Numerical study of magneto-convective heat and mass transfer from inclined surface with Soret diffusion and heat generation effects : a model for ocean magnetohydrodynamics energy generator fluid dynamics

A mathematical model is developed for steady state magnetohydrodynamic (MHD) heat and mass transfer flow along an inclined surface in an ocean MHD energy generator device with heat generation and thermo-diffusive (Soret) effects. The governing equations are transformed into nonlinear ordinary differential equations with appropriate similarity variables. The emerging two-point boundary value problem is shown to depend on six dimensionless thermophysical parameters - magnetic parameter, Grashof number, Prandtl number, modified Prandtl number, heat source parameter and Soret number in addition to plate inclination. Numerical solutions are obtained for the nonlinear coupled ordinary differential equations for momentum, energy and salinity (species) conservation, numerically, using the Nachtsheim-Swigert shooting iteration technique in conjunction with the Runge- Kutta sixth order iteration scheme. Validation is achieved with Nakamura’s implicit finite difference method. Further verification is obtained via the semi-numerical Homotopy analysis method (HAM). With an increase in magnetic parameter, skin friction is depressed whereas it generally increases with heat source parameter. Salinity magnitudes are significantly reduced with increasing heat source parameter. Temperature gradient is decreased with Prandtl number and salinity gradient (mass transfer rate) is also reduced with modified Prandtl number. Furthermore, the flow is decelerated with increasing plate inclinations and temperature also depressed with increasing thermal Grashof number

B-spline collocation simulation of non-linear transient magnetic nanobio-tribological squeeze-film flow

A mathematical model is presented for magnetized nanofluid bio-tribological squeeze film flow between two approaching disks. The nanofluid comprises a suspension of metal oxide nanoparticles with an electrically-conducting base fluid, making the nano-suspension responsive to applied magnetic field. The governing viscous momentum, heat and species (nano-particle) conservation equations are normalized with appropriate transformations which renders the original coupled, nonlinear partial differential equation system into a more amenable ordinary differential boundary value problem. The emerging model is shown to be controlled by a number of parameters, viz nanoparticle volume fraction, squeeze number, Hartmann magnetic body force number, disk surface transpiration parameter, Brownian motion parameter, thermophoretic parameter, Prandtl number and Lewis number. Computations are conducted with a B-spline collocation numerical method. Validation with previous homotopy solutions is included. The numerical spline algorithm is shown to achieve excellent convergence and stability in nonlinear bio-tribological boundary value problems. The interaction of heat and mass transfer with nanofluid velocity characteristics is explored. In particular smaller nanoparticle (high Brownian motion parameter) suspensions are studied. The study is relevant to enhanced lubrication performance in novel bio-sensors and intelligent knee joint (orthopaedic) systems

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

Ankle Sprain Injuries in the ED: Assessing Quality of Discharge Instructions and Compliance of Physicians with Ottawa Ankle Rules

Annually a large number of patients seen in the emergency department are diagnosed with an ankle sprain. If not treated properly, these injuries can result in long term complications such as pain, swelling and instability. Appropriate patient discharge instructions using evidence based treatment principles can be utilized to avoid these complications. Many patients seen in the emergency department with a final diagnosis of ankle sprain receive x-rays to rule out a fracture, despite the development of the Ottawa Ankle Rules (OAR) to determine when x-rays are necessary. Use of the Ottawa Ankle Rules has been shown to decrease the number of necessary x-rays by 35%. In this study, we conducted a retrospective chart review of patients discharged from theUniversityHospitalemergency department with a diagnosis of ankle sprain to determine: a) the quality and content of treatment and discharge instructions, b) the compliance with the Ottawa Ankle Rules for the determination of ordering an x-ray. We found there to be inadequate documentation of the use of OAR in the Emergency department and that the discharge instructions given to patients were not at a level that would provide for the best recovery from the injur

Numerical computation of nonlinear oscillatory two-immiscible magnetohydrodynamic flow in dual porous media system : FTCS and FEM study

