MHD Flow of a Micropolar Fluid past a Stretched Permeable Surface with Heat Generation or Absorption

This work considers steady, laminar, MHD flow of a micropolar fluid past a stretched semi-infinite, vertical and permeable surface in the presence of temperature dependent heat generation or absorption, magnetic field and thermal radiation effects. A set of similarity parameters is employed to convert the governing partial differential equations into ordinary differential equations. The obtained self-similar equations are solved numerically by an efficient implicit, iterative, finite-difference method. The obtained results are checked against previously published work for special cases of the problem in order to access the accuarcy of the numerical method and found to be in excellent agreement. A parametric study illustrating the influence of the various physical parameters on the skin friction coefficient, microrotaion coefficient or wall couple stress as well as the wall heat transfer coefficient or Nusselt number is conducted. The obtained results are presented graphically and in tabular form and the physical aspects of the problem are discussed

Unsteady nonlinear magnetohydrodynamic micropolar transport phenomena with hall and ion-slip current effects : numerical study

Unsteady viscous two-dimensional magnetohydrodynamic micropolar flow, heat and mass transfer from an infinite vertical surface with Hall and Ion-slip currents is investigated theoretically and numerically. The simulation presented is motivated by electro-conductive polymer (ECP) materials processing in which multiple electromagnetic effects arise. The primitive boundary layer conservation equations are transformed into a non-similar system of coupled non-dimensional momentum, angular momentum, energy and concentration equations, with appropriate boundary conditions. The resulting two-point boundary value problem is solved numerically by an exceptionally stable and welltested implicit finite difference technique. A stability analysis is included for restrictions of the implicit finite difference method (FDM) employed. Validation with a Galerkin finite element method (FEM) technique is included. The influence of various parameters is presented graphically on primary and secondary shear stress, Nusselt number, Sherwood number and wall couple stress. Secondary (cross flow) shear stress is strongly enhanced with greater magnetic parameter (Hartmann number) and micropolar wall couple stress is also weakl y enhanced for small time values with Hartmann number. Increasing thermo-diffusive Soret number suppresses both Nusselt and Sherwood numbers whereas it elevates both primary and secondary shear stress and at larger time values also increases the couple stress. Secondary shear stress is strongly boosted with Hall parameter. Ion slip effect induces a weak modification in primary and secondary shear stress distributions. The present study is relevant to electroconductive non-Newtonian (magnetic polymer) materials processing systems

Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet in a micropolar fluid

An analysis is carried out for the steady two-dimensional mixed convection flow adjacent to a stretching vertical sheet immersed in an incompressible electrically conducting micropolar fluid. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the leading edge. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically using a finite difference scheme known as the Keller box method. The effects of magnetic and material parameters on the flow and heat transfer characteristics are discussed. It is found that the magnetic field reduces both the skin friction coefficient and the heat transfer rate at the surface for any given K and λ. Conversely, both of them increase as the material parameter increases for fixed values of M and λ

Chebyshev collocation computation of magneto-bioconvection nanofluid flow over a wedge with multiple slips and magnetic induction

In this paper the steady two dimensional stagnation point flow of a viscous incompressible electrically conducting bio-nanofluid over a stretching/shrinking wedge in the presence of passively control boundary condition, Stefan blowing and multiple slips is numerically investigated. Magnetic induction is also taken into account. The governing conservation equations are rendered into a system of ordinary differential equations via appropriate similarity transformations. The reduced system is solved using a fast, convergent Chebyshev collocation method. The influence of selected parameters on the dimensionless velocity, induced magnetic field, temperature, nanoparticle volume fraction and density of motile microorganisms as well as on the local skin friction, local Nusselt number, local Sherwood number and density of motile microorganism numbers are discussed and presented graphically. Validation with previously published results is performed and an excellent agreement is found. The study is relevant to electromagnetic manufacturing processes involving bionano-fluids

Multiple slip and variable transport property effects on magnetohydromagnetic dissipative thermo-solutal convection in porous media

