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A mathematical model is developed for viscous slip flow and heat transfer in water/Ethylene\ud glycol-based nanofluids containing metallic oxide nanoparticles, through a\ud converging/diverging channel geometry. Our approach is based on the single-phase Tiwari–\ud Das nanofluid model considering nanoparticles and base fluid masses as a substitute volume\ud concentration of nanoparticles. The governing (dimensional partial differential) equations are\ud transformed to a set of dimensionless ordinary differential equations with the help of similarity\ud transformation, before being solved numerically using Maple17. Extensive validation of the\ud velocity gradient and temperature solutions is achieved with the second order implicit finite\ud difference Keller Box method (KBM). Further validation is included for the special case of noslip nanofluid flow in the absence of viscous heating. The effects of the emerging parameters\ud namely velocity slip, thermal jump, channel apex angle, Eckert number, Prandtl number,\ud Reynolds number and nano-particle volume fraction on velocity, temperature, skin friction and\ud heat transfer rate are investigated in detail. Two different nanofluids are studied, namely\ud water-Titanium oxide- and Ethylene glycol-Titanium oxide. Both convergent and divergent\ud channels are addressed, and significantly different thermofluid characteristics are computed\ud due to slip and viscous heating effects. The novelty of the current work is that it extends\ud previous studies to include multiple slip effects and viscous heating (Eckert number effects)\ud which are shown to exert a significant influence on heat and momentum transfer\ud characteristics. The study is relevant to certain pharmaco-dynamics devices (drug delivery),\ud next generation 3-D nanotechnological printers and also nano-cooling systems in energy\ud engineering where laminar flows in diverging/converging channels arise.

The dynamic and static problems of finding stress component under four moving punches (a ≤ |X| ≤ b, c ≤ |X| ≤ d), located closely to each other over an elastic half-plane (Y = 0), are solved. Employing the Fourier integral transform, the problem is converted to a set of integral equations. Using Hilbert transform technique, the integral equations are solved to obtain the stress and the displacement components. Finally, exact expressions for the stress components under the punches and the normal displacement component in the regions outside the punches have been derived. Numerical results showing the variations in stress intensity factors (SIF) at the punch ends and absolute value of torque applied over the contact regions with different values of the parameters used in the problems have been presented in the form of graphs.

Two-dimensional laminar hemodynamics through a diseased artery featuring an overlapped\ud stenosis was simulated theoretically and computationally. This study presented a mathematical model for the unsteady\ud blood flow with hybrid biocompatible nanoparticles (Silver and Gold) inspired by drug delivery applications. A\ud modified Tiwari-Das volume fraction model was adopted for nanoscale effects. Motivated by the magnetohemodynamics effects, a uniform magnetic field was applied in the radial direction to the blood flow. For realistic\ud blood behavior, Reynolds’ viscosity model was applied in the formulation to represent the temperature dependency\ud of blood. Fourier’s heat conduction law was assumed, and heat generation effects were included. Therefore, the\ud governing equations were an extension of the Navier-Stokes equations with magneto-hydrodynamic body force\ud included. The two-dimensional governing equations were transformed and normalized with appropriate variables,\ud and the mild stenotic approximation was implemented. The strongly nonlinear nature of the resulting dimensionless\ud boundary value problem required a robust numerical method, and therefore the FTCS algorithm was deployed.\ud Validation of solutions for the particular case of constant viscosity and non-magnetic blood flow was included. Using\ud clinically realistic hemodynamic data, comprehensive solutions were presented for silver, and silver-gold hybrid\ud mediated blood flow. A comparison between silver and hybrid nanofluid was also included, emphasizing the use of\ud hybrid nanoparticles for minimizing the hemodynamics. Enhancement in magnetic parameter decelerated the axial\ud blood flow in stenotic region. Colored streamline plots for blood, silver nano-doped blood, and hybrid nano-doped\ud blood were also presented. The simulations were relevant to the diffusion of nano-drugs in magnetic targeted treatment\ud of stenosed arterial diseases

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.

The non-linear, non-isothermal, magnetohydrodynamic (MHD) laminar convection flows of\ud Buongiorno’s nanofluid past a vertical surface with Darcy-Forchheimer model is mathematically\ud investigated in the present article. Keller’s Box implicit finite difference technique is utilized to\ud solve the dimensionless conservation equations. Graphical and tabulated results are analyzed to\ud study the behavior of primary and secondary velocity, temperature, nanoparticle volume fraction,\ud shear stress rate, heat transfer rate and mass transfer rate for various emerging thermos-physical\ud parameters. The Hall current and ion slip current effects are also considered. Validations of earlier\ud solutions in the literature is also included. The study finds applications in nanomaterial fabrication\ud processing, biomedical, polymer processing, chemical engineering, crude oil purifying, etc.

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

Buoyancy-driven reactive flows feature extensively in geophysics, materials processing and energy systems. In respect to the latter, geothermal energy holds great promise in India and other Asian geographical locations and offers immense resources in the 21st century. Motivated by such applications, in the current study a mathematical model is developed for thermo-solutal convection flow in an open two-dimensional vertical channel containing a porous medium saturated with reactive Newtonian fluid is studied. Robin boundary conditions are prescribed and a first order homogenous chemical reaction is considered. The Darcy-Forchheimer model is used to simulate both first and second order porous medium drag effects. The reference temperatures are taken as symmetric or asymmetric. Viscous heating is also included in the model. The conservation equations are written in dimensionless form taking into account the effects of viscous dissipation. For the case of small Brinkman number (i.e.viscous heating parameter) and neglecting the Forchheimer quadratic drag effect, perturbation solution of the simpler Darcian boundary value problem is developed. For the general non-Darcy-case, a numerical solution is presented with the Runge-Kutta quadrature and a shooting method. Good correlation between analytical and numerical solutions is demonstrated. The influence of thermal and solute Grahsof numbers, Biot numbers, Brinkman number, first order chemical reaction parameter, porous medium parameter and Forchheimer (inertial drag) parameter on velocity, temperature and concentration (species) distributions is visualized graphically. Nusselt number and skin friction at the walls are computed for selected parameters relevant to real geothermics. Increasing porous media parameter (decreasing medium permeability) reduces temperatures for both equal and unequal Biot numbers. Increasing thermal Grashof number accelerates the flow and elevates temperatures for both equal and unequal Biot numbers. With higher values of solutal Grashof number velocity and temperature near the cold plate (wall) are reduced whereas the converse behaviour is induced at the hot wall. Increasing chemical reaction parameter elevates the species concentration in the left half space of the channel whereas it suppresses concentration in the right half space and in both scenarios a parabolic distribution is observed. In the absence of chemical reaction, a linear growth in concentration is computed from the left plate to the right plate. With increasing porous medium parameter and Forchheimer inertial parameter the flow is strongly decelerated across the channel span whereas there is a much weaker reduction in temperatures. Skin friction is consistently lowered at both plates with increasing thermal Grashof number for equal Biot numbers. However, with unequal Biot numbers, skin friction at the left plate is increased whereas it is still reduced at the right plate. With increasing solutal Grashof number, skin friction is always reduced at both plates for both equal and unequal Biot numbers. There is also a consistent decrease in Nusselt numbers at both plates with increasing solutal Grashof number.

Motivated by recent developments in bio-inspired medical engineering microscale pumps, in\ud the present article a 3-dimensional sequential simulation of a peristaltic micro-pump is\ud described to provide deeper insight into the hydromechanics of laminar, viscous flow in\ud peristaltic propulsion. The Carreau and power-law models are employed for non-Newtonian\ud behavior. The commercial software package ANSYS Fluent is utilized to conduct a numerical\ud simulation of laminar peristaltic pump fluid dynamics, based on the finite volume method and\ud steady space laminar solver. Details are provided for the geometric pump design (conducted\ud with AUTOCAD), pre-processing (meshing) and necessary boundary conditions to simulate\ud the peristaltic flow within the pump. Extensive visualization of velocity, pressure and vorticity\ud contours is included. The present simulations provide a benchmark for future comparison with\ud experimental studies and indeed more advanced numerical simulations with alternative nonNewtonian models. Applications of the study include biomimetic blood flow pumps, blood\ud dialysis machines, microscale infusion pumps etc.

The hydrodynamics of immiscible micropolar fluids is important in a variety of engineering problems, including biofluid dynamics of arterial blood flows, pharmacodynamics, Principle of Boundary layers, lubrication technology, short waves for heat-conducting fluids, sediment transportation, magnetohydrodynamics, multicomponent hydrodynamics, and electrohydrodynamic. Motivated by the development of biological fluid modeling and medical diagnosis instrumentation, this article examines the combined effects of ion slip, viscous dissipation, Joule heating, and Hall current on unsteady generalized magnetohydrodynamic (MHD) Couette flow of two immiscible fluids. Two non-Newtonian incompressible magnetohydrodynamic micropolar and micropolar dusty (fluid-particle suspension) fluids are considered in a horizontal duct with heat transfer. No-slip boundary conditions are assumed at the channel walls and constant pressure gradient. Continuous shear stress and fluid velocity are considered across the interface between the two immiscible fluids. The coupled partial differential equations are formulated for fluids and particle phases and the velocities, temperatures, and microrotation profiles are obtained. Under the physically realistic boundary and interfacial conditions, the Modified cubic B-spline differential quadrature method (MCB-DQM) is deployed to obtain numerical results. The influence of the magnetic, thermal, and other pertinent parameters, i.e. Hartmann magnetic number, Eckert (dissipation) number, Reynolds number, Prandtl number, micropolar material parameters, Hall and ion-slip parameters, particle concentration parameter, viscosity ratio, density ratio, and time on velocity, microrotation, and temperature characteristics are illustrated through graphs. The MCB-DQM is found to be in good agreement with accuracy and the skin friction coefficient and Nusselt number are also explored. It is found that fluids and particle velocities are reduced with increasing Hartmann numbers whereas they are elevated with increment in ion-slip and Hall parameters. Temperatures are generally enhanced with increasing Eckert number and viscosity ratio. The simulations are relevant to nuclear heat transfer control, MHD energy generators, and electromagnetic multiphase systems in chemical engineering.

In present paper, we simulate the electro-kinetic transport of aqueous solution through a microchannel containing porous media. The micro-channel walls are simulated as complex wavy\ud surface and are modelled by superimposing the three wave functions of different amplitudes\ud but the same wavelength. The micro-channel contains an isotropic, homogenous porous\ud medium, which is analysed with a generalized Darcy law. The nonlinear-coupled governing\ud equations for mass, momentum and electrical potential conservation are simplified using low\ud Reynolds number and long wavelength approximations, and the Debye electro-kinetic\ud linearization. Following non-dimensional transformation of the linearized boundary value\ud problem, closed-form analytical solutions are presented for the velocity components, pressure\ud gradient, local wall shear stress, average flow rate and stream function subject to physically\ud appropriate boundary conditions. Validation with a finite difference method is also conducted.\ud The effect of permeability parameter, Debye length (i.e. characteristic thickness of electrical\ud double layer) and electro-osmotic velocity on flow characteristics is illustrated graphically and\ud interpreted at length. The study finds applications in chromatography, hybrid electro-osmotic\ud micro-pumps, transport phenomena in chemical engineering and energy systems exploiting\ud electro-kinetics.

Heat and mass transfer in variable thermal conductivity micropolar axisymmetric stagnation enrobing flow on a cylinder is studied. Numerical solutions are obtained with an optimized variational finite element procedure and also a finite difference method. Graphical variations of velocity, angular velocity, temperature and concentration are presented for the effects of Reynolds number, viscosity ratio, curvature parameter, Prandtl number and Schmidt number. Excellent agreement is obtained for both finite element method (FEM) and finite difference method (FDM) computations. Further validation is achieved with a Chebyshev spectral collocation method (SCM). Skin friction is elevated with greater Reynolds number whereas it is suppressed with increasing micropolar parameter. Heat transfer rate decreases with an increase in the thermal conductivity parameter. Temperature and thermal boundary layer thickness is reduced with increasing thermal conductivity parameter and Reynolds number. Greater Reynolds number accelerates the micro-rotation values. Higher Schmidt number reduces the mass transfer function (species concentration) values. The mathematical model is relevant to polymeric manufacturing coating (enrobing) flows.

A mathematical model is presented for the nonlinear steady, forced convection, hydromagnetic flow of electro-conductive magnetic nanopolymer 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 subject to appropriate boundary conditions. Keller’s implicit finite difference “box” method 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 nanomaterials (fluids) processing technologies.

In this study heat transfer effects on cilia induced mucus flow in human airways is presented. The elliptic wave pattern of cilia tips produces metachronal wave which enables the transportation of highly viscous mucus with nonzero inertial forces. Upper Convective Maxwell model is considered as mucus. The governing partial differential equations are transformed from the fixed frame to the wave frame by using Galilean transformation and viscous dissipation is also incorporated in the energy equation. The non-linear governing equations are evaluated by the perturbation technique by using software “MATHEMATICA” and pressure rise is computed by numerical integration. The impact of interested parameters on temperature profile, velocity, pressure rise and pressure gradient are plotted by the graphs. The comparison of velocities due to symplectic and antiplectic metachronal wave are also achieved graphically.

Mathematical modelling of mechanical system in microfluidics is an emerging area of interest in micro scale engineering. Since microfluidic devices use the hair like structure of artificial cilia for pumping, mixing and sensing in different fields, therefore; electro osmotic cilia driven flow help to generate the fluid velocity for the Newtonian and viscoelastic fluid. Due to the deployment of artificial ciliated walls, the present research reports the combined effect of an electro osmotic flow and convective heat transfer on Jeffrey viscoelastic electrolytic fluid flow in a two-dimensional ciliated vertical channel. Heat generation/absorption and nonlinear radiation effects are included in the present mathematical model. After applying Debye-Huckel approximation and small Reynolds number approximation to momentum and energy equation, the system of nonlinear partial differential equation is reduced into non-homogenous boundary value problem. The problem determines the velocity, pressure and temperature profiles by the application of semi-analytical technique known as Homotopy Perturbation Method (HPM) with the help of software Mathematica. The graphical results of the study suggest that HPM is a reliable methodology for thermo physical electro-osmotic rheological transport in micro channels. [Abstract copyright: Copyright © 2021 by ASME.]

Blood flow dynamics contributes an elemental part in the formation and expansion of cardiovascular\ud diseases in human body. Computational simulation of blood flow in the human arterial system has been widely\ud used in recent decades for better understanding the symptomatic spectrum of various diseases, in order to improve\ud already existing or develop new therapeutic techniques. The characteristics of the blood flow in an artery can be\ud changed significantly by arterial diseases, such as aneurysms and stenoses. The progress of atherosclerosis or\ud stenosis in a blood vessel is quite common which may be caused due to the addition of lipids in the arterial wall.\ud Nanofluid is a colloidal mixture of nanometer sized (which ranges from 10-100m) metallic and non-metallic\ud particles in conventional fluid (such as water, oil). The delivery of nanoparticles is an interesting and growing\ud field in the development of diagnostics and remedies for blood flow complications. An enhancement of nano-drug\ud delivery performance in biological systems, nanoparticles properties such as size, shape and surface characteristics\ud can be regulated. Nanoparticle offers remarkably advantages over the traditional drug delivery in terms of high\ud specificity, high stability, high drug carrying capacity, ability for controlled release. Highly dependency has been\ud found for their behavior under blood flow while checking for their ability to target and penetrate tissues from the\ud blood. In the field of nano-medicine, organic (including polymeric micelles and vesicles, liposomes) and inorganic\ud (gold and mesoporous silica, copper) nanoparticles have been broadly studied as particular carriers because as\ud drug delivery systems they delivered a surprising achievement as a result of their biocompatibility with tissue and\ud cells, their subcellular size, decreased toxicity and sustained release properties. For the extension of nanofluids\ud research, the researchers have also tried to use hybrid nanofluid recently, which is synthesized by suspending\ud dissimilar nanoparticles either in mixture or composite form. The main idea behind using the hybrid nanofluid is\ud to further improve the heat transfer and pressure drop characteristics. Nanoparticles are helpful as drug carriers to\ud minimize the effects of resistance impedance to blood flow or coagulation factors due to stenosis. Discussed\ud various robust approaches have been employed for the nanoparticle transport through blood in arterial system.\ud The main objective of the paper is to provide a comprehensive review of computational simulations of blood flow\ud containing hybrid-nanoparticles as drug carriers in the arterial system of the human body. The recent developments\ud and analysis of convective flow of particle-fluid suspension models for the axi-symmetric arterial bodies in\ud hemodynamics are summarized. Detailed existing mathematical models for simulating blood flow with\ud nanoparticles in stenotic regions are reviewed. The review focuses on selected numerical simulations of\ud physiological convective flows under various stenosis approximations and computation of the temperature, velocity, resistance impedance to flow, wall shear stress and the pressure gradient with the corresponding boundary\ud conditions. The current review also highlights that the drug carrier nanoparticles are efficient mechanisms for\ud reducing hemodynamics of stenosis and could be helpful for other biomedical applications. The review considers\ud flows through various stenoses and the significances of numerical fluid mechanics in clinical medicine. The review\ud examines nano-drug delivery systems, nanoparticles and describes recent computational simulations of nanopharmacodynamics.

The composite effects of nonlinear radiation, melting (phase change) heat transfer and Soret and Dufour cross-diffusion in nanofluid boundary layer flow external to an inclined stretching cylinder are studied theoretically. Buongiorno’s nanoscale model is deployed, and viscous dissipation, first-order chemical reaction and internal heat source effects are included. Curvature of the cylinder is also examined in the mathematical model. The transformed non-dimensional conservation equations are solved under pertinent wall and free stream boundary conditions numerically with shooting quadrature and a fourth-order Runge–Kutta method (RKM). Validation with a generalized differential quadrature (GDQ) numerical scheme is included. Graphs are presented to study the impact of various pertinent parameters on axial velocity, temperature and nanofluid concentration profiles. Additionally, skin friction, Nusselt number and Sherwood number are tabulated for selected parameters. Temperature and nanoparticle concentration magnitudes are reduced with increasing melting heat transfer parameter, whereas the flow is accelerated. Velocity is decreased with increasing inclination of the cylinder to the vertical, i.e. decreasing tilt relative to the horizontal owing to a reduction in thermal and species buoyancy forces. Increasing curvature parameter, Prandtl number, thermophoresis and Brownian motion, nanoscale parameters elevate the Nusselt number whereas higher values of melting parameter, Soret number, Dufour number, radiation parameter and temperature ratio parameter produce the opposite effect. Sherwood number at the cylinder surface is suppressed with greater melting parameter, Soret number and Dufour number, whereas it is boosted with greater curvature of the cylinder. The simulations are relevant to nanomaterial coating dynamics in manufacturing technologies.

Non-Newtonian flow from a wedge constitutes a fundamental problem in chemical engineering systems and is relevant to processing of polymers, coating systems, etc. Motivated by such applications, the homotopy analysis method (HAM) was employed to obtain semi-analytical solutions for thermal convection boundary layer flow of incompressible micropolar fluid from a two-dimensional body (wedge). Viscous dissipation and heat sink effects were included. The non-dimensional boundary value problem emerges as a system of nonlinear coupled ordinary differential equations, by virtue of suitable coordinate transformations. The so-called Falkner-Skan flow cases are elaborated. Validation of the HAM solutions was achieved with earlier simpler models, as well as with a Nakamura finite difference method for the general model. The micropolar model employed simulates certain polymeric solutions quite accurately, and features rotary motions of micro-elements. Primary and secondary shear stress, wall couple stress, Nusselt number, microrotation velocity, and temperature were computed for the effect of vortex viscosity parameter (micropolar rheological), Eckert number (viscous dissipation), Falkner-Skan (pressure gradient) parameter, micro-inertia density, and heat sink parameter. The special cases of Blasius and stagnation flow were also addressed. It was observed from the study that the temperature and thermal boundary layer thickness are both suppressed with increasing wedge parameter and wall heat sink effect, which is beneficial to temperature regulation in polymer coating dynamics. Further, strong reverse spin was generated in the microrotation with increasing vortex viscosity, which resulted in increase in angular momentum boundary layer thickness. Also, both primary and secondary skin friction components were reduced with increasing wedge parameter. Nusselt number was also enhanced substantially with greater wedge parameter.

Thermal coating of components with non-Newtonian materials is a rich area of chemical and process\ud mechanical engineering. Many different rheological characteristics can be simulated for such coatings with a\ud variety of different mathematical models. In this work we study the steady-state coating flow and heat transfer\ud of a non-Newtonian liquid (polymer) on an inverted isothermal cone with variable wall temperature. The\ud Eringen micropolar and three-parameter Eyring-Powell models are combined to simulate microstructural and\ud shear characteristics of the polymer. The governing partial differential conservation equations and wall and free\ud stream boundary conditions are rendered into dimensionless form and solved computationally with the KellerBox finite difference method (FDM). Validation with earlier Newtonian solutions from the literature is also\ud included. Graphical and tabulated results are presented to study the variations of fluid velocity, micro-rotation\ud (angular velocity), temperature, skin friction, wall couple stress (micro-rotation gradient) and wall heat transfer\ud rate. With increasing values of the first Eyring-Powell parameter temperatures are elevated, micro-rotation is\ud suppressed and velocities are enhanced near the cone surface but reduced further into the boundary layer.\ud Increasing values of the second Eyring-Powell parameter induce strong flow deceleration, decrease temperatures\ud but enhance micro-rotation values. An increase in non-isothermal power law index suppresses velocities,\ud temperatures and micro-rotations i.e. all transport characteristics are maximum for the isothermal case (n =0).\ud Increasing Eringen vortex viscosity parameter significantly enhances temperatures and also micro-rotations. The\ud present numerical simulations find applications in thermal polymer coating operations and industrial deposition\ud techniques and provide a useful benchmark for more general computational fluid dynamics (CFD) simulations.

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.

Physiological transport phenomena often feature ciliated internal walls. Heat, momentum and multi-species mass transfer may arise and additionally non-Newtonian biofluid characteristics are common in smaller vessels. Blood (containing hemoglobin) or other physiological fluids containing ionic constituents in the human body respond to magnetic body forces when subjected to external (extra-corporeal) magnetic fields. Inspired by such applications, in the present work we consider the forced convective flow of an electrically-conducting viscoelastic physiological fluid through a ciliated channel under the action of a transverse magnetic field. The flow is generated by a metachronal wave formed by the tips of cilia which move to and fro in a synchronized fashion. The presence of deposits (fats, cholesterol etc) in the channel is mimicked with a Darcy porous medium drag force model. The two-dimensional unsteady momentum equation and energy equation are simplified with a stream function and small Reynolds' number approximation. The effect of energy loss is simulated via the inclusion of viscous dissipation in the energy conservation (heat) equation. The non-dimensional, transformed moving boundary value problem is solved with appropriate wall conditions via the semi-numerical Adomian decomposition method (ADM). The velocity, temperature and pressure distribution are computed in the form of infinite series constructed by ADM and numerically evaluated in a symbolic software (MATHEMATICA). Streamline distributions are also presented. The influence of Hartmann number (magnetic parameter), Jeffrey first and second viscoelastic parameters, permeability parameter (modified Darcy number), and Brinkman number (viscous heating parameter) on velocity, temperature, pressure gradient and bolus dynamics is visualized graphically. The flow is decelerated with increasing with increasing Hartmann number and Jeffery first parameter in the core flow whereas it is accelerated in the vicinity of the walls. Increasing permeability and Jeffery second parameter are observed to accelerate the core flow and decelerate the peripheral flow near the ciliated walls. Increasing Hartmann number elevates pressure gradient whereas it is reduced with permeability parameter. Temperatures are elevated with increasing magnetic parameter, Brinkman number and Jeffery second parameter. Increasing magnetic field is also observed to reduce the quantity of trapped boluses. Increasing permeability parameter suppresses streamline amplitudes. Both the magnitude and quantity of trapped boluses is elevated with an increase in both first and second Jeffery parameters.

