. The local skin friction co-efficient and the surface temperature profiles for different values of viscosity variation parameter are compared with previously published works and are found to be in good agreement.Keywords: Viscosity; thermal conductivity; Joule heating; MHD; conduction; free convection.DOI: 10.3329/jname.v6i2.4994

On the structure of similarity solutions of a differential equation arising from boundary layer problem

We consider an ordinary differential equation f‴−ff″−βf′2=0 with f(0)=a, f′(0)=1, f′(∞):=limt→∞f′(t)=0, where β is a real constant. The given problem may arise from the study of steady free convection flow over a vertical semi-infinite flat plate in a porous medium, or the study of a boundary layer flow over a vertical stretching wall. In this paper, the structure of solutions for the cases of β⩾−2 is studied. Combining the results of [B. Brighi, T. Sari, Blowing-up coordinates for a similarity boundary layer equation, Discrete Contin. Dyn. Syst. 5 (2005) 929–948; J.-S. Guo, J.-C. Tsai, The structure of solution for a third order differential equation in boundary layer theory, Japan J. Indust. Appl. Math. 22 (2005) 311–351; J.-C. Tsai, Similarity solutions for boundary layer flows with prescribed surface temperature, Appl. Math. Lett. 21 (1) (2008) 67–73], we conclude that the given problem may possess at most two types solutions for β∈R. Moreover, multiple solutions are also verified for various pairs of (a,β).

Non-Newtonian Natural Convection Along a Vertical Flat Plate With Uniform Surface Temperature

Natural-convection boundary-layer flow of a non-Newtonian fluid along a heated semi-infinite vertical flat plate with uniform surface temperature has been investigated using a four-parameter modified power-law viscosity model. In this model, there are no physically unrealistic limits of zero or infinite viscosity that are encountered in the boundary-layer formulation for two-parameter Ostwald–de Waele power-law fluids. The leading-edge singularity is removed using a coordinate transformation. The boundary-layer equations are solved by an implicit finite-difference marching technique. Numerical results are presented for the case of a shear-thinning fluid. The results indicate that a similarity solution exists locally in a region near the leading edge of the plate, where the shear rate is not large enough to induce non-Newtonian effects; this similarity solution is identical to the similarity solution for a Newtonian fluid. The size of this region depends on the Prandtl number. Downstream of this region, the solution of the boundary-layer equations is nonsimilar. As the shear rate increases beyond a threshold value, the viscosity of the shear-thinning fluid is reduced. This leads to a decrease in the wall shear stress compared with that for a Newtonian fluid. The reduction in the viscosity accelerates the fluid in the region close to the wall, resulting in an increase in the local heat transfer rate compared with the case of a Newtonian fluid.

Mixed Convection Along a Semi-Infinite Vertical Flat Plate With Uniform Surface Heat Flux

Mixed-convection boundary-layer flow over a heated semi-infinite vertical flat plate with uniform surface heat flux, placed in a uniform isothermal upward freestream, has been investigated. Near the leading edge, the effect of natural convection can be treated as a small perturbation term. The effects of natural convection are accumulative and increase downstream. In the second region, downstream of the leading-edge region, natural convection eventually becomes as important as forced convection. The boundary-layer equations have been solved by an adaptive finite-difference marching technique. The numerical solution indicates that the series solution of the leading-edge region is included in that of the second region. This property is shared by many developing flows. However, the series solutions of local similarity or local nonsimilarity are only valid for very small distances from the leading edge. Numerical results for the local skin-friction factor, wall temperature, and local Nusselt number are presented for Pr=1 for a wide range of Grx*∕Rex5∕2, where Grx* is a local modified Grashof number and Rex is a local Reynolds number. The results indicate that cfxRex1∕2 and NuxRex–1∕2 increase monotonically with distance from the leading edge, where cfx is the local skin-friction factor and Nux is the local Nusselt number, and approach the free-convection limit at large values of Grx*∕Rex5∕2, although the velocity distribution differs from the velocity distribution in a free-convection boundary layer.

Authors’ reply to the comments on “Similarity analysis in magnetohydrodynamics: Hall effects on forced convective heat and mass transfer of non–Newtonian power law fluids past a semi-infinite vertical flat plate” by A. Pantokratoras (Acta Mech. 2007)

Authors’ reply to the comments on “Similarity analysis in magnetohydrodynamics: Hall effects on forced convective heat and mass transfer of non–Newtonian power law fluids past a semi-infinite vertical flat plate” by A. Pantokratoras (Acta Mech. 2007)

Comment on “Similarity analysis in magnetohydrodynamics: Hall effects on forced convective heat and mass transfer of non–Newtonian power law fluids past a semi-infinite vertical flat plate” by A.A. Afify, E.M. Aboeldahab and E.S. Mohamed (Acta Mech. 177, 71–87, 2005)

Comment on “Similarity analysis in magnetohydrodynamics: Hall effects on forced convective heat and mass transfer of non–Newtonian power law fluids past a semi-infinite vertical flat plate” by A.A. Afify, E.M. Aboeldahab and E.S. Mohamed (Acta Mech. 177, 71–87, 2005)

Effects of radiation and Hall current on MHD free convective heat-generating flow past a semi-infinite vertical flat plate with an aligned magnetic field

Effects of radiation and Hall current on MHD free convective heat-generating flow past a semi-infinite vertical flat plate with an aligned magnetic field

Similarity analysis in magnetohydrodynamics: Hall effects on forced convective heat and mass transfer of non–Newtonian power law fluids past a semi-infinite vertical flat plate

The forced convective heat and mass transfer along a semi-infinite vertical flat plate is investigated for non–Newtonian power law fluids in the presence of a strong nonuniform magnetic field, and the Hall currents are taken into account. The similarity solutions are obtained using transformations group theory. These are the only symmetry transformations admitted by the field equations. The application of one-parameter groups reduces the number of independent variables by one, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with the appropriate boundary conditions. Furthermore the similarity equations are solved numerically by using a fourth-order Runge-Kutta scheme with the shooting method. Numerical results for the velocity profiles, the temperature profiles and the concentration profiles are presented graphically for various values of the power-law viscosity index n, generalized Schmidt number Sc, generalized Prandtl number Pr, the magnetic parameter M and the Hall parameter m.

Viscous dissipation and Joule heating effects on MHD-free convection from a vertical plate with power-law variation in surface temperature in the presence of Hall and ion-slip currents

An analysis is presented to study the effects of viscous dissipation and Joule heating on MHD-free convection flow past a semi-infinite vertical flat plate in the presence of the combined effect of Hall and ion-slip currents for the case of power-law variation of the wall temperature. The fluid is permeated by a strong transverse magnetic field imposed perpendicularly to the plate on the assumption of a small magnetic Reynolds number. The governing differential equations are transformed by introducing proper non-similarity variables and solved numerically. The effects of various parameters on the velocity and temperature profiles as well as the local wall shear stresses and the local Nusselt number are presented graphically and in tabular form. It is found that the magnetic field acts as a retarding force on the tangential flow but has a propelling effect on the induced lateral flow. The skin-friction factor for the tangential flow and the local Nusselt number decrease but the skin-friction factor for the lateral flow increases as the magnetic field increases. The skin-friction factor for the tangential and lateral flows are increased while the local Nusselt number is decreased if the effect of viscous dissipation, Joule heating and heat generation are considered. The opposite trend was observed as the temperature power coefficient n is increased. Also, the skin-friction factor for the tangential flow and the local Nusselt number are increased due to the Hall and ion-slip currents, whereas the skin-friction factor for the tangential flow increases when Hall values increase to one and decreases for values of Hall greater than one, but reduces by rising ion-slip values.