A mathematical study is presented to investigate the influence of variable transport properties and momentum, thermal and mass slip on magnetohydrodynamic (MHD) momentum, heat and mass transfer in a porous media. Slip effects are simulated via careful imposition of boundary conditions at the wall. Joule heating and viscous dissipation are also studied. The governing partial differential boundary layer equations are analyzed using Lie group theory and rendered with appropriate transformations into a system of nonlinear, coupled ordinary differential equations. The multi-physical boundary value problem is dictated by twelve thermophysical parameters- concentration diffusivity parameter (Dc), Hartmann magnetic number (M), permeability parameter (omaga), Eckert number (Ec), momentum slip (a), thermal slip (b), mass (species) slip (d), Prandtl number (Pr), Schmidt number (Sc), power law index for non-isothermal and non-iso-solutal effects (m), viscosity variation parameter (A) and thermal conductivity variation parameter (S). A numerical solution is obtained for the effects of selected parameters on transport characteristics using the robust Runge-Kutta-Fehlberg fourth-fifth order numerical quadrature method in Maple16. Excellent correlation is achieved between the present computational results and for the constant transport properties (A=S=Dc=0), nonporous (omega=0), non-thermal slip (b=0), non-solutal slip (d = 0) and non-dissipative solutions without Joule heating (Ec= 0) of Yazdi et al. [35]. Increasing momentum slip enhances temperatures whereas increasing thermal slip reduces them. An increase in thermal conductivity boosts temperatures whereas greater viscosity reduces temperatures. Increasing magnetic parameter suppresses velocity and increasing permeability parameter elevates temperatures. Species concentration is enhanced with increasing concentration diffusivity and permeability parameter but depressed with increasing viscosity. Furthermore concentration is enhanced with momentum slip but reduced with mass slip parameter. Moreover increasing magnetic field is observed to aid species diffusion in the regime. The present study finds applications in trickle-bed reactor hydromagnetics, magnetic polymeric materials processing and MHD energy generator slip flows

Computation of electroconductive gyrotactic bioconvection from a nonlinear inclined stretching sheet under non-uniform magnetic field : simulation of smart bio-nano-polymer coatings for solar energy

Incompressible, steady-state, boundary layer magneto-bioconvection of a nanofluid (containing motile gyrotactic micro-organisms) over a nonlinear inclined stretching sheet subjected to non-uniform magnetic field is studied theoretically and numerically. This regime is encountered in novel bio-nano-material electroconductive polymeric processing systems currently being considered for third generation organic solar coatings, anti-fouling marine coatings etc. Buongiorno’s two-component nanofluid model is deployed with the OberbeckBoussinesq approximation. Ohmic dissipation (Joule heating) is included. The governing nonlinear partial differential equations are reduced to a system of ordinary differential equations and appropriate similarity transformations. The normalized system of equations with associated boundary conditions features a number of important dimensionless parameters including magnetohydrodynamic body force parameter (M), sheet inclination (δ), Brownian motion nanoscale parameter (Nb), thermophoresis nanoscale parameter (Nt), Richardson number (Ri=GrRe2 , where Gr is thermal Grashof number and Re is Reynolds number), buoyancy ratio parameter (Nr), Eckert (viscous dissipation) number (Ec), bioconvection Rayleigh number (Rb), Lewis number (Le), bioconvection Lewis number (Lb), Péclet number (Pe), nonlinear stretching parameter (n) are solved with a variational Finite Element Method (FEM). Validation is conducted with earlier published studies of Khan and Pop (2010) for the case of non-magnetic stretching sheet nanofluid flow without bioconvection. Further validation of the general magnetic bioconvection nanofluid model is achieved with a generalized differential quadrature (GDQ) numerical technique developed by Bég and Kuharat (2017). The response of non-dimensional velocity, temperature, nanoparticle concentration, motile microorganism density function, local skin friction coefficient, Nusselt number, Sherwood number, wall motile density gradient function to variation in physically pertinent values of selected control parameters (representative of real solar bio-nano-magnetic materials manufacturing systems) are studied in detail. Interesting features of the flow dynamics are elaborated and new future pathways for extension of the study identified in bio-magneto-nano polymers (BMNPs) for solar coatings

Mathematical models for heat and mass transfer in nanofluid flows.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.The behaviour and evolution of most physical phenomena is often best described using mathematical models in the form of systems of ordinary and partial differential equations. A typical example of such phenomena is the flow of a viscous impressible fluid which is described by the Navier-Stokes equations, first derived in the nineteenth century using physical approximations and the principles of mass and momentum conservation. The flow of fluids, and the growth of flow instabilities has been the subject of many investigations because fluids have wide uses in engineering and science, including as carriers of heat, solutes and aggregates. Conventional heat transfer fluids used in engineering applications include air, water and oil. However, each of these fluids has an inherently low thermal conductivity that severely limit heat exchange efficiency. Suspension of nanosized solid particles in traditional heat transfer fluids significantly increases the thermophysical properties of such fluids leading to better heat transfer performance. In this study we present theoretical models to investigate the flow of unsteady nanofluids, heat and mass transport in porous media. Different flow configurations are assumed including an inclined cylinder, a moving surface, a stretching cone and the flow of a polymer nanocomposite modeled as an Oldroyd-B fluid. The nanoparticles assumed include copper, silver and titanium dioxide with water as the base fluid. Most recent boundary-layer nanofluid flow studies assume that the nanoparticle volume fraction can be actively controlled at a bounding solid surface, similar to temperature controls. However, in practice, such controls present significant challenges, and may, in practice, not be possible. In this study the nanoparticle flux at the boundary surface is assumed to be zero. Unsteadiness in fluid flows leads to complex system of partial differential equations. These transport equations are often highly nonlinear and cannot be solved to find exact solutions that describe the evolution of the physical phenomena modeled. A large number of numerical or semi-numerical techniques exist in the literature for finding solutions of nonlinear systems of equations. Some of these methods may, however be subject to certain limitations including slow convergence rates and a small radius of convergence. In recent years, innovative linearization techniques used together with spectral methods have been suggested as suitable tools for solving systems of ordinary and partial differential equations. The techniques which include the spectral local linearization method, spectral relaxation method and the spectral quasiliearization method are used in this study to solve the transport equations, and to determine how the flow characteristics are impacted by changes in certain important physical and fluid parameters. The findings show that these methods give accurate solutions and that the speed of convergence of solutions is comparable with methods such as the Keller-box, Galerkin, and other finite difference or finite element methods. The study gives new insights, and result on the influence of certain events, such as internal heat generation, velocity slip, nanoparticle thermophoresis and random motion on the flow structure, heat and mass transfer rates and the fluid properties in the case of a nanofluid

Hall current, viscous and Joule heating effects on steady radiative 2-D magneto-power-law polymer dynamics from an exponentially stretching sheet with power-law slip velocity : a numerical study

A mathematical model is developed for 2-D laminar, incompressible, electrically conducting non-Newtonian (Power-law) fluid boundary layer flow along an exponentially stretching sheet with power-law slip velocity conditions in the presence of Hall currents, transverse magnetic field and radiative flux. The secondary flow has been induced with appliance of Hall current. The distinguish features of Joule heating and viscous dissipation are included in the model since they are known to arise in thermal magnetic polymeric processing. Rosseland’s diffusion model is employed for radiation heat transfer. The non-linear partial differential equations describing the flow (mass, primary momentum, secondary momentum and energy conservation) are transformed into non-linear ordinary differential equations by employing local similarity transformations. The non-dimensional nonlinear formulated set of equations is numerically evaluated with famous shooting algorithm by using MATLAB software. The validation of simulated numerical results has been completed with generalized differential quadrature (GDQ). Extensive visualization of primary and secondary velocities and temperature distributions for the effects of the emerging parameters is presented for both pseudo-plastic fluids (n=0.8) and dilatant fluids (n=1.2). The study is relevant to the manufacturing transport phenomena in electro-conductive polymers (ECPs)

Numerical Solution of the Momentum and Heat Transfer Equations for a Hydromagnetic Flow Due to a Stretching Sheet of a non-uniform Property Micropolar Liquid

A study of the hydromagnetic flow due to a stretching sheet and heat transfer in an incompressible micropolar liquid is made. Temperature-dependent thermal conductivity and a non-uniform heat source/sink render the problem analytically intractable and hence a numerical study is made using the shooting method based on Runge-Kutta and Newton-Raphson methods. The two problems of horizontal and vertical stretching are considered to implement the numerical method. The former problem involves one-way coupling between linear momentum and heat transport equations and the latter involves two-way coupling. Further, both the problems involve two-way coupling between the non-linear equations of conservation of linear and angular momentums. A similarity transformation arrived at for the problem using the Lie group method facilitates the reduction of coupled, non-linear partial differential equations into coupled, non-linear ordinary differential equations. The algorithm for solving the resulting coupled, two-point, non-linear boundary value problem is presented in great detail in the paper. Extensive computation on velocity and temperature profiles is presented for a wide range of values of the parameters, for prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions