M. Ferdows

Lie Group Solution for Free Convective Flow of a Nanofluid Past a Chemically Reacting Horizontal Plate in a Porous Media

The optimal homotopy analysis method (OHAM) is employed to investigate the steady laminar incompressible free convective flow of a nanofluid past a chemically reacting upward facing horizontal plate in a porous medium taking into account heat generation/absorption and the thermal slip boundary condition. Using similarity transformations developed by Lie group analysis, the continuity, momentum, energy, and nanoparticle volume fraction equations are transformed into a set of coupled similarity equations. The OHAM solutions are obtained and verified by numerical results using a Runge-Kutta-Fehlberg fourth-fifth order method. The effect of the emerging flow controlling parameters on the dimensionless velocity, temperature, and nanoparticle volume fraction have been presented graphically and discussed. Good agreement is found between analytical and numerical results of the present paper with published results. This close agreement supports our analysis and the accuracy of the numerical computations. This paper also includes a representative set of numerical results for reduced Nusselt and Sherwood numbers in a table for various values of the parameters. It is concluded that the reduced Nusselt number increases with the Lewis number and reaction parameter whist it decreases with the order of the chemical reaction, thermal slip, and generation parameters.

Numerical study of transient magnetohydrodynamic radiative free convection nanofluid flow from a stretching permeable surface

Transient mixed convective laminar boundary layer flow of an incompressible, viscous, dissipative, electrically conducting nanofluid from a continuously stretching permeable surface in the presence of magnetic field and thermal radiation flux is studied. The model used for the unsteadiness in the momentum, temperature, and concentration fields is based on the time-dependent stretching velocity and surface temperature and concentration. Similarity transformations are used to convert the governing time-dependent nonlinear boundary layer equations for momentum, thermal energy, and concentration to a system of nonlinear ordinary coupled differential equations with appropriate boundary conditions. The transformed model is shown to be controlled by a number of thermophysical parameters, namely the magnetic parameter, thermal convective parameter, mass convective parameter, suction parameter, radiation-conduction parameter, Eckert number, Prandtl number, Lewis number, Brownian motion parameter, thermophoresis parameter, and the unsteadiness parameter. Numerical solutions are obtained with the robust Nactsheim–Swigert shooting technique together with Runge–Kutta sixth-order iteration schemes. Comparisons with previously published work are performed and are found to be in excellent agreement. The effects of selected parameters on velocity, temperature, and concentration distributions and furthermore on skin friction coefficients, heat transfer rate (Nusselt number), and mass transfer rate (Sherwood number) are presented graphically. The current study has applications in high-temperature nano-technological materials processing.

Explicit numerical study of unsteady hydromagnetic mixed convective nanofluid flow from an exponentially stretching sheet in porous media

A numerical investigation of unsteady magnetohydrodynamic mixed convective boundary layer flow of a nanofluid over an exponentially stretching sheet in porous media, is presented. The transformed, non-similar conservations equations are solved using a robust, explicit, finite difference method (EFDM). A detailed stability and convergence analysis is also conducted. The regime is shown to be controlled by a number of emerging thermophysical parameters i.e. combined porous and hydromagnetic parameter (R), thermal Grashof number (Gr), species Grashof number (Gm), viscosity ratio parameter (Λ), dimensionless porous media inertial parameter (∇), Eckert number (Ec), Lewis number (Le), Brownian motion parameter (Nb) and thermophoresis parameter (Nt). The flow is found to be accelerated with increasing thermal and species Grashof numbers and also increasing Brownian motion and thermophoresis effects. However, flow is decelerated with increasing viscosity ratio and combined porous and hydromagnetic parameters. Temperatures are enhanced with increasing Brownian motion and thermophoresis as are concentration values. With progression in time the flow is accelerated and temperatures and concentrations are increased. EFDM solutions are validated with an optimized variational iteration method. The present study finds applications in magnetic nanomaterials processing.

MHD Mixed Convective Boundary Layer Flow of a Nanofluid through a Porous Medium due to an Exponentially Stretching Sheet

Magnetohydrodynamic (MHD) boundary layer flow of a nanofluid over an exponentially stretching sheet was studied. The governing boundary layer equations are reduced into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration schemes. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. The numerical solutions for the wall skin friction coefficient, the heat and mass transfer coefficient, and the velocity, temperature, and concentration profiles are computed, analyzed, and discussed graphically. Comparison with previously published work is performed and excellent agreement is observed.

GROUP THEORY AND DIFFERENTIAL TRANSFORM ANALYSIS OF MIXED CONVECTIVE HEAT AND MASS TRANSFER FROM A HORIZONTAL SURFACE WITH CHEMICAL REACTION EFFECTS

Viscous, laminar mixed convection boundary-layer flow over a horizontal plate, with chemical reaction, is considered. The governing equations are expressed in nondimensional form. Group theory is employed to determine the invariant solutions of these equations under a particular continuous one-parameter group. Series solutions of the transformed coupled system of equations are then generated for velocity, temperature, and concentration functions using the Differential Transform Method (DTM) with Padé approximants. The influence of thermal buoyancy parameter, species buoyancy parameter, chemical reaction parameter, order of chemical reaction, Prandtl number, and Schmidt number on the flow characteristics is evaluated in detail The obtained solutions are verified by comparison with the numerical shooting quadrature results. Applications of the study arise in sheet materials processing, bio-reactors, and catalytic systems in chemical engineering.

Group analysis and numerical computation of magneto-convective non-Newtonian nanofluid slip flow from a permeable stretching sheet

Two-dimensional magnetohydrodynamic boundary layer flow of non-Newtonian power-law nanofluids past a linearly stretching sheet with a linear hydrodynamic slip boundary condition is investigated numerically. The non-Newtonian nanofluid model incorporates the effects of Brownian motion and thermophoresis. Similarity transformations and corresponding similarity equations of the transport equations are derived via a linear group of transformations. The transformed equations are solved numerically using Runge–Kutta–Fehlberg fourth-fifth order numerical method available in the Maple 14 software for the influence of power-law (rheological) index, Lewis number, Prandtl number, thermophoresis parameter, Brownian motion parameter, magnetic field parameter and linear momentum slip parameter. Validation is achieved with an optimized Nakamura implicit finite difference algorithm (NANONAK). Representative results for the dimensionless axial velocity, temperature and concentration profiles have been presented graphically. The present results of skin friction factor and reduced heat transfer rate are also compared with the published results for several special cases of the model and found to be in close agreement. The study has applications in electromagnetic nano-materials processing.

Numerical simulation of Dean number and curvature effects on magneto-biofluid flow through a curved conduit.

A numerical study is performed to investigate the magnetohydrodynamic viscous steady biofluid flow through a curved pipe with circular cross section under various conditions. A spectral method is applied as the principal tool for the numerical simulation with Fourier series, Chebyshev polynomials, collocation methods and an iteration method as secondary tools. The combined effects of Dean number, Dn, magnetic parameter, Mg, and tube curvature, δ, are studied. The flow patterns have been shown graphically for large Dean numbers as well as magnetic parameter and a wide range of curvatures, 0.01 ≤δ≤ 0.2. Two-vortex solutions have been found. Axial velocity has been found to increase with an increase of Dean number, whereas it is suppressed with greater curvature and magnetic parameters. For high magnetic parameter and Dean number and low curvature, almost all the fluid vortex strengths are weak. The study is relevant to magnetohydrodynamic blood flow in the cardiovascular system.

Boundary layer flow and heat transfer of a nanofluid over a permeable unsteady stretching sheet with viscous dissipation

A numerical study of the boundary layer flow past unsteady stretching surface in nanofluid under the effects of suction and viscous dissipation is investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented, which depends on the unsteadiness parameter A, Eckert number Ec, ζ suction or injection parameter, Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt. The governing partial differential equations were converted to nonlinear ordinary differential equations by using a suitable similarity transformation, which are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration scheme. The accuracy of the numerical method is tested by performing various comparisons with the previously published work, and the results are found to be in excellent agreement. Numerical results are presented both in tabular and graphical forms illustrating the effects of these parameters on thermal and nanoparticle volume fraction boundary layers. The thermal boundary layer thickens with a rise in the local temperature as the Brownianmotion, thermophoresis, and convective heating each intensify.

NUMERICAL SIMULATION OF MARANGONI MAGNETOHYDRODYNAMIC BIO-NANOFLUID CONVECTION FROM A NON-ISOTHERMAL SURFACE WITH MAGNETIC INDUCTION EFFECTS: A BIO-NANOMATERIAL MANUFACTURING TRANSPORT MODEL

Laminar magnetohydrodynamic Marangoni-forced convection boundary layer flow of a water-based biopolymer nanofluid containing nanoparticles from a non-isothermal plate is studied. Magnetic induction effects are incorporated. A variety of nanoparticles are studied, specifically, silver, copper, aluminium oxide and titanium oxide. The Tiwari–Das model is utilized for simulating nanofluid effects. The normalized ordinary differential boundary layer equations (mass, magnetic field continuity, momentum, induced magnetic field and energy conservation) are solved subject to appropriate boundary conditions using Maple shooting quadrature. The influence of Prandtl number (Pr), magnetohydrodynamic body force parameter (β), reciprocal of magnetic Prandtl number (α) and nanofluid solid volume fraction (φ) on velocity, temperature and magnetic stream function distributions is investigated in the presence of strong Marangoni effects (ξ i.e., Marangoni parameter is set as unity). Magnetic stream function is accentuated with body force parameter. The flow is considerably decelerated as is magnetic stream function gradient, with increasing nanofluid solid volume fraction, whereas temperatures are significantly enhanced. Interesting features in the flow regime are explored. The study finds applications in the fabrication of complex biomedical nanofluids, biopolymers, etc.

MHD Natural Convection with Convective Surface Boundary Condition over a Flat Plate

We apply the one parameter continuous group method to investigate similarity solutions of magnetohydrodynamic (MHD) heat and mass transfer flow of a steady viscous incompressible fluid over a flat plate. By using the one parameter group method, similarity transformations and corresponding similarity representations are presented. A convective boundary condition is applied instead of the usual boundary conditions of constant surface temperature or constant heat flux. In addition it is assumed that viscosity, thermal conductivity, and concentration diffusivity vary linearly. Our study indicates that a similarity solution is possible if the convective heat transfer related to the hot fluid on the lower surface of the plate is directly proportional to where is the distance from the leading edge of the solid surface. Numerical solutions of the ordinary differential equations are obtained by the Keller Box method for different values of the controlling parameters associated with the problem.