The transient Hartmann magnetohydrodynamic (MHD) flow of two immiscible fluids flowing through a horizontal channel containing two porous media with oscillating lateral wall mass flux is studied. A two-dimensional spatial model is developed for the two fluids, one of which is electrically-conducting and the other electrically-insulating (as is the wall in the second region). Both fluid regimes are driven by a common pressure gradient. A Darcy-Forchheimer drag force model is used to simulate the porous medium effects on the flow in both fluid regions. Special boundary conditions are imposed at the interface. The governing second order nonlinear partial differential equations are non-dimensionalized for each region using a set of transformations. The resulting transport equations are shown to be controlled by the Hartmann hydromagnetic parameter (Ha), viscosity ratio parameter (α), two Darcy numbers (Da1, Da2), two Forchheimer numbers (Fs1, Fs2), two Reynolds numbers (Re1, Re2), frequency parameter (εA) associated with the transpiration (lateral wall flux) velocity and a periodic frequency parameter (ω*t*). Numerical FTCS finite difference solutions are obtained for a wide range of the governing parameters. Benchmarking is performed with a Galerkin finite element method code (MAGNETO-FEM) and the results are found to be in excellent agreement. Applications of the model include magnetic cleanup operations in coastal/ocean seabed oil spills and electromagnetic purification of petroleum reservoir fluids

Effects of coagulation on the two-phase peristaltic pumping of magnetized Prandtl biofluid through an endoscopic annular geometry containing a porous medium

In this article, motivated by more accurate simulation of electromagnetic blood flow in annular vessel geometries in intravascular thrombosis, a mathematical model is developed for elucidating the effects of coagulation (i.e. a blood clot) on peristaltically induced motion of an electrically-conducting (magnetized) Prandtl fluid physiological suspension through a non-uniform annulus containing a homogenous porous medium. Magnetohydrodynamics is included owing to the presence of iron in the hemoglobin molecule and also the presence of ions in real blood. Hall current which generates a secondary (cross) flow at stronger magnetic field is also considered in the present study. A small annular tube (endoscopic) with sinusoidal peristaltic waves traveling along the inner and outer walls at constant velocity with a clot present is analyzed. The governing conservation equations which comprise the continuity and momentum equations for the fluid phase and particle phase are simplified under lubrication approximations (long wavelength and creeping flow conditions). The moving boundary value problem is normalized and solved analytically (with appropriate wall conditions) for the fluid phase and particle phase using the homotopy perturbation method (HPM) with MATHEMATICA software. Validation is conducted with MAPLE numerical quadrature. A parametric study of the influence of clot height (δ), particle volume fraction (C), Prandtl fluid material parameters (α, β), Hartmann number (M), Hall parameter (m), permeability parameter (k), peristaltic wave amplitude (φ) and wave number (δ̅ ) on pressure difference and wall shear (friction forces) is included. Pressure rise is elevated with clot height, medium permeability and Prandtl rheological material parameters whereas it is reduced with increasing particle volume fraction and magnetic Hartmann number. Friction forces on the outer and inner tubes of the endoscope annulus are enhanced with clot height and particle volume fraction whereas they are decreased with Prandtl rheological material parameters, Hall parameter and permeability parameter. The simulations provide a good benchmark for more general computational fluid dynamics studies of magnetic endoscopic multi-phase peristaltic pumping

Modeling magnetic nanopolymer flow with induction and nanoparticle solid volume fraction effects : solar magnetic nanopolymer fabrication simulation

A mathematical model is presented for the nonlinear steady, forced convection, hydromagnetic flow of electro-conductive magnetic nano-polymer with magnetic induction effects included. The transformed two-parameter, non-dimensional governing partial differential equations for mass, momentum, magnetic induction and heat conservation are solved with the local non-similarity method (LNM) subject to appropriate boundary conditions. Keller’s implicit finite difference “box” method (KBM) is used to validate solutions. Computations for four different nanoparticles and three different base fluids are included. Silver nanoparticles in combination with various base fluids enhance temperatures and induced magnetic field and accelerate the flow. An elevation in magnetic body force number decelerates the flow whereas an increase in magnetic Prandtl number elevates the magnetic induction. Furthermore, increasing nanoparticle solid volume fraction is found to substantially boost temperatures. Applications of the study arise in advanced magnetic solar nano-materials (fluids) processing technologies

Numerical solution of bio-nano-convection transport from a horizontal plate with blowing and multiple slip effects

In this paper, a new bio-nano-transport model is presented. The effects of first and second order velocity slips, thermal slip, mass slip, and gyro-tactic (torque-responsive) microorganism slip of bioconvectivenanofluid flow from amoving plate under blowing phenomenon are numerically examined. The flow model is expressed by partial differential equations which areconverted to a similar boundary value problem bysimilarity transformations. The boundary value problem is converted to a system of nonlinear equationswhich are then solved by a Matlab nonlinear equation solver fsolveintegrated with a Matlab ODEsolverode15s. The effects of selected control parameters (first order slip, second order slip, thermal slip, microorganism slip, blowing, nanofluid parameters) on the non-dimensional velocity, temperature, nanoparticle volume fraction, density ofmotile micro-organism, skin friction coefficient, heat transfer rate, mass flux of nanoparticles andmass fluxof microorganismsare analyzed. Our analysis reveals that a higher blowing parameter enhances micro-organism propulsion, flow velocityand nano-particle concentration, and increases the associated boundary layerthicknesses. A higher wall slip parameter enhances mass transfer and accelerates the flow. The MATLAB computations have been rigorously validated with the second-order accurate finite difference Nakamura tri-diagonal method.The current study is relevant to microbial fuel cell technologies which combine nanofluid transport, bioconvection phenomena and furthermore finds applications in nano-biomaterials sheetprocessing systems

Energy conversion under conjugate conduction, magneto-convection, diffusion and nonlinear radiation over a non-linearly stretching sheet with slip and multiple convective boundary conditions

Energy conversion under conduction, convection, diffusion and radiation has been studied for MHD free convection heat transfer of a steady laminar boundary-layer flow past a moving permeable non-linearly extrusion stretching sheet. The nonlinear Rosseland thermal radiation flux model, velocity slip, thermal and mass convective boundary conditions are considered to obtain a model with fundamental applications to real world energy systems. The Navier slip, thermal and mass convective boundary conditions are taken into account. Similarity differential equations with corresponding boundary conditions for the flow problem, are derived, using a scaling group of transformation. The transformed model is shown to be controlled by magnetic field, conduction-convection, convection-diffusion, suction/injection, radiation-conduction, temperature ratio, Prandtl number, Lewis number, buoyancy ratio and velocity slip parameters. The transformed non-dimensional boundary value problem comprises a system of nonlinear ordinary differential equations and physically realistic boundary conditions, and is solved numerically using the efficient Runge-Kutta-Fehlberg fourth fifth order numerical method, available in Maple17 symbolic software. Validation of results is achieved with previous simulations available in the published literature. The obtained results are displayed both in graphical and tabular form to exhibit the effect of the controlling parameters on the dimensionless velocity, temperature and concentration distributions. The current study has applications in high temperature materials processing utilizing magnetohydrodynamics, improved performance of MHD energy generator wall flows and also magnetic-microscale fluid devices

Mathematical modelling of nonlinear thermal radiation effects on EMHD peristaltic pumping of viscoelastic dusty fluid through a porous medium duct

Biologically-inspired propulsion systems are currently receiving significant interest in the aerospace sector. Since many spacecraft propulsion systems operate at high temperatures, thermal radiation is important as a mode of heat transfer. Motivated by these developments, in the present article, the influence of nonlinear thermal radiation (via the Rosseland diffusion flux model) has been studied on the laminar, incompressible, dissipative EMHD (Electro-magneto-hydrodynamic) peristaltic propulsive flow of a non-Newtonian (Jefferys viscoelastic) dusty fluid containing solid particles through a porous planar channel. The fluid is electrically-conducting and a constant static magnetic field is applied transverse to the flow direction (channel walls). Slip effects are also included. Magnetic induction effects are neglected. The mathematical formulation is based on continuity, momentum and energy equations with appropriate boundary conditions, which are simplified by neglecting the inertial forces and taking the long wavelength and lubrication approximations. The boundary value problem is then rendered non-dimensional with appropriate variables and the resulting system of reduced ordinary differential equations is solved analytically. The impact of various emerging parameters dictating the non-Newtonian propulsive flow i.e. Prandtl number, radiation parameter, Hartmann number, permeability parameter, Eckert number, particle volume fraction, electric field and slip parameter are depicted graphically. Increasing particle volume fraction is observed to suppress temperature magnitudes. Furthermore the computations demonstrate that an increase in particle volume fraction reduces the pumping rate in retrograde pumping region whereas it causes the opposite effect in the co-pumping region. The trapping mechanism is also visualized with the aid of streamline contour plots. Increasing thermal radiation elevates temperatures. Increasing Hartmann (magnetic body force) number decreases the size of the trapping bolus whereas the quantity of the does not effected. Conversely increasing particle volume fraction reduces the magnitude of the trapping bolus whereas the number of trapped bolus remains constant