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Abstract Measurement errors play an important role in the development of goniometric equipment, devices used to measure range of motion. Reasonable validity and reliability are critical for both the device and examiner before and after to testing in human subjects. The objective is to evaluate the concurrent validity and reliability of five different clinical goniometric devices for the purpose of establishing an acceptable measurement error margin for a novel device. We explored the validity and inter- and intrarater reliability scores of five goniometric devices namely (i) the universal goniometer (UG), a two-armed hand-held goniometer, (ii) the inclinometer (IC), featuring a single base, fluid level, and gravity-weighted inclinometer, (iii) the digital inclinometer (DI), functioning as both a DI and dynamometer, (iv) the smartphone application (SA), employing gyroscope-based technology within a smartphone platform application and (v) the modified inclinometer (MI), a gravity pendulum-based inclinometer equipped with a specialized fixing apparatus. Measurements were obtained at 12 standard angles and 8 human shoulder flexion angles ranging from 0° to 180°. Over two testing sessions, 120 standardized angle measurements and 160 shoulder angle measurements from 20 shoulders were repetitively taken by three examiners for each device. The intraclass correlation coefficient (ICC), standard error of measurement (SEM), and minimal detectable change (MDC) were calculated to assess reliability and validity. Concurrent validity was also evaluated through the execution of the 95% limit of agreement (95% LOA) and Bland–Altman plots, with comparisons made to the UG. The concurrent validity for all device pairs was excellent in both study phases (ICC > 0.99, 95% LOA − 4.11° to 4.04° for standard angles, and − 10.98° to 11.36° for human joint angles). Inter- and intrarater reliability scores for standard angles were excellent across all devices (ICC > 0.98, SEM 0.59°–1.75°, MDC 1°–4°), with DI showing superior reliability. For human joint angles, device reliability ranged from moderate to excellent (ICC 0.697–0.975, SEM 1.93°–4.64°, MDC 5°–11° for inter-rater reliability; ICC 0.660–0.996, SEM 0.77°–4.06°, MDC 2°–9° for intra-rater reliability), with SA demonstrating superior reliability. Wider angle measurement however resulted in reduced device reliability. In conclusion, our study demonstrates that it is essential to assess measurement errors independently for standard and human joint angles. The DI is the preferred reference for standard angle testing, while the SA is recommended for human joint angle testing. Separate evaluations across the complete 0°–180° range offer valuable insights.

A theoretical and numerical study is conducted on nonlinear, steady-state thermal convection boundary layer flow of a magnetized incompressible Tangent Hyperbolic non-Newtonian fluid from a rotating cone to a non-Darcy porous medium. Power-law variation in temperature on the cone surface is considered and thermal radiation heat transfer is also present. The Brinkman-Darcy-Forchheimer model is deployed for the porous medium. The study is motivated by rotational (spin) coating with new emerging magnetic rheological polymers, a process which often utilizes filtration media and high temperatures. The transformed non-dimensional conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. Extensive visualization of axial, tangential velocity components and temperature distributions with variation in key parameters including Rosseland radiative number, Darcy number, Forchheimer number (non-Darcy inertial parameter), magnetic interaction parameter, tangent-hyperbolic non-Newtonian power-law index and Weissenberg (non-Newtonian) number is included. Additionally, axial and tangential (circumferential) skin friction and Nusselt number values are tabulated for variation in key control parameters. With increasing Weissenberg number, axial velocity is depleted near the cone surface, tangential velocity is suppressed throughout the boundary layer regime and temperature is strongly enhanced. Axial flow is strongly decelerated further from the cone surface with increasing tangent-hyperbolic power-law index and there is also a significant depletion in tangential (swirl) velocity. Temperature is however boosted throughout the boundary layer transverse to the cone surface with a rise in tangent-hyperbolic power-law index. Both tangential and axial velocity are suppressed with increment in magnetic interaction parameter whereas temperature and thermal boundary layer thickness are enhanced. With larger Darcy number (i.e. greater permeability), axial velocity is strongly increased near the cone surface with no tangible modification further from the cone; However tangential velocity is consistently elevated throughout the boundary layer with greater Darcy number whereas temperature is depleted. An increase in Forchheimer number substantially damps both axial and tangential velocity whereas it elevates temperature. Increasing radiative flux strongly energizes the magnetic polymer and elevates temperature but suppresses the axial and tangential velocities. With elevation in non-isothermal wall exponent, axial skin friction is suppressed whereas Nusselt number are elevated at the cone vertex. Further along the cone surface a similar response is observed but there is also a reduction in magnitudes of tangential skin friction.

Abstract Modern smart coating systems are increasingly exploiting functional materials which combine multiple features including rheology, electromagnetic properties and nanotechnological capabilities and provide a range of advantages in diverse operations including medical, energy and transport designs (aerospace, marine, automotive). The simulation of the industrial synthesis of these multi-faceted coatings (including stagnation flow deposition processes) requires advanced mathematical models which can address multiple effects simultaneously. Inspired by these requests, this study investigates the interconnected magnetohydrodynamic non-Newtonian movement and thermal transfer in the Hiemenz plane's stagnation flow. Additionally, it explores the application of a transverse static magnetic field to a ternary hybrid nanofluid coating through theoretical and numerical analysis. The base fluid (polymeric) considered is engine-oil (EO) doped with graphene $$\left(GO\right)$$ G O , gold $$\left(Au\right)$$ A u and Cobalt oxide $$\left(C{o}_{3}{O}_{4}\right)$$ C o 3 O 4 nanoparticles. The model includes the integration of non-linear radiation, heat source, convective wall heating, and magnetic induction effects. For non-Newtonian characteristics, the Williamson model is utilized, while the Rosseland diffusion flux model is used for radiative transfer. Additionally, a non-Fourier Cattaneo–Christov heat flux model is utilized to include thermal relaxation effects. The governing partial differential conservation equations for mass, momentum, energy and magnetic induction are rendered into a system of coupled self-similar and non-linear ordinary differential equations (ODEs) with boundary restrictions using appropriate scaling transformations. The dimensionless boundary value problem that arises is solved using the bvp4c built-in function in MATLAB software, which employs the fourth-order Runge–Kutta (RK-4) method. An extensive examination is conducted to evaluate the impact of essential control parameters on the velocity $$f{^{\prime}}\left(\zeta \right)$$ f ′ ζ , induced magnetic field stream function gradient $$g{^{\prime}}\left(\zeta \right)$$ g ′ ζ and temperature $$\theta \left(\zeta \right)$$ θ ζ is conducted. The relative performance of ternary, hybrid binary and unitary nanofluids for all transport characteristics is evaluated. The inclusion of verification of the MATLAB solutions with prior studies is incorporated. Fluid velocity is observed to be minimized for the ternary $$\mathrm{GO}$$ GO – $$\mathrm{Au}$$ Au – $${\mathrm{Co}}_{3}{\mathrm{O}}_{4}$$ Co 3 O 4 nanofluid whereas the velocity is maximized for the unitary cobalt oxide $$\left({\mathrm{Co}}_{3}{\mathrm{O}}_{4}\right)$$ Co 3 O 4 nanofluid with increasing magnetic parameter ( $$\beta ).$$ β ) . Temperatures are elevated with increment in thermal radiation parameter (Rd). Streamlines are strongly modified in local regions with greater viscoelasticity i.e. higher Weissenberg number $$(We)$$ ( W e ) . Dimensionless skin friction is significantly greater for the ternary hybrid $$GO$$ GO – $$Au$$ Au – $$C{o}_{3}{O}_{4}/EO$$ C o 3 O 4 / E O nanofluid compared with binary hybrid or unitary nanofluid cases.

Abstract Hybrid nanofluids (HNFs) comprise combinations of different nanoparticles suspended in base fluid. Applications of such nanofluids are rising in the areas of energy and biomedical engineering including smart (functional) coatings. Motivated by these developments, the present article examines theoretically the magnetohydrodynamic coating boundary layer flow of HNFs from a stretching sheet under the transverse magnetic field in porous media with chemically reactive nanoparticles. Darcy’s law is deployed. Momentum slips of both first and second order are included as is solutal slip. The transformed boundary value problem is solved analytically. Closed form solutions for velocity are derived in terms of exponential functions and for the concentration field in terms of incomplete Gamma functions by the application of the Laplace transformation technique. The influence of selected parameters e.g. suction/injection, magnetic field and slips on velocity and concentration distributions are visualized graphically. Concentration magnitudes are elevated with stronger magnetic field whereas they are suppressed with greater wall solutal slip. Magnetic field suppresses velocity and increases the thickness of the hydrodynamic boundary layer. The flow is accelerated with reduction in inverse Darcy number and stronger suction direct to reduce in skin friction. The concentration magnitudes are boosted with magnetic field whereas they are depleted with increasing solutal slip. The analysis provides a good foundation for further investigations using numerical methods.

Abstract A mathematical model is developed for stagnation point flow toward a stretching or shrinking sheet of liquid nano-biofilm containing spherical nano-particles and bioconvecting gyrotactic micro-organisms. Variable transport properties of the liquid (viscosity, thermal conductivity, nano-particle species diffusivity) and micro-organisms (species diffusivity) are considered. Buongiorno’s two-component nanoscale model is deployed and spherical nanoparticles in a dilute nanofluid considered. Using a similarity transformation, the nonlinear systems of partial differential equations is converted into nonlinear ordinary differential equations. These resulting equations are solved numerically using a central space finite difference method in the CodeBlocks Fortran platform. Graphical plots for the distribution of reduced skin friction coefficient, reduced Nusselt number, reduced Sherwood number and the reduced local density of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and the density of motile microorganisms are presented for the influence of wall velocity power-law index (m), viscosity parameter $$({c}_{2})$$ ( c 2 ) , thermal conductivity parameter (c 4 ), nano-particle mass diffusivity (c 6 ), micro-organism species diffusivity (c 8 ), thermophoresis parameter $$(Nt)$$ ( N t ) , Brownian motion parameter $$(Nb)$$ ( N b ) , Lewis number $$(Le)$$ ( L e ) , bioconvection Schmidt number $$(Sc)$$ ( S c ) , bioconvection constant (σ) and bioconvection Péclet number $$(Pe)$$ ( P e ) . Validation of the solutions via comparison related to previous simpler models is included. Further verification of the general model is conducted with the Adomian decomposition method (ADM). Extensive interpretation of the physics is included. Skin friction is elevated with viscosity parameter ( $${\mathrm{c}}_{2})$$ c 2 ) whereas it is suppressed with greater Lewis number and thermophoresis parameter. Temperatures are elevated with increasing thermal conductivity parameter ( $${\mathrm{c}}_{4})$$ c 4 ) whereas Nusselt numbers are reduced. Nano-particle volume fraction (concentration) is enhanced with increasing nano-particle mass diffusivity parameter ( $${c}_{6}$$ c 6 ) whereas it is markedly reduced with greater Lewis number (Le) and Brownian motion parameter (Nb). With increasing stretching/shrinking velocity power-law exponent ( $$m),$$ m ) , skin friction is decreased whereas Nusselt number and Sherwood number are both elevated. Motile microorganism density is boosted strongly with increasing micro-organism diffusivity parameter ( $${\mathrm{c}}_{8}$$ c 8 ) and Brownian motion parameter (Nb) but reduced considerably with greater bioconvection Schmidt number (Sc) and bioconvection Péclet number (Pe). The simulations find applications in deposition processes in nano-bio-coating manufacturing processes.

The present study deals with the electrically conducting micropolar nanofluid flow from a vertical stretching surface adjacent to a porous medium under a transverse magnetic field. Eringen’s micropolar model is deployed for non-Newtonian characteristics and the Buongiorno nanofluid model employed for nanoscale effects (thermophoresis and Brownian motion). The model includes double stratification (thermal and solutal) and also chemical reaction effects, heat source, and viscous dissipation. Darcy’s model is employed for the porous medium and a Rosseland diffusion flux approximation for nonlinear thermal radiation. The nonlinear governing partial differential conservation equations are rendered into nonlinear ordinary differential equations via relevant transformations. An innovative semi-numerical methodology combining the Adomian decomposition method (ADM) with Padé approximants and known as ADM-Padé is deployed to solve the emerging nonlinear ordinary differential boundary value problem with appropriate wall and free stream conditions in MATLAB software. A detailed parametric study of the influence of key parameters on stream function, velocity, microrotation (angular velocity), temperature, and nanoparticle concentration profiles is conducted. Furthermore, skin friction coefficient, wall couple stress coefficient, Nusselt number, and Sherwood number are displayed in tables. The validation of both numerical techniques used, i.e., ADM and ADM-Padé, against a conventional numerical 4th order Runge–Kutta method is also included and significant acceleration in convergence of solutions achieved with the ADM-Padé approach. The flow is decelerated with greater buoyancy ratio parameter whereas microrotation (angular velocity) is enhanced. Increasing thermal and solutal stratification suppresses microrotation. Concentration magnitudes are boosted with greater chemical reaction parameter and Lewis number. Temperatures are significantly enhanced with radiative parameter. Increasing Brownian motion parameter depletes concentration values. The study finds applications in thermomagnetic coating processes involving nanomaterials with microstructural characteristics.

Motivated by emerging high-temperature manufacturing processes deploying nano-polymeric coatings, the present study investigates nonlinear thermally radiative Oldroyd-B viscoelastic nanoliquid stagnant-point flow from a heated vertical stretching permeable surface. Robin (mixed derivative) conditions were utilized in order to better represent coating fabrication conditions. The nanoliquid analysis was based on Buongiorno’s two-component model, which features Brownian movement and thermophoretic attributes. Nonlinear buoyancy force and thermal radiation formulations are included. Chemical reactions (constructive and destructive) were also considered since coating synthesis often features reactive transport phenomena. An ordinary differential equation model was derived from the primitive partial differential boundary value problem using a similarity approach. The analytical solutions were achieved by employing a homotopy analysis scheme. The influence of the emerging dimensionless quantities on the transport characteristics was comprehensively explained using appropriate data. The obtained analytical outcomes were compared with the literature and good correlation was achieved. The computations show that the velocity profile was diminished with an increasing relaxation parameter, whereas it was enhanced when the retardation parameter was increased. A larger thermophoresis parameter induces an increase in temperature and concentration. The heat and mass transfer rates at the wall were increased with incremental increases in the temperature ratio and first order chemical reaction parameters, whereas contrary effects were observed for larger thermophoresis, fluid relaxation and Brownian motion parameters. The simulations can be applied to the stagnated nano-polymeric coating of micromachines, robotic components and sensors.

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. Keywords: Magnetohydrodynamics, Metachronal waves, Cilia, Synchronous beating, Polar couple stress fluid, Physiological transport, Magnetic blood pumps

Stimulated by thermal optimization in magnetic materials process engineering, the present investigation investigates theoretically the entropy generation in mixed convection magnetohydrodynamic (MHD) flow of an electrically-conducting nanofluid from a vertical cylinder. The mathematical model includes the effects of viscous dissipation, second order velocity slip and thermal slip, has been considered. The cylindrical partial differential form of the two-component non-homogenous nanofluid model has been transformed into a system of coupled ordinary differential equations by applying similarity transformations. The effects of governing parameters with no-flux nanoparticle concentration have been examined on important quantities of interest. Furthermore, the dimensionless form of the entropy generation number has also been evaluated using homotopy analysis method (HAM). The present analytical results achieve good correlation with numerical results (shooting method). Entropy is found to be an increasing function of second order velocity slip, magnetic field and curvature parameter. Temperature is elevated with increasing curvature parameter and magnetic parameter whereas it is reduced with mixed convection parameter. The flow is accelerated with curvature parameter but decelerated with magnetic parameter. Heat transfer rate (Nusselt number) is enhanced with greater mixed convection parameter, curvature parameter and first order velocity slip parameter but reduced with increasing second order velocity slip parameter. Entropy generation is also increased with magnetic parameter, second order slip velocity parameter, curvature parameter, thermophoresis parameter, buoyancy parameter and Reynolds number whereas it is suppressed with first order velocity slip parameter, Brownian motion parameter and thermal slip parameter. Keywords: Magnetohydrodynamic (MHD), Nanofluid, Vertical cylinder, Homotopy analysis method (HAM), Second order slip, Entropy, Curvature

In this paper, we have examined the magnetohydrodynamic flow of a nanofluid past a radiating sheet. The Navier velocity slip, Newtonian heating and passively controlled wall boundary conditions are considered. The governing equations are reduced into similarity equations with the help of Lie group. A collocation method is used for simulation. The influence of emerging parameters on velocity, temperature, nanoparticle volumetric fraction profiles, as well as on local skin friction factor and local Nusselt number is illustrated in detail. It is found that the friction (heat transfer rate) is lower (higher) for passively controlled boundary conditions as compared to the case of an actively controlled boundary condition. The magnetic field effects decrease both the skin friction and the rate of heat transfer. The findings are validated with existing results and found an excellent agreement. The model explores new applications in solar collectors with direct solar radiative input using magnetic nanofluids. Keywords: Lie group, Navier slip flow, Newtonian heating, Nonlinear radiation, Passively controlled boundary condition, MHD

Electrokinetic transport of fluids through microchannels by micro-pumping and micro- peristaltic pumping has stimulated considerable interest in biomedical engineering and other areas of medical technology. Deeper elucidation of the fluid dynamics of such transport requires the continuous need for more elegant mathematical models and numerical simulations, in parallel with laboratory investigations. In this article we therefore investigate analytically the unsteady viscous flow driven by the combined effects of peristalsis and electro-osmosis through microchannel. An integral number of waves propagating in the microchannel are considered as a model for transportation of fluid bolus along the channel length. Debye-Hückel linearization is employed to evaluate the potential function. Low Reynolds number and large wavelength approximations are employed. Closed-form solutions are derived for the non-dimensional boundary value problem. The computations demonstrate that magnitude of electric potential function is increased with a decrease in the thickness of the electrical double layer (EDL). Stronger electric field also decelerates the flow and decreases local wall shear stress. Hydrodynamic pressure is increased with EDL thickness whereas it is suppressed with electric field. Streamline visualization reveals that the quantity of trapped bolus is decreased with increase in EDL thickness and also with higher external electric field. Keywords: Peristalsis, Electrokinetic phenomenon, Trapping, Electric double layer, Analytical approach

Gliding bacteria are virtually everywhere. These organisms are phylogenetically diverse with their hundreds of types, different shapes and several modes of motility. One possible mode of gliding motility in the rod shaped bacteria is that they propel themselves by producing undulating waves in their body. Few bacteria glides near the solid surface over the slime without any aid of flagella so the classical Navier-Stokes equations are incapable of explaining the slime rheology at the microscopic level. Micropolar fluid dynamics however provides a solid framework for mimicking bacterial physical phenomena at both micro and nano-scales, and therefore we use the micropolar fluid to characterize the rheology of a thin layer of slime and its dominant microrotation effects. It is also assumed that there is a certain degree of slip between slime and bacterial undulating surface and also between slime and solid substrate. The flow equations are formulated under long wavelength and low Reynolds number assumptions. Exact expressions for stream function and pressure gradient are obtained. The speed of the gliding bacteria is numerically calculated by using a modified Newton-Raphson method. Slip effects and effects of non-Newtonian slime parameters on bacterial speed and power are also quantified. In addition, when the glider is fixed, the effects of slip and rheological properties of micropolar slime parameters on the velocity, micro-rotation (angular velocity) of spherical slime particles, pressure rise per wavelength, pumping and trapping phenomena are also shown graphically and discussed in detail. The study is relevant to emerging biofuel cell technologies and also bacterial biophysics. Keywords: Gliding bacteria, Undulating surface model, Micropolar fluid, Slip effects, Exact solution, Modified Newton-Raphson method

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.

Inherent irreversibility in the flow of a reactive third grade fluid though a channel with convective heating is examined. It is well known that heat dissipated from the exothermic chemical reaction passes through fluid in an irreversible manner and as a result entropy is generated continuously within the channel. Analytical solutions of the resulting dimensionless nonlinear boundary-value-problems arising from the governing equations were obtained by using perturbation method. These solutions are utilized to obtain the entropy generation rate and Bejan number for the system. The influence of various important parameters on the entropy generation rate and Bejan number are shown graphically and discussed accordingly.

The present study investigates the entropy generation in magnetized-micropolar fluid flow in between two vertical concentric rotating cylinders of infinite length. The surface of the inner cylinder is heated while the surface of the outer cylinder is cooled. Internal heat generation is incorporated. The Eringen thermo-micropolar fluid model is used to simulate the micro-structural rheological flow characteristics in the annulus region. The flow is subjected to a constant, static, axial magnetic field. The surface of the inner cylinder is prescribed to be isothermal whereas the surface of the outer cylinder was exposed to convection cooling. The conservation equations are normalized and closed-form solutions are obtained for the velocity, microrotation, temperature, entropy generation number, Bejan number and total entropy generation rate. The effects of the relevant parameters are displayed graphically. It is observed that the external magnetic force enhances the entropy production rate and it is maximum in the proximity of the inner cylinder. This causes more wear and tear at the surface of the inner cylinder. Greater Hartmann number also elevates microrotation values in the entire annulus region. The study is relevant to optimization of chemical engineering processes, nuclear engineering cooling systems and propulsion systems utilizing non-Newtonian fluids and magnetohydrodynamics.

A numerical investigation of two dimensional steady state laminar boundary layer flow of a viscous electrically-conducting nanofluid in the vicinity of a stretching/shrinking porous flat plate located in a Darcian porous medium is performed. The nonlinear Rosseland radiation effect is taken into account. Velocity slip and thermal slip at the boundary as well as the newly developed zero mass flux boundary conditions are also implemented to achieve physically applicable results. The governing transport equations are reduced to a system of nonlinear ordinary differential equations using appropriate similarity transformations and these are then solved numerically using a variational finite element method (FEM). The influence of the governing parameters (Darcy number, magnetic field, velocity and thermal slip, temperature ratio, transpiration, Brownian motion, thermophoresis, Lewis number and Reynolds number) on the dimensionless velocity, temperature, nanoparticle volume fraction as well as the skin friction, the heat transfer rates and the mass transfer rates are examined and illustrated in detail. The FEM code is validated with earlier studies for non-magnetic non-slip flow demonstrating close correlation. The present study is relevant to high-temperature nano-materials processing operations.

A mathematical study for two-phase unsteady pulsatile flow of blood through a vessel in the presence of body acceleration is presented in this paper. The blood in the core region is modeled as a non-Newtonian fluid while in the peripheral region it is described as a Newtonian fluid. The effects of body acceleration are also taken into account in this study. The continuity and momentum equations are used to model the proposed problem in terms of a nonlinear partial differential equation. This equation along with initial and boundary conditions is made dimensionless and then solved numerically using finite difference method. The behavior of various flow quantitates is analyzed through a parametric study.

A theoretical and numerical study is presented to analyze the nonlinear, non-isothermal, magnetohydrodynamic (MHD) free convection boundary layer flow and heat transfer in a non-Darcian, isotropic, homogenous porous medium, in the presence of Hall currents, Ionslip currents, viscous heating and Joule heating. A power-law variation is used for the temperature at the wall. The governing nonlinear coupled partial differential equations for momentum conservation in the x and z directions and heat conservation, in the flow regime are transformed from an (x, y, z) coordinate system to a (ξ,η) coordinate system in terms of dimensionless x-direction velocity (∂F/∂η) and z-direction velocity (G) and dimensionless temperature function (H) under appropriate boundary conditions. Both Darcian and Forchheimer porous impedances are incorporated in both momentum equations. Computations are also provided for the variation of the x and z direction shear stress components and also local Nusselt number. Excellent correlation is achieved with a Nakamura tridiagonal finite difference scheme (NTM). The model finds applications in magnetic materials processing, MHD power generators and purification of crude oils.

In this article, we investigate the nonlinear steady boundary layer flow and heat transfer of an incompressible Tangent Hyperbolic fluid from a sphere. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely Weissenberg number (We), power law index (n), Prandtl number (Pr), Biot number (γ) and dimensionless tangential coordinate (ξ) on velocity and temperature evolution in the boundary layer regime is examined in detail. Furthermore, the effects of these parameters on heat transfer rate and skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation is achieved. It is found that the velocity, Skin friction and the Nusselt number (heat transfer rate) are decreased with increasing Weissenberg number (We), whereas the temperature is increased. Increasing power law index (n) increases the velocity and the Nusselt number (heat transfer rate) but decreases the temperature and the Skin friction. An increase in the Biot number (γ) is observed to increase velocity, temperature, local skin friction and Nusselt number. The study is relevant to chemical materials processing applications.

Buoyancy-driven convective heat and mass transfer in boundary layer flow of a viscoelastic Jeffrey fluid from a permeable isothermal sphere embedded in a porous medium is studied. Thermal radiation flux and heat generation/absorption are also incorporated in the model. A non-Darcy drag force model is employed to simulate the effects of linear porous media drag and second order Forchheimer drag. The Rosseland diffusion algebraic approximation is utilized to simulate thermal radiation effects. The non-dimensionalized boundary layer equations are solved using implicit, finite-difference scheme. The influence of Darcy number (Da), Deborah number (De), ratio of relaxation to retardation times (λ), radiation parameter (F), Forchheimer inertial parameter (Λ) and heat generation/absorption parameter (Δ), on normalized velocity, temperature, concentration, skin friction, heat and mass transfer rates are also studied. The present study has applications in the storage of nuclear waste materials.

