Electro-osmotic nanofluid flow in a curved microchannel

Biological mechanisms offer significant improvement in the efficiency of next generation energy systems. Motivated by new developments in distensible pumping systems, ionic electro-kinetic manipulation and nanoscale liquids (”nanofluids”), in the present study a mathematical model is developed to simulate the entropy generation and electro-osmotic transport of nanofluids in a curved deformable microchannel driven by peristaltic transport. Both thermal and species (nano-particle) buoyancy effects are included and Soret and Dufour cross-diffusion effects. The appropriate conservation equations are normalized with scaled variables and the resulting dimensionless nonlinear boundary value problem is solved in a transformed coordinate system. Simplification of the mathematics is achieved via lubrication approximations and low zeta potential (Debye Hückel linearization). The effects of various parameters, i.e. electro-osmotic velocity, EDL (electrical double layer) thickness and zeta potential ratio on velocity profile and temperature profiles are computed. The effects of Brinkman number (viscous heating parameter) and Joule (electrical field heating) parameter on nano-particle concentration profiles are also simulated. The micro-channel curvature effects on the nanofluid flow characteristics and thermal characteristics are also computed. Furthermore, streamline patterns, temperature contours, nano-particles concentration contours and entropy generation rate contours are plotted for various curvature parameters. Results indicate that the curvature of the channel and electro-osmotic body force influence strongly the sources of entropy generation rate. The study finds applications in bio-inspired electro-osmotic nanofluid pumping in microscale energy applications.     

Significance of Stefan blowing effect on flow and heat transfer of Casson nanofluid over a moving thin needle

The current mathematical model explains the influence of non-linear thermal radiation on the Casson liquid flow over a moving thin needle by considering Buongiorno's nanofluid model.The influences of Stefan blowing, Dufour and Soret effects are also considered in the model. The equations which represent the described flow pattern are reduced to ordinary differential equations(ODEs) by using apt similarity transformations and then they are numerically solved with Runge–Kutta-Fehlberg's fourth fifth-order method(RKF-45) with shooting process. The impacts of pertinent parameters on thermal, mass and velocity curves are deliberated graphically.Skin friction, rate of heat and mass transfer are also discussed graphically. Results reveal that, the increase in values of Brownian motion, thermophoresis, Dufour number, heating and radiative parameters improves the heat transfer. The increasing values of the Schmidt number deteriorates the mass transfer but a converse trend is seen for increasing values of the Soret number. Finally,the escalating values of the radiative parameter decays the rate of heat transfer.     

Significance of power average of sinusoidal and non-sinusoidal periodic excitations in nonlinear non-autonomous system

The steady laminar boundary layer flow of Carreau nanofluid over a stretching sheet is investigated. Effects of Brownian motion and thermophoresis are present. Heat transfer is characterized using convective boundary condition at the sheet. The governing partial differential equations are reduced into a set of nonlinear ordinary differential equations through suitable transformations. Results of velocity, temperature and concentration fields are computed via homotopic procedure. Numerical values of skin-friction coefficient, local Nusselt and Sherwood numbers are computed and discussed. A comparative study with existing solutions in a limiting sense is made.     

Unsteady MHD flow and heat transfer of fractional Maxwell viscoelastic nanofluid with Cattaneo heat flux and different particle shapes

The paper aims to investigate the unsteady natural convection flow and heat transfer of fractional Maxwell viscoelastic nanofluid in magnetic field over a vertical plate. The effect of nanoparticle shape is first introduced to the study of fractional Maxwell viscoelastic nanofluid. Fractional shear stress and Cattaneo heat flux model are applied to construct the governing boundary layer equations of momentum and energy, which are solved numerically. The quantities of physical interest are graphically presented and discussed in detail. It is found that particle shape and fractional derivative parameters have profound influence on the flow and heat transfer.     

Convective heat transfer and MHD effects on Casson nanofluid flow over a shrinking sheet

Current study examines the magnetohydrodynamic (MHD) boundary layer flow of a Casson nanofluid over an exponentially permeable shrinking sheet with convective boundary condition. Moreover, we have considered the suction/injection effects on the wall. By applying the appropriate transformations, system of non-linear partial differential equation along with the boundary conditions are transformed to couple non-linear ordinary differential equations. The resulting systems of non-linear ordinary differential equations are solved numerically using Runge-Kutta method. Numerical results for velocity, temperature and nanoparticle volume concentration are presented through graphs for various values of dimensionless parameters. Effects of parameters for heat transfer at wall and nanoparticle volume concentration are also presented through graphs and tables. At the end, fluid flow behavior is examined through stream lines. Concluding remarks are provided for the whole analysis.     

Mixed Convection Heat and Mