Body Force Parameter Research Articles

Parametric model for a cutting edge contour of the geokhod cutting body blade

a parametric model for a cutting body blade cutting edge contour of geokhod, which is a new class of mining equipment. The research relevance is due to the need to create a unified methodology for forming the cutting body cutting edge for geokhods of various sizes, since the cutting edge design parameters are heavily dependent on geokhod geometry and force parameters. The research objective is to obtain parametric equations for determining the geometric coordinates of the points of the geokhod cutting body blade cutting edge in Cartesian coordinates. Methods of research. The paper describes the principles of parameterization of the complex geometry of geokhod cutting body blade cutting edge. Research methods include the study of blade edge geometry, as well as its design parameters dependence on geokhod’s force and design parameters. To achieve that, analytical dependencies were selected from the method of calculating the cutting body force parameters, and then parametric functions affecting the cutting body cutting edge geometry were selected. Results. As a result, a geometric model of the cutting body cutting edge in a parametric form was obtained. To demonstrate the formation of the blade cutting edge contact with rock based on the obtained parametric-time dependencies, a computer program was developed with the calculated values probability construction. The dependence between the cutting edge geometry and the geokhod design parameters dictated the modeling of the cutting edge shape for geokhods of different diameters. Conclusions. The obtained parametric expressions for calculating the coordinates of geokhod cutting body contact make it possible to build contact lines of the blade and the rock mass according to the input data. Is has also been proved that geokhod cutting edge shape depends on the geokhod diameter, and its geometric parameters will be individual for each type of geokhod

THERMAL RADIATION AND HALL CURRENT EFFECTS IN A MHD NON-DARCY FLOW IN A DIFFERENTIALLY HEATED SQUARE ENCLOSURE -LATTICE BOLTZMANN SIMULATION

A computational study of radiative-convection flow on incompressible magnetohydrodynamic (MHD) convection in a heated square enclosure containing a non-Darcy square cavity with Hall currents and heat generation/absorption is presented. The Rosseland algebraic flux model is deployed for radiative heat transfer. The equations of conservation for mass, momentum, and energy with associated boundary conditions are rendered non-dimensional with suitable transformations. The results dimensionless nonlinear boundary value problem is then solved with the D2Q9-based lattice Boltzmann method (LBM) in MATLAB. A grid independence test is included for validation of the D2Q9-LBM code accuracy. A parametric study of the impact of the Hartmann number (magnetic body force parameter), heat generation (<i>Q</i>), thermal radiation (<i>Rd</i>), Darcy number (permeability parameter), and Rayleigh number (thermal buoyancy force) on the temperature contours, streamline, and Nusselt number distributions with Prandtl number (Pr = 0.71) is conducted.

Radiative magneto‐thermogravitational flow in a porous square cavity with viscous heating and Hall current effects: A numerical study of ψ–v scheme

AbstractA numerical study presented for the natural convection two‐dimensional incompressible flow of a magnetized fluid in a square enclosure filled with porous medium. Viscous dissipation, thermal radiation, and Hall current effects are included. The formulated computational domain comprising the mass, momentum, and energy conservation equations with appropriate boundary conditions, is rendered dimensionless via appropriate scaling transformations. The resulting nondimensional partial governing equations are solved by the ψ–v scheme. A detailed parametric investigation of the influence of Hartman number (magnetic body force parameter), Rayleigh number (thermal buoyancy parameter), Darcy number (permeability parameter), Eckart number for porous medium, Hall parameter, and radiation parameter on the streamline, temperature contours, local Nusselt number along the hot wall and mid‐section velocity profiles are computed. Thermal Rayleigh number can be a control key parameter on heat and flow in enclosures. In addition, the heat transfer rate is intensified with increasing thermal Rayleigh numbers. With increasing Darcy number (i.e., greater permeability of the porous medium and progressively lower Darcian drag force) there is a strong elevation in the average Nusselt number at the left hot wall.

Bio-magnetic pulsatile CuO−Fe3O4 hybrid nanofluid flow in a vertical irregular channel in a suspension of body acceleration

Mathematical modelling of biological fluids is essential in various medical disciplines. The current work has many biomechanical applications, including radiation therapy for lung cancer treatment and magnetic field strength to regulate blood flow during surgery. The current model deals with the pulsatile hybrid nanofluid flow in a vertically permeable irregular channel under the influence of externally applied body acceleration. Thermal radiation and heat source have been included in the heat transfer analysis. The velocity, temperature, heat transfer rate, and isothermal lines are produced using the perturbation approach to evaluate coupled equations with the nonlinear problem. In addition, response surface method is executed to probe the sensitivity of effective flow field parameters on the heat transfer rate. It is found that the hybrid nanoparticles expose a lower blood temperature than the mono nanoparticles; as a result, the hybrid nanoparticles have better drug delivery performance. The blood velocity decreases with increasing the values of the body force parameter. In addition, the blood flow is higher for CuO nanofluid than the CuO-Fe3O4 hybrid nanofluid, but this case is quite the opposite for lower values of frequency parameter.

Magneto-convective flow through a porous enclosure with Hall current and thermal radiation effects: numerical study

This paper reports the numerical study of magnetohydrodynamic radiative-convective flow in a square cavity containing a porous medium with Hall currents. This study is relent to hydromagnetic fuel cell design and thermofluidic dynamics of complex magnetic liquid fabrication in enclosures. The governing equations of this fluid system are solved by a finite-difference vorticity stream function approach executed in MATLAB software. A detailed parametric investigation of the impact of Rayleigh number (thermal buoyancy parameter), Hartman number (magnetic body force parameter), Darcy number (permeability parameter), Hall parameter and radiation parameter on the streamline, temperature contours, local Nusselt number along the hot wall and mid-section velocity profiles is computed. Validation with previous special cases in the literature is included. Hall current and radiative effects are found to significantly modify thermofluidic characteristics. From the numerical results, it is found that the magnetic field suppresses the natural convection only for small buoyancy ratios. But, for larger buoyancy ratio, the magnetic field is effective in suppressing the thermal convective flow.

Duel Solutions in Hiemenz Flow of an Electro-Conductive Viscous Nanofluid Containing Elliptic Single-/Multi-Wall Carbon Nanotubes With Magnetic Induction Effects

Abstract Modern magnetic nanomaterials are increasingly embracing new technologies including smart coatings, intelligent lubricants, and functional working fluids in energy systems. Motivated by studying the manufacturing magnetofluid dynamics of electroconductive viscous nanofluids, in this work, we analyzed the magnetohydrodynamics (MHD) convection flow and heat transfer of an incompressible viscous nanofluid containing carbon nanotubes (CNTs) past a stretching sheet. Magnetic induction effects are included. Similarity solutions are derived where possible in addition to dual branch solutions. Both single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) are considered taking water and kerosene oil as base fluids. The governing continuity, momentum, magnetic induction, and heat conservation partial differential equations are converted to coupled, nonlinear systems of ordinary differential equations via similarity transformations. The emerging control parameters are shown to be Prandtl number (Pr), nanoparticle volume fraction parameter (φ), inverse magnetic Prandtl number (λ), magnetic body force parameter (β) and stretching rate parameter (A), and the type of carbon nanotube. Numerical solutions to the ordinary differential boundary value problem are conducted with the efficient bvp4c solver in matlab. Validation with earlier studies is included. Computations of reduced skin friction and reduced wall heat transfer rate (Nusselt number) are also comprised in order to identify the critical parameter values for the existence of dual solutions (upper and lower branch) for velocity, temperature, and induced magnetic field functions. Dual solutions are shown to exist for some cases studied. The simulations indicate that when the stretching rate ratio parameter is less than 1, SWCNT nanofluids exhibit higher velocity than MWCNT nanofluids with increasing magnetic parameters for water- and kerosene-oil-based CNT nanofluids. Generally, SWCNT nanofluids achieve enhanced heat transfer performance compared to MWCNT nanofluids. Water-based CNT nanofluids also attain greater flow acceleration compared with kerosene-oil-based CNT nanofluids.

Unsteady magnetohydrodynamic couple stress fluid flow from a shrinking porous sheet: Variational iteration method study

AbstractMotivated by magnetic polymer manufacturing applications, the present research article examines theoretically the hydromagnetic boundary layer flow of an electrically conducting non‐Newtonian couple stress fluid due to a transient shrinking (contracting) porous sheet. The conservation partial differential equations for mass and momentum are rendered into a fifth‐order nonlinear ordinary differential equation via similarity transformations with associated boundary conditions. A semi‐analytical/numerical scheme employing Lagrangian multipliers and known as the variational iteration method (VIM) is implemented to solve the ordinary differential boundary value problem. Validation of the solutions is conducted by benchmarking against earlier Newtonian studies and very good agreement is achieved. A detailed assessment of the impact of couple stress (rheological), unsteadiness, magnetic body force parameter, and wall transpiration (suction/injection) parameter on flow characteristics is conducted with the aid of graphs. A significant deceleration in the flow is computed with increasing injection (acceleration is caused with greater suction) and acceleration is induced with higher unsteadiness parameter values. Increasing magnetic field (higher magnetic number) generates flow acceleration, rather than the customary deceleration, due to the shrinking sheet dynamics. A stronger couple stress effect manifests in strong retardation in the boundary layer flow and an increase in momentum (hydrodynamic|) boundary layer thickness. VIM demonstrates excellent convergence and accuracy and shows significant promise in studying further magnetic polymer fabrication flow problems.

Finite element computation of magneto-hemodynamic flow and heat transfer in a bifurcated artery with saccular aneurysm using the Carreau-Yasuda biorheological model.

"Existing computational fluid dynamics studies of blood flows have demonstrated that the lower wall stress and higher oscillatory shear index might be the cause of acceleration in atherogenesis of vascular walls in hemodynamics. To prevent the chances of aneurysm wall rupture in the saccular aneurysm at distal aortic bifurcation, clinical biomagnetic studies have shown that extra-corporeal magnetic fields can be deployed to regulate the blood flow. Motivated by these developments, in the current study a finite element computational fluid dynamics simulation has been conducted of unsteady two-dimensional non-Newtonian magneto-hemodynamic heat transfer in electrically conducting blood flow in a bifurcated artery featuring a saccular aneurysm. The fluid flow is assumed to be pulsatile, non-Newtonian and incompressible. The Carreau-Yasuda model is adopted for blood to mimic non-Newtonian characteristics. The transformed equations with appropriate boundary conditions are solved numerically by employing the finite element method with the variational approach in the FreeFEM++ code. Hydrodynamic and thermal characteristics are elucidated in detail for the effects of key non-dimensional parameters i.e. Reynolds number (Re = 14, 21, 100, 200), Prandtl number (Pr = 14, 21) and magnetic body force parameter (Hartmann number) (M = 0.6, 1.2, 1.5) at the aneurysm and throughout the arterial domain. The influence of vessel geometry on blood flow characteristics i.e. velocity, pressure and temperature fields are also visualized through instantaneous contour patterns. It is found that an increase in the magnetic parameter reduces the pressure but increases the skin-friction coefficient in the domain. The temperature decreases at the parent artery (inlet) and both the distant and prior artery with the increment in the Prandtl number. A higher Reynolds number also causes a reduction in velocity as well as in pressure. The blood flow shows different characteristic contours with time variation at the aneurysm as well as in the arterial segment. The novelty of the current research is therefore to present a combined approach amalgamating the Carreau-Yasuda model, heat transfer and magnetohydrodynamics with complex geometric features in realistic arterial hemodynamics with extensive visualization and interpretation, in order to generalize and extend previous studies. In previous studies these features have been considered separately and not simultaneously as in the current study. The present simulations reveal some novel features of biomagnetic hemodynamics in bifurcated arterial transport featuring a saccular aneurysm which are envisaged to be of relevance in furnishing improved characterization of the rheological biomagnetic hemodynamics of realistic aneurysmic bifurcations in clinical assessment, diagnosis and magnetic-assisted treatment of cardiovascular disease."

Spectral relaxation computation of electroconductive nanofluid convection flow from a moving surface with radiative flux and magnetic induction

Abstract A theoretical model is developed for steady magnetohydrodynamic viscous flow resulting from a moving semi-infinite flat plate in an electrically conducting nanofluid. Thermal radiation and magnetic induction effects are included in addition to thermal convective boundary conditions. Buongiorno’s two-component nanoscale model is deployed, which features Brownian motion and thermophoresis effects. The governing nonlinear boundary layer equations are converted to nonlinear ordinary differential equations by using suitable similarity transformations. The transformed system of differential equations is solved numerically, employing the spectral relaxation method (SRM) via the MATLAB R2018a software. SRM is a simple iteration scheme that does not require any evaluation of derivatives, perturbation, and linearization for solving a nonlinear system of equations. Effects of embedded parameters such as sheet velocity parameter$\lambda$, magnetic field parameter$\beta$, Prandtl number$Pr$, magnetic Prandtl number$Prm$, thermal radiation parameter$Rd$, Lewis number$Le$, Brownian motion parameter$Nb$, and thermophoresis parameter$Nt$ on velocity, induced magnetic field, temperature, and nanoparticle concentration profiles are investigated. The skin-friction results, local Nusselt number, and Sherwood number are also discussed for various values of governing physical parameters. To show the convergence rate against iteration, residual error analysis has also been performed. The flow is strongly decelerated, and magnetic induction is suppressed with greater magnetic body force parameter, whereas temperature is elevated due to extra work expended as heat in dragging the magnetic nanofluid. Temperatures are also boosted with increment in nanoscale thermophoresis parameter and radiative parameter, whereas they are reduced with higher wall velocity, Brownian motion, and Prandtl numbers. Both hydrodynamic and magnetic boundary layer thicknesses are reduced with greater reciprocal values of the magnetic Prandtl number Prm. Nanoparticle (concentration) boundary layer thickness is boosted with higher values of thermophoresis and Prandtl number, whereas it is diminished with increasing wall velocity, nanoscale Brownian motion parameter, radiative parameter, and Lewis number. The simulations are relevant to electroconductive nanomaterial processing.

Computation of ferromagnetic/nonmagnetic nanofluid flow over a stretching cylinder with induction and curvature effects

AbstractMotivated by enrobing processes in manufacturing technology with intelligent coatings, this study analyses the flow of an electroconductive incompressible nanofluid with heat distribution in a boundary layer containing metallic nanoparticles or ferroparticles along an extending cylindrical body with magnetic induction effects. The quasilinear boundary conditions for the partial derivative formulations connecting to the far stream and cylinder wall are converted to ordinary nonlinear derivatives by applying appropriate similarity transformations. The emerging system of derivatives is solved by a stable, efficient spectral relaxation method (SRM). The SRM procedure is benchmarked with special limiting cases in the literature and found to corroborate exceptionally well with other studies in the literature. Here, water is taken as the base liquid containing homogenously suspended nonmagnetic (Nimonic 80a, silicon dioxide [SiO2]) or magnetic nanoparticles (ferric oxide [Fe3O4] and manganese franklinite [Mn–ZnFe2O4]). The influence of all key parameters on the velocity and temperature distributions is displayed in graphs and tables with extensive elucidation. The wall local drag force (skin friction) and local temperature gradient (Nusselt number) are also visualized graphically for various parameters. The rate of convergence of the SRM convergence is compared with that of the successive over‐relaxation method, and it is observed to converge faster. Larger magnetohydrodynamic body force parameter and inverse Prandtl magnetic number induce flow deceleration and enhance temperature. Flow acceleration is computed for SiO2 nonmagnetic nanoparticles, and good heat conduction augmentation is produced with magnetic nanoparticle Fe3O4.

Numerical Study of a Williamson Fluid Past a Semi-Infinite Vertical Plate with Convective Heating and Radiation Effects

In the present paper, we investigated mathematical model of the magnetohydrodynamic flow and heat transfer in an electro-conductive polymer on the externalsurface of a semi-infinite vertical plate under radial magnetic field. Thermal radiation andconvective heating effects are considered at the semi-infinite plate surface with modifiedboundary conditions. The Williamson viscoelastic model is employed which isrepresentative of certain industrial polymers. The non-dimensional, transformedboundary layer equations for momentum and energy are solved with the second orderaccurate implicit Keller box finite difference method under appropriate boundaryconditions. Validation of the numerical solutions is achieved via benchmarking withearlier published results. The influence of Williamson viscoelastic fluid parameter,magnetic body force parameter, convective heating, radiation parameter, stream wisevariable and Prandtl number on thermos-fluid characteristics are studied graphically. Themodel is relevant to the simulation of magnetic polymer materials processing.

Second law thermodynamic analysis of thermo-magnetic Jeffery–Hamel dissipative radiative hybrid nanofluid slip flow: existence of multiple solutions

In this article, a detailed theoretical examination is conducted for the steady, incompressible, MHD hybrid nanofluid (Al2O3/Cu–water) dissipative slip flow between non-parallel (i.e., diverging or converging) shrinking/stretching walls in the presence of appreciable thermal radiation. Appropriate similarity transformations have been applied to render the hybrid transport model conservation equations dimensionless. The diffusion flux approximation is employed for radiative heat transfer. The well-posed boundary value problem has been analyzed for solution bifurcations with a predictor homotopy analysis method (PHAM) along with stability analysis. The eigenvalues obtained predict the upper branch (Ist solution) to be physically acceptable. The critical values ( $$\chi_{c} \le \chi < 0$$ ) of stretching/shrinking parameter are evaluated by varying slip and magnetic body force parameters. The impact of significant parameters on skin friction coefficient, Nusselt number and entropy generation number is also visualized and elaborated in detail. With stronger magnetic field parameter (M), i.e., enhancement in magnetohydrodynamic Lorentz drag force, the existence domain of the dual solutions is shown to be expanded and the critical points of the stretching parameter ( $$\chi$$ ) for $$M = 0.1,0.5,1$$ are identified, respectively, as $$\chi_{c} = - 3.2455, - 3.2680,$$ $$- 3.2987$$ . The upper branch of skin friction, Cfr decreases as the volume fraction $$\varphi$$ increases whereas the lower branch increases with an increase in the volume fraction of copper nanoparticles. Entropy generation is observed to be elevated with stronger radiation, inertial effect (Reynolds number) and Prandtl number (i.e., lower thermal conductivity) whereas it is suppressed with increasing hybrid nanoparticle volume fraction and wall hydrodynamic slip effect. Magnetic field is found to induce a weak modification in entropy generation. Increasing angular coordinate $$\left( {\xi = \frac{\theta }{\beta }} \right)$$ is observed to elevate the entropy generation. The computations find applications in thermo-magnetic nozzle design, electromagnetic propulsion systems and electroconductive materials processing.

Non-similar radiative bioconvection nanofluid flow under oblique magnetic field with entropy generation

Motivated by exploring the near-wall transport phenomena involved in bioconvection fuel cells combined with electrically conducting nanofluids, in the present article, a detailed analytical treatment using homotopy analysis method (HAM) is presented of non-similar bioconvection flow of a nanofluid under the influence of magnetic field (Lorentz force) and gyrotactic microorganisms. The flow is induced by a stretching sheet under the action of an oblique magnetic field. In addition, nonlinear radiation effects are considered which are representative of solar flux in green fuel cells. A second thermodynamic law analysis has also been carried out for the present study to examine entropy generation (irreversibility) minimization. The influence of magnetic parameter, radiation parameter and bioconvection Rayleigh number on skin friction coefficient, Nusselt number, micro-organism flux and entropy generation number (EGN) is visualized graphically with detailed interpretation. Validation of the HAM solutions with published results is also included for the non-magnetic case in the absence of bioconvection and nanofluid effects. The computations show that the flow is decelerated with increasing magnetic body force parameter and bioconvection Rayleigh number whereas it is accelerated with stronger radiation parameter. EGN is boosted with increasing Reynolds number, radiation parameter and Prandtl number whereas it is reduced with increasing inclination of magnetic field.

MHD Free Convection-Radiation Interaction in a Porous Medium - Part II: Soret/Dufour Effects

This paper is focused on the study of two dimensional steady magnetohydrodynamics heat and mass transfer by laminar free convection from a radiative horizontal circular cylinder in a non-Darcy porous medium by taking into account of the Soret/Dufour effects. The boundary layer equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller–Box finite-difference scheme. Numerical results are obtained for the velocity, temperature and concentration distributions, as well as the local skin friction, Nusselt number and Sherwood number for several values of the parameters, namely the buoyancy ratio parameter, Prandtl number, Forchheimer number, magnetohydrodynamic body force parameter, Soret and Dufour numbers. The dependency of the thermophysical properties has been discussed on the parameters and shown graphically. Increasing the Forchheimer inertial drag parameter reduces velocity but elevates temperature and concentration. Increasing the Soret number and simultaneously reducing the Dufour number greatly boosts the local heat transfer rate at the cylinder surface. A comparative study of the previously published and present results in a limiting sense is made and an excellent agreement is found between the results.

Study of non-isothermal incompressible flow and heat flux of nano-ferrofluid with induced magnetic induction

Presently we have studied the nonlinear magnetohydrodynamic convective boundary-layer flow of water- based nano-ferrofluid adjacent to a non-isothermal stretching sheet. Three different ferrofluid suspensions are considered, namely water containing magnetite (Fe3O4), (Mn − Zn)and cobalt ferrite (CoFe2O4) ferriteferro-particles. Magnetic field is sufficiently strong to induce induction effects. Applying similarity transformations, the boundary region equations for mass, momentum, magnetic induction and energy are reduced to coupled, multi-degree, nonlinear differential equations. The non-dimensional boundary value problem is then solved computationally under specified wall and free stream conditions, with Maple quadrature and shooting techniques. Non-isothermal as well as constant heat flux cases are examined. The key parameters emerging in the model are the reciprocal of magnetic Prandtl number, Prandtl number, the reciprocal of magnetic body force parameter, heat source/sink parameter, nano-particle volume fraction and power-law index. The influence of these parameters on flow fields like velocity, temperature, and gradient of magnetic stream function for different ferro-particle cases, is presented graphically. Detailed elucidation of the results is also included. Validation is conducted with a finite element method (FEM). Significantly greater temperatures are observed for magnetite ferro-particles as compared with cobalt or Manganese-Zinc ferroparticles. Stream function (Magnetic) is found to be suppressed with increasing power-law index. With increasing magnetic force number there is a substantial elevation in induced magnetic field. Increasing reciprocal of magnetic Prandtl number i.e. decreasing magnetic Prandtl number leads to a depression in velocity i.e. flow deceleration, for the Fe3O4 − H2O magnetite ferrofluid. The study proposed here is of concern to the processing of nano-ferro-materials.

Finite element analysis of non‐Newtonian magnetohemodynamic flow conveying nanoparticles through a stenosed coronary artery

AbstractThe present study considers two‐dimensional mathematical modeling of non‐Newtonian nanofluid hemodynamics with heat and mass transfer in a stenosed coronary artery in the presence of a radial magnetic field. The second‐grade differential viscoelastic constitutive model is adopted for blood to mimic non‐Newtonian characteristics, and blood is considered to contain a homogenous suspension of nanoparticles. The Vogel model is employed to simulate the variation of blood viscosity as a function of temperature. The governing equations are an extension of the Navier‐Stokes equations with linear Boussinesq's approximation and Buongiorno's nanoscale model (which simulates both heat and mass transfer). The conservation equations are normalized by employing appropriate nondimensional variables. It is assumed that the maximum height of the stenosis is small in comparison with the radius of the artery, and, furthermore, that the radius of the artery and length of the stenotic region are of comparable magnitude. To study the influence of vessel geometry on blood flow and nanoparticle transport, variation in the design and size of the stenosis is considered in the domain. The transformed equations are solved numerically by means of the finite element method based on the variational approach and simulated using the FreeFEM++ code. A detailed grid‐independence study is included. Blood flow, heat, and mass transfer characteristics are examined for the effects of selected geometric, nanoscale, rheological, viscosity, and magnetic parameters, that is, stenotic diameter (d), viscoelastic parameter (), thermophoresis parameter (), Brownian motion parameter (), and magnetic body force parameter (M) at the throat of the stenosis and throughout the arterial domain. The velocity, temperature, and nanoparticle concentration fields are also visualized through instantaneous patterns of contours. An increase in magnetic and thermophoresis parameters is found to enhance the temperature, nanoparticle concentration, and skin‐friction coefficient. Increasing Brownian motion parameter is observed to accelerate the blood flow. Narrower stenosis significantly alters the temperature and nanoparticle distributions and magnitudes. The novelty of the study relates to the combination of geometric complexity, multiphysical nanoscale, and thermomagnetic behavior, and also the simultaneous presence of biorheological behavior (all of which arise in actual cardiovascular heat transfer phenomena) in a single work with extensive visualization of the flow, heat, and mass transfer characteristics. The simulations are relevant to the diffusion of nano‐drugs in magnet‐targeted treatment of stenosed arterial disease.

Cilia-assisted hydromagnetic pumping of biorheological couple stress fluids

A theoretical study is conducted for magnetohydrodynamic pumping of electro-conductive couple stress physiological liquids (e.g. blood) through a two-dimensional ciliated channel. A geometric model is employed for the cilia which are distributed at equal intervals and produce a whip-like motion under fluid interaction which obeys an elliptic trajectory. A metachronal wave is mobilized by the synchronous beating of cilia and the direction of wave propagation is parallel to the direction of fluid flow. A transverse static magnetic field is imposed transverse to the channel length. The Stokes’ couple stress (polar) rheological model is utilized to characterize the liquid. The normalized two-dimensional conservation equations for mass, longitudinal and transverse momentum are reduced with lubrication approximations (long wavelength and low Reynolds number assumptions) and feature a fourth order linear derivative in axial velocity representing couple stress contribution. A coordinate transformation is employed to map the unsteady problem from the wave laboratory frame to a steady problem in the wave frame. No slip conditions are imposed at the channel walls. The emerging linearized boundary value problem is solved analytically and expressions presented for axial (longitudinal) velocity, volumetric flow rate, shear stress function and pressure rise. The flow is effectively controlled by three geometric parameters, viz cilia eccentricity parameter, wave number and cilia length and two physical parameters, namely magnetohydrodynamic (MHD) body force parameter and couple stress non-Newtonian parameter. Analytical solutions are numerically evaluated with MATLAB software. Axial velocity is observed to be enhanced in the core region with greater wave number whereas it is suppressed markedly with increasing cilia length, couple stress and magnetic parameters, with significant flattening of profiles with the latter two parameters. Axial pressure gradient is decreased with eccentricity parameter whereas it is elevated with cilia length, in the channel core region. Increasing couple stress and magnetic field parameter respectively enhance and suppress pressure gradient across the entire channel width. The pressure-flow rate relationship is confirmed to be inversely linear and pumping, free pumping and augmented pumping zones are all examined. Bolus trapping is also analyzed. The study is relevant to MHD biomimetic blood pumps.

Computation of Melting Dissipative Magnetohydrodynamic Nanofluid Bioconvection with Second-order Slip and Variable Thermophysical Properties

This paper studies the combined effects of viscous dissipation, first and second-order slip and variable transport properties on phase-change hydromagnetic bio-nanofluid convection flow from a stretching sheet. Nanoscale materials possess a much larger surface to volume ratio than bulk materials, significantly modifying their thermodynamic and thermal properties and substantially lowering the melting point. Gyrotactic non-magnetic micro-organisms are present in the nanofluid. The transport properties are assumed to be dependent on concentration and temperature. Via appropriate similarity variables, the governing equation with boundary conditions are converted to nonlinear ordinary differential equations and are solved using the BVP4C subroutine in the symbolic software MATLAB. The non-dimensional boundary value features a melting (phase change) parameter, temperature-dependent thermal conductive parameter, first as well as second-order slip parameters, mass diffusivity parameter, Schmidt number, microorganism diffusivity parameter, bioconvection Schmidt number, magnetic body force parameter, Brownian motion and thermophoresis parameters. Extensive computations are visualized for the influence of these parameters. The present simulation is of relevance in the fabrication of bio-nanomaterials for bio-inspired fuel cells.

Magnetohydrodynamic viscous fluid flow and heat transfer in a circular pipe under an externally applied constant suction

An analytical investigation of two-dimensional heat transfer behavior of an axisymmetric incompressible dissipative viscous fluid flow in a circular pipe is considered. The flow is subjected to an externally applied uniform suction over the pipe wall in the transverse direction and a constant magnetic field opposite to the wall. The reduced Navier-Stokes equations in the cylindrical system are applied for the velocity and temperature fields. Constant wall temperature is considered as the thermal boundary condition. The velocity components are expressed into stream function and its solution is acquired by the Homotopy analysis method (HAM). The effects of magnetic body force parameter(M), suction Reynolds number (Re), Prandtl number (Pr)and Eckert number (Ec) on velocity and temperature are examined and are presented in a graphical frame. Streamlines, isotherms and pressure contours are likewise pictured. It is observed that with increasing suction Reynold number decelerates axial flow, whereas it enhances the radial flow. The temperature distribution increases with an increase in Prandtl number, whereas it decreases with an increase in Eckert number (viscous dissipation effect).

Unsteady Chemo-Tribological Squeezing Flow of Magnetized Bioconvection Lubricants: Numerical Study

Corrosion in lubricating systems involves many complex phenomena including chemical reaction, surfacial degradation, heat dissipation and unsteady effects. Biomimetic design is increasingly being employed in many branches of engineering (including tribology) and involves the mimicking of biological phenomena to achieve enhanced performance of systems. One such mechanism is known as bioconvection and characterizes micro-organism propulsion. Smart lubricants may exploit electromagnetic properties. Motivated by these developments, the current study examines the unsteady mixed bioconvection magnetohydrodynamic squeeing flow of a Newtonian lubricant doped with both gyrotactic micro-organisms and a species which is reactive, and intercalated between two surfaces squeezing together. No slip velocity conditions are imposed at the channel walls. The lubricant is chemically reactive and obeys a first order homogenous destructive reaction.The time-dependent conservation equations for mass (continuity), momentum, heat, species diffusion and motile miro-organism species are normalized with the aid of appropriate similarity transformationss to yield a non-linear, coupled, multi-degree ordinary differential boundary value problem (BVP). This BVP is solved using MATLAB bvp4c quadrature. Validation with earlier studies is included. Further verification of the MATLAB solutions is achieved with a Multi-Step DTM Algorithm, “MS-DTM”. The key parameters dictating the flow problem emerge as bioconvection Lewis number, bioconvection Peclet number (ratio of advection to diffusion of micro-organisms), Schmidt number, Prandtl number, magnetic body force parameter, reaction parameter, heat source/sink parameter and squeeze flow parameter. Selected computations for velocity, temperature, species concentration and motile micro-organism density function are visualized and exhibit considerable sensitivity to variation in most parameters. Detailed interpretation is included.