We present a mathematical model and numerical simulation of the unsteady 2-D g-jitter-free and forced the convective flow of water-based nanofluid from a flat plate, considering both the velocity slip and thermal slip conditions imposed on the wall of the plate. The Darcian model is used, and both cases of a calm and moving free stream are considered. In place of the extensively used linearly varying radiative heat flux, the nonlinearly varying heat flux calculation is applied to produce practically useful results. Further, we incorporate the “zero mass flux boundary condition” which is believed to be more realistic than the earlier extensively used “actively” controlled model. The parameter influences the non-dimensional velocity, temperature, nanoparticle volume fraction, skin friction and heat transfer rates are visualized graphically and discussed in detail. Special cases of the results are benchmarked with those existing in the literature, and a good arrangement is obtained. It is found that the rate of heat transfer is lower for the calm free stream rather than the moving free stream.

This study focuses analytically on the oscillatory hydromagnetic flow of a viscous, incompressible, electrically-conducting, non-Newtonian fluid in an inclined, rotating channel with non-conducting walls, incorporating couple stress effects. The model is then non-dimensionalized with appropriate variables and shown to be controlled by the inverse Ekman number (K2 = 1/Ek), the hydromagnetic body force parameter (M), channel inclination (α), Grashof number (Gr), Prandtl number (Pr), oscillation frequency (ω) and time variable (ωT). Analytical solutions are derived using complex variables. Excellent agreement is obtained between both previous and present work. The influence of the governing parameters on the primary velocity, secondary velocity, temperature (θ), primary and secondary flow discharges per unit depth in the channel, and frictional shear stresses due to primary and secondary flow, is studied graphically and using tables. Applications of the study arise in the simulation of the manufacture of electrically-conducting polymeric liquids and hydromagnetic energy systems exploiting rheological working fluids.

A semi-analytical solution for the convection of a power-law nanofluid external to three different geometries (i.e., cone, wedge and plate), subject to convective boundary condition is presented. A revised Buongiorno model is employed for the nanofluid transport over the various geometries with variable wall temperature and nanoparticle concentration conditions (non-isothermal and non-iso-solutal). Wall transpiration is included. The dimensional governing equations comprising the conservation of mass, momentum, energy and nanoparticle volume fraction are transformed to dimensionless form using appropriate transformations. The transformed equations are solved using a robust semi-analytical power series method known as the Homotopy analysis method (HAM). The convergence and validation of the series solutions is considered in detail. The variation of order of the approximation and computational time with respect to residual errors for temperature for the different geometries is also elaborated. The influence of thermophysical parameters such as wall temperature parameter, wall concentration parameter for nanofluid, Biot number, thermophoresis parameter, Brownian motion parameter and suction/blowing parameter on the velocity, temperature and nanoparticle volume fraction is visualized graphically and tabulated. The impact of these parameters on the engineering design functions, e.g., coefficient of skin fraction factor, Nusselt number and Sherwood number is also shown in tabular form. The outcomes are compared with the existing results from the literature to validate the study. It is found that thermal and solute Grashof numbers both significantly enhance the flow velocity whereas they suppress the temperature and nanoparticle volume fraction for the three different configurations, i.e., cone, wedge and plate. Furthermore, the thermal and concentration boundary layers are more dramatically modified for the wedge case, as compared to the plate and cone. This study has substantial applications in polymer engineering coating processes, fiber technology and nanoscale materials processing systems.

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.

The magneto-hemodynamic laminar viscous flow of a conducting physiological fluid in a semi-porous channel under a transverse magnetic field has been analyzed by the optimal Homotopy Analysis Method (OHAM) and Differential Transform Method (DTM) under physically realistic boundary conditions first. Then as the main purpose of this study the important designing subject, entropy generation of this system, has been analyzed. The influence of Hartmann number (Ha) and transpiration Reynolds number (mass transfer parameter, Re) on the fluid velocity profiles in the channel are studied in detail first. After finding the fluid velocity profiles, graphical results are presented to investigate effects of the Reynolds number, Hartmann number, x-velocity of the moving plate, suspension height and dimensionless horizontal coordinate on the entropy generation.

A mathematical model is presented for three-dimensional unsteady boundary layer slip flow of Newtonian nanofluids containing gyrotactic microorganisms over a stretching cylinder. Both hydrodynamic and thermal slips are included. By applying suitable similarity transformations, the governing equations are transformed into a set of nonlinear ordinary differential equations with appropriate boundary conditions. The transformed nonlinear ordinary differential boundary value problem is then solved using the Runge-Kutta-Fehlberg fourth-fifth order numerical method in Maple 18 symbolic software. The effects of the controlling parameters on the dimensionless velocity, temperature, nanoparticle volume fractions and microorganism motile density functions have been illustrated graphically. Comparisons of the present paper with the existing published results indicate good agreement and supports the validity and the accuracy of our numerical computations. Increasing bioconvection Schmidt number is observed to depress motile micro-organism density function. Increasing thermal slip parameter leads to a decrease in temperature. Thermal slip also exerts a strong influence on nano-particle concentration. The flow is accelerated with positive unsteadiness parameter (accelerating cylinder) and temperature and micro-organism density function are also increased. However nano-particle concentration is reduced with positive unsteadiness parameter. Increasing hydrodynamic slip is observed to boost temperatures and micro-organism density whereas it decelerates the flow and reduces nano-particle concentrations. The study is relevant to nano-biopolymer manufacturing processes.

A mathematical study on creeping flow of non-Newtonian fluids (power law model) through a nonuniform peristaltic channel, in which amplitude is varying across axial displacement, is presented, with slip effects included. The governing equations are simplified by employing the long wavelength and low Reynolds number approximations. The expressions for axial velocity, stream function, pressure gradient, and pressure difference are obtained. Computational and numerical results for velocity profile, pressure gradient, and trapping under the effects of slip parameter, fluid behavior index, angle between the walls, and wave number are discussed with the help of Mathematica graphs. The present model is applicable to study the behavior of intestinal flow (chyme movement from small intestine to large intestine). It is also relevant to simulations of biomimetic pumps conveying hazardous materials, polymers, and so forth.

The present analysis is motivated by the need to elucidate with more accuracy and sophistication the hydrodynamics of non-Newtonian flow via a channel containing a porous material under pulsating pressure gradient. A one-dimensional transient rheological model for pulsating flow through a Darcy-Forcheimmer porous channel is used. A modified Casson non-Newtonian constitutive model is employed for the transport fluid with a drag force formulation for the porous body force effects. The model is transformed and solved using a finite element numerical technique. Rheological effects are examined using a β parameter which vanishes in the limit (Newtonian flow). Velocity profiles are plotted for studying the influence of Reynolds number, Darcy number, Forchheimer number and the β (non-Newtonian) parameter. The channel considered is rigid with a pulsatile pressure applied via an appropriate pressure gradient term. The model finds applications in industrial filtration systems, pumping of polymeric fluids etc.

In the present paper we examine the steady double-diffusive free convective heat and mass transfer of a chemically-reacting micropolar fluid flowing through a Darcian porous regime adjacent to a vertical stretching plane. Viscous dissipation effects are included in the energy equation. Assuming incompressible, micro-isotropic fluid behaviour the transport equations are formulated in a two-dimensional coordinate system (x, y) using boundary-layer theory. The influence of the bulk porous medium retardation is modeled as a drag force term in the translational momentum equation. Transformations render the conservation equations into dimensionless form in terms of a single independent variable, η, transverse to the stretching surface. A simplified first order homogenous reaction model is also used to simulate chemical reaction in the flow. Using the finite element method solutions are generated for the angular velocity field, translational velocity field, temperature and species transfer fields. The effects of buoyancy, porous drag and chemical reaction rate are studied. Chemical reaction is shown to decelerate the flow and also micro-rotation values, in particular near the wall. Mass transfer is also decreased with increasing chemical reaction rate. Increasing Darcy number is shown to accelerate the flow. Applications of the study include cooling of electronic circuits, packed-bed chemical reactors and also the near field flows in radioactive waste geo-repositories.

The convective heat transfer on a rotating sphere in the presence of magnetic field, buoyancy forces and impulsive motion is examined theoretically and numerically in this paper. We apply a boundary layer model comprising the balance equations for x and y direction translational momentum and heat transfer, and solve these coupled non-linear partial differential equations using Blottner’s finite-difference method [1]. The numerical solutions are benchmarked with the earlier study by Lee [2] on laminar boundary layer flow over rotating bodies in forced flow and found to be in excellent agreement. The effects of magnetic field, buoyancy parameter, Prandtl number and thermal conductivity parameter on translational velocities and temperature and other variables (shear stress etc) are presented graphically and discussed at length. The problem finds applications in chemical engineering technologies, aerodynamics and planetary astrophysics.