The mathematics of imaging is a growing field of research and is evolving rapidly parallel to evolution in the field of imaging. Imaging, which is a sub-field of biomedical engineering, considers novel approaches to visualize biological tissues with the general goal of improving health. "Medical imaging research provides improved diagnostic tools in clinical settings and supports the development of drugs and other therapies. The data acquisition and diagnostic interpretation with minimum error are the important technical aspects of medical imaging. The image quality and resolution are really important in portraying the internal aspects of patient's body. Although there are several user friendly resources for processing image features, such as enhancement, colour manipulation and compression, the development of new processing methods is still worthy of efforts. In this article we aim to present the role of fractional calculus in imaging with the aid of practical examples. (C) 2018 Elsevier Ltd. All rights reserved.

Buoyancy-driven (“Falkner-Skan”) mixed convection flow of a nanofluid from a nonisothermal wedge has been investigated numerically using an implicit finite difference scheme. The model used for nanofluid includes the effects of Brownian motion, buoyancy ratio and thermophoresis. A non-similarity solution is developed which depends on the Prandtl number (Pr), Schmidt number (Sc), Brownian motion number (Nb), buoyancy ratio parameter (Nr), thermophoresis number (Nt), mixed convection parameter (λ) and pressure gradient parameter (m). The variation of the skin friction, the reduced heat transfer rate and reduced mass transfer rate with Nb, Nr and Nt for various values of Pr, m and Sc are also tabulated.

In this article, the combined magnetohydrodynamic heat, momentum and mass (species) transfer in external boundary layer flow of Casson nanofluid from a horizontal circular cylinder surface with convective condition under an applied magnetic field is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer convective conditions. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum, energy and concentration equations via appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. The influences of the emerging parameters i.e. magnetic parameter (M), Casson fluid parameter (β), Brownian motion parameter (Nb) and thermophoresis parameter (Nt), Lewis number (Le), Prandtl number (Pr) and thermal slip (ST) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. Validation of solutions with a Nakamura tridiagonal method has been included. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace and other industries.

A theoretical and computational study of the magnetohydrodynamic flow and free convection heat transfer in an electroconductive polymer on the external surface of a vertical plate under radial magnetic field is presented. The Biot number effects are considered at the vertical plate surface via modified boundary conditions. The Williamson viscoelastic model is employed which is representative of certain industrial polymers. The nondimensional, transformed boundary layer equations for momentum and energy are solved with the second-order accurate implicit Keller box finite difference method under appropriate boundary conditions. Validation of the numerical solutions is achieved via benchmarking with earlier published results. The influence of Weissenberg number (ratio of the relaxation time of the fluid and time scale of the flow), magnetic body force parameter, stream-wise variable, and Prandtl number on thermo fluid characteristics are studied graphically and via tables. A weak elevation in temperature accompanies increasing Weissenberg number, whereas a significant acceleration in the flow is computed near the vertical plate surface with increasing Weissenberg number. Nusselt number is reduced with increasing Weissenberg number. Skin friction and Nusselt number are both reduced with increasing magnetic field effect. The model is relevant to the simulation of magnetic polymer materials processing.

To provide a deeper insight of the transport phenomena inherent to the manufacturing of magnetic nano-polymer materials, in the present work a mathematical model is developed for time-dependent hydromagnetic rheological nano-polymer boundary layer flow and heat transfer over a stretching sheet in the presence of a transverse static magnetic field. Joule heating (Ohmic dissipation) and viscous heating effects are included since these phenomena arise frequently in magnetic materials processing. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. The Tiwari–Das nanoscale model is adopted which permits different nanoparticles to be simulated (in this article, both copper–water and aluminium oxide–water nanofluids are considered). Similarity transformations are utilized to convert the governing partial differential conservation equations into a system of coupled, non-linear ordinary differential equations with appropriate wall and free stream boundary conditions. The shooting technique is used to solve the reduced non-linear coupled ordinary differential boundary value problem via MATLAB symbolic software. Validation with published results from the literature is included for the special cases of non-dissipative and Newtonian nanofluid flows. Fluid velocity and temperature profiles for both copper and aluminium oxide (Al2O3) nanofluids are observed to be enhanced with greater non-Newtonian couple stress parameter and magnetic parameter, whereas the opposite trend is computed with greater values of unsteadiness parameter. The boundary layer flow is accelerated with increasing buoyancy parameter, elastic sheet stretching parameter and convection parameter. Temperatures are generally increased with greater couple stress rheological parameter and are consistently higher for the aluminium oxide nanoparticle case. Temperatures are also boosted with magnetic parameter and exhibit an overshoot near the wall when magnetic parameter exceeds unity (magnetic force exceeds viscous force). A decrease in temperatures is induced with increasing sheet stretching parameter. Increasing Eckert number elevates temperatures considerably. With greater nanoparticle volume fraction, both skin friction and Nusselt number are elevated, and copper nanoparticles achieve higher magnitudes than aluminium oxide.

This paper presents an analytical study of magnetohydrodynamics and convective heat transfer of nanofluids synthesized by three different shaped (brick, platelet and cylinder) silver (Ag) nanoparticles in water. A two-phase nanoscale formulation is adopted which is more appropriate for biophysical systems. The flow is induced by metachronal beating of cilia and the flow geometry is considered as a cylindrical tube. The analysis is carried out under the low Reynolds number and long wavelength approximations and the fluid and cilia dynamics is of the creeping type. A Lorentzian magnetic body force model is employed and magnetic induction effects are neglected. Solutions to the transformed boundary value problem are obtained via numerical integration. The influence of cilia length parameter, Hartmann (magnetic) number, heat absorption parameter, Grashof number (free convection), solid nanoparticle volume fraction, and cilia eccentricity parameter on the flow and heat transfer characteristics (including effective thermal conductivity of the nanofluid) are examined in detail. Furthermore a comparative study for different nanoparticle geometries (i.e. bricks, platelets and cylinders) is conducted. The computations show that pressure increases with enhancing the heat absorption, buoyancy force (i.e. Grashof number) and nanoparticle fraction however it reduces with increasing the magnetic field. The computations also reveal that pressure enhancement is a maximum for the platelet nano-particle case compared with the brick and cylinder nanoparticle cases. Furthermore the quantity of trapped streamlines for cylinder type nanoparticles exceeds substantially that computed for brick and platelet nanoparticles, whereas the bolus magnitude (trapped zone) for brick nanoparticles is demonstrably greater than that obtained for cylinder and platelet nanoparticles.The present model is applicable in biological and biomimetic transport phenomena exploiting magnetic nanofluids and ciliated inner tube surfaces.

Laminar natural convection plume of a microstructural non-Newtonian fluid along a vertical surface about a line heat source in a saturated high permeability porous medium is studied. The transformed non-linear boundary value problem is solved numerically using a rigorously tested SQLM algorithm, which combines a spectral collocationmethod with the quasilinearization method (QLM). The effects of Grashof number, Prandtl number, Darcy number and Eringen micropolar rheological material parameters are examined. Excellent stability and convergence of the spectral method is demonstrated. Validation of solutions with the Keller box finite difference is included. Applications of the study arise in geological (petroleum) fluid dynamics.

This paper is devoted to the investigation of the propagation of magneto-thermo-elastic waves in a rotating monoclinic system. The system is electrically conducting in the presence of an applied magnetic field. A general dispersion relation is obtained for magneto-thermo-elastic waves. The propagation of wave produced two elastic waves and two thermal waves. It is found that the elastic waves depend on the applied magnetic field and the rotational frequency, where the thermal waves are independent of these effects. The numerical simulations are presented in this article to support the findings.

The present paper investigates analytically the two-dimensional heat transfer and entropy generation characteristics of axisymmetric, incompressible viscous fluid flow in a horizontal circular pipe. The flow is subjected to an externally applied uniform suction across the wall in the normal direction and a constant magnetic field. Constant wall temperature is considered as the thermal boundary condition. The reduced Navier–Stokes equations in a cylindrical coordinate system are solved to obtain the velocity and temperature distributions. The velocity distributions are expressed in terms of stream function and the solution is obtained using the homotopy analysis method (HAM). Validation with earlier nonmagnetic solutions in the literature is incorporated. The effects of various parameters on axial and radial velocities, temperature, axial and radial entropy generation numbers, and axial and radial Bejan numbers are presented graphically and interpreted at length. Streamlines, isotherms, pressure, entropy generation number, and Bejan number contours are also visualized. Increasing magnetic body force parameter shifts the peak of the velocity curve near to the axis, whereas it accelerates the radial flow. The study is relevant to thermodynamic optimization of magnetic blood flows and electromagnetic industrial flows featuring heat transfer.

In the present article, the transient rheological boundary layer flow over a stretching sheet\ud with heat transfer is investigated, a topic of relevance to non-Newtonian thermal materials\ud processing. Stokes couple stress model is deployed to simulate non-Newtonian characteristics. Similarity transformations are utilized to convert the governing partial differential equations into nonlinear ordinary differential equations with appropriate wall and free stream boundary conditions. The non-dimensional boundary value problem emerging is shown to be controlled by a number of key thermophysical and rheological parameters, namely the rheological couple stress parameter, unsteadiness parameter, Prandtl number (Pr), buoyancy parameter. The semi-analytical Differential Transform Method (DTM) is used to solve the reduced nonlinear coupled ordinary differential boundary value problem. A numerical solution is also obtained via the MATLAB built in solver ‘bvp4c’ to validate the results. Further validation with published results from the literature is included. Fluid velocity is enhanced with increasing couple stress parameter whereas it is decreased\ud with unsteadiness parameter. Temperature is elevated with couple stress parameter whereas it is initially reduced with unsteadiness parameter. The flow is accelerated with increasing positive buoyancy parameter (for heating of the fluid) whereas it is decelerated with increasing negative buoyancy parameter (cooling of the fluid). Temperature and thermal boundary layer thickness are boosted with increasing positive values of buoyancy parameter. Increasing Prandtl number decelerates the flow, reduces temperatures, increases momentum boundary layer thickness and decreases thermal boundary layer thickness. Excellent accuracy is achieved with the DTM approach.

Nanofluids are becoming increasingly popular in novel hematological treatments and also advanced nanoscale biomedical devices. Motivated by recent developments in this area, a theoretical and numerical study is described for unsteady pulsatile flow, heat and mass transport through a tapered stenosed artery in the presence of nanoparticles. An appropriate geometric expression is employed to simulate the overlapping stenosed arterial segment. The Sisko non-Newtonian model is employed for hemodynamic rheology. Buongiorno’s formulation is employed to model nanoscale effects. The two-dimensional non-linear, coupled equations are simplified for the case of mild stenosis. An explicit forward time central space (FTCS) finite difference scheme is employed to obtain a numerical solution of these equations. Validation of the computations is achieved with another numerical method, namely the variational finite element method (FEM). The effects of various emerging rheological, nanoscale and thermofluid parameters on flow and heat/mass characteristics of blood are shown via several plots and discussed in detail. The circulating regions inside the flow field are also investigated through instantaneous patterns of streamlines. The work is relevant to nanopharmacological transport phenomena, a new and exciting area of modern medical fluid dynamics which integrates coupled diffusion, viscous flow and nanoscale drug delivery mechanisms.

Micropolar fluids provide an alternative mechanism for simulating micro-scale and molecular fluid mechanics which require less computational effort. In the present paper, a numerical analysis is conducted for the primary and secondary flow characterizing dissipative micropolar convective heat and mass transfer from a rotating vertical plate with oscillatory plate velocity, adjacent to a permeable medium. Owing to high temperature, thermal radiation effects are also studied. The micropolar fluid is also chemically-reacting, both thermal and species (concentration) buoyancy effects and heat source/sink are included. The entire system rotates with uniform angular velocity about an axis normal to the plate. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. The partial differential equations governing the flow problem are rendered dimensionless with appropriate transformation variables. A Galerkin finite element method is employed to solve the emerging multi-physical components of fluid dynamics problem are examined for a variety of parameters including rotation parameter, radiation-conduction parameter, micropolar coupling parameter, Eckert number (dissipation), reaction parameter, magnetic body force parameter and Schmidt number. A comparison with previously published article is made to check the validity and accuracy of the present finite element solutions under some limiting case and excellent agreement is attained. The current simulations may be applicable to various chemical engineering systems, oscillating rheometry, and rotating MHD energy generator near-wall flows.

Ayesha Sohail,1 Lubna Sherin,2 Saad I Butt,1 Sana Javed,1 Zhiwu Li,3,4 Sohail Iqbal,5 O Anwar Be’g6 1Department of Mathematics, Comsats Institute of Information Technology, Lahore, Pakistan; 2Department of Chemistry, Comsats Institute of Information Technology, Lahore Pakistan; 3Institute of Systems Engineering, Macau University of Science and Technology, Taipa, Macau; 4School of Electro-Mechanical Engineering, Xidian University, Xi’an, China; 5Department of Medicine, Sir Ganga Ram Hospital, Fatima Jinnah Medical College, Lahore, Pakistan; 6Fluid Mechanics, Spray Research Group, Mechanical and Petroleum Engineering, School of Computing, Science and Engineering, University of Salford, Manchester, UK Abstract: The decreased bone mineral density and compromised bone strength predispose individuals to skeletal osteoporosis. Both prostate cancer and bone metastasis caused by cancer invasion have remained a great challenge to researchers. With the advancement in the fields of biochemistry and biomechanics, the molecular mechanisms that make prostate cancer metastasize to bone have recently been identified, and they provide new molecular targets for drug development. Many biochemical by-products have been identified to help in understanding the interaction between the bone and the tumor. Enhanced clinical management of patients with bone metastases was reported during the past decade; however, the anticipated risk and the response to the therapy are still challenging to assess. In this review, the key players that play a dominant role in secondary osteoporosis are addressed. An attempt is made to provide the readers with a clear understanding of the communication pathways between each of the cell types involved in this vicious cycle. Furthermore, the role of Wnts, sclerostin, RANKL, PTHrP, and their respective clinical studies are addressed in this study. Keywords: prostate cancer metastatic bone disease (PCa MBD), vicious cycle, macrophages, Wnts signaling

Thermal radiation features in many high temperature materials processing operations. To evaluate the influence of radiative flux on spin coating systems, we consider herein the thermo-solutal (coupled heat and mass transfer) in steady laminar boundary layer natural convection flow from a rotating permeable vertical cone to an anisotropic Darcian porous medium. Surface slip effects are also included in the model presented. The conservation equations are rendered into self-similar form and solved as an ordinary differential two-point boundary value problem with surface and free stream boundary conditions using MAPLE 17 software. The transport phenomena are observed to be controlled by ten parameters, viz primary and secondary Darcy numbers (Dax and Da), rotational (spin) parameter (NR), velocity slip parameter (a), suction/injection parameter (S), thermal slip parameter (b), mass slip parameter (c) buoyancy ratio parameter (N), and conduction-radiation parameter (Rc). Tangential velocity and temperature are observed to be enhanced with greater momentum slip whereas swirl velocity and concentration are reduced. Increasing swirl Darcy number strongly accelerates both the tangential and swirl flow and also heats the regime whereas it decreases concentrations. Conversely a rise in tangential Darcy number accelerates only the tangential flow and decelerates swirl flow, simultaneously depressing temperatures and concentrations. Increasing thermal slip accelerates the swirl flow and boosts concentration but serves to retard the tangential flow and decrease temperatures. With higher radiation contribution (lower Rc values) temperatures are elevated and concentrations are reduced. Verification of the MAPLE 17 solutions is achieved using a Keller-box finite difference method (KBM). A number of interesting features in the thermo-fluid and species diffusion characteristics are addressed.\ud Key words: Stefan blowing; Spinning cone; MAPLE 17; Anisotropic

A biofluid dynamics mathematical model is developed to study peristaltic flow of non-Newtonian physiological liquid in a two-dimensional asymmetric channel containing porous media as a simulation of obstructed digestive (intestinal) transport. The fractional Oldroyd-B viscoelastic rheological model is utilized. The biophysical flow regime is constructed as a wave-like motion and porous medium is simulated with a modified Darcy-Brinkman model. This model is aimed at describing the digestive transport in intestinal tract containing deposits which induce impedance. A low Reynolds number approximation is employed to eliminate inertial effects and the wavelength to diameter ratio is assumed to be large. The differential transform method (DTM), a semi-computational technique is employed to obtain approximate analytical solutions to the boundary value problem. The influences of fractional (rheological material) parameters, relaxation time, retardation time, amplitude of the wave, and permeability parameter on peristaltic flow characteristics such as volumetric flow rate, pressure difference and wall friction force are computed. The present model is relevant to flow in diseased intestines.

A theoretical study of two-dimensional magnetohydrodynamics viscous incompressible free convective boundary layer flow of an electrically conducting, chemically reacting nanofluid from a convectively heated permeable vertical surface is presented. Scaling group of transformations is used in the governing equations and the boundary conditions to determine absolute invariants. A third-order ordinary differential equation which corresponds to momentum conservation and two second-order ordinary differential equations which correspond to energy and nanoparticle volume fraction (species) conservation are derived. Our (group) analysis indicates that, for the similarity solution, the convective heat transfer coefficient and mass transfer velocity are proportional tox-1/4whilst the reaction rate is proportional tox-1/2, wherexis the axial distance from the leading edge of the plate. The effects of the relevant controlling parameters on the dimensionless velocity, temperature, and nanoparticle volume fraction are examined. The accuracy of the technique we have used was tested by performing comparisons with the results of published work and the results were found to be in good agreement. The present computations indicate that the flow is accelerated and temperature enhanced whereas nanoparticle volume fractions are decreased with increasing order of chemical reaction. Furthermore the flow is strongly decelerated, whereas the nanoparticle volume fraction and temperature are enhanced with increasing magnetic field parameter. Increasing convection-conduction parameter increases velocity and temperatures but has a weak influence on nanoparticle volume fraction distribution. The present study demonstrates the thermal enhancement achieved with nanofluids and also magnetic fields and is of relevance to nanomaterials processing.

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 &ldquo, zero mass flux boundary condition&rdquo, which is believed to be more realistic than the earlier extensively used &ldquo, actively&rdquo, 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 paper investigates combined heat and mass transfer by mixed magneto-convective flow of an electrically conducting flow along a moving radiating vertical flat plate with hydrodynamic slip and thermal convective boundary conditions. The governing transport equations are converted into a system of coupled nonlinear ordinary differential equations with prescribed boundary conditions using similarity variables developed by Lie group theory. The transformed nondimensional boundary value problem is then solved numerically with MAPLE13 quadrature. Excellent correlation with previous nonmagnetic, no-slip studies is achieved. Surface shear stress function and local Nusselt number (heat transfer gradient at the wall) are increased with Richardson number, whereas local Sherwood number is found to initially decrease then subsequently increase. The “thermally thick” scenario (Biot number > 0.1) is investigated and increasing Biot number is observed to enhance shear stress function (skin friction), local Nusselt number, and local Sherwood number. Increasing thermal radiation flux increases thermal boundary layer thickness as does increasing the magnetic field effect. Increasing hydrodynamic slip parameter reduces skin friction but enhances local Nusselt and Sherwood numbers. The study has applications in high-temperature polymeric synthesis and magnetic field flow control.

Mathematical simulations of embryological fluid dynamics are fundamental to improving clinical understanding of the intricate mechanisms underlying sperm locomotion. The strongly rheological nature of reproductive fluids has been established for a number of decades. Complimentary to clinical studies, mathematical models of reproductive hydrodynamics provide a deeper understanding of the intricate mechanisms involved in spermatozoa locomotion which can be of immense benefit in clarifying fertilization processes. Although numerous non-Newtonian studies of spermatozoa swimming dynamics in non-Newtonian media have been communicated, very few have addressed the micro-structural characteristics of embryological media. This family of micro-continuum models include Eringen’s micro-stretch theory, Eringen’s microfluid and micropolar constructs and V. K. Stokes’ couple stress fluid model, all developed in the 1960s. In the present paper we implement the last of these models to examine the problem of micro-organism (spermatozoa) swimming at low Reynolds number in a homogenous embryological fluid medium with couple stress effects. The micro-organism is modeled as with Taylor’s classical approach, as an infinite flexible sheet on whose surface waves of lateral displacement are propagated. The swimming speed of the sheet and rate of work done by it are determined as function of the parameters of orbit and the couple stress fluid parameter ([Formula: see text]). The perturbation solutions are validated with a Nakamura finite difference algorithm. The perturbation solutions reveal that the normal beat pattern is effective for both couple stress and Newtonian fluids only when the amplitude of stretching wave is small. The swimming speed is observed to decrease with couple stress fluid parameter tending to its Newtonian limit as alpha tends to infinity. However the rate of work done by the sheet decreases with [Formula: see text] and approaches asymptotically to its Newtonian value. The present solutions also provide a good benchmark for more advanced numerical simulations of micro-organism swimming in couple-stress rheological biofluids.

An analytical study of the MHD boundary layer flow of electrically conducting nanofluid over a horizontal cylinder with the effects of chemical reaction and viscous dissipation is presented. Similarity transformations have been applied to transform the cylindrical form of the governing equations into the system of coupled ordinary differential equations and then homotopy analysis method has been implemented to solve the system. Homotopy analysis method (HAM) does not contain any small or large parameter like perturbation technique and also provides an easiest approach to ensure the convergence of the series of solution. The effects of chemical reaction parameter, magnetic parameter and other important governing parameters with no flux nanoparticles concentration is carried out to describe important physical quantities.

This study examines theoretically and computationally the transient magneto-hydrodynamic boundary layer flow and heat transfer in an incompressible rotating nanofluid over a stretching continuous sheet, with a transverse magnetic field applied normal to the sheet plane. The three-dimensional conservation equations for mass, momentum, energy and species (nanoparticle) diffusion, are normalized into a system of two-dimensional dimensionless boundary layer equations, using appropriate scaling transformations. The resulting nanofluid transport model incorporates a Brownian motion parameter, thermophoresis parameter, rotation parameter, unsteady parameter, Prandtl number, Hartmann magnetic parameter and Lewis number, and physically realistic boundary conditions at the sheet surface and in the free stream. The nonlinear two-point boundary value problem is solved using a robust, efficient finite element method based on the variational formulation. A detailed evaluation of the effects of the governing physical parameters on the velocity components, temperature and nanoparticle concentration via graphical plots is conducted. Primary velocity is strongly retarded with increasing Hartmann number and there is also a reduction in secondary velocity magnitude. Both temperature and nanoparticle concentration are positively affected by the Hartmann number. Increasing rotational parameter decreases both primary and secondary velocity, and also depresses temperature and nanoparticle concentration. Unsteadiness parameter is generally found to enhance primary velocity and temperatures but exhibits a varied influence on secondary velocity and nanoparticle concentration. The reduced Nusselt number (wall temperature gradient) is observed to be depressed with both Brownian motion and thermophoresis effects, whereas the contrary behaviour is computed for the reduced Sherwood number (wall mass transfer gradient). The reduced Nusselt number and the Sherwood number also show a steady decrease with increasing rotational parameter. The present finite element method solutions have been validated extensively with the previously published results, demonstrating excellent correlation. The study has important applications in the manufacture and electromagnetic control of complex magnetic nanofluid materials of relevance to biomedical, energy systems and aerospace systems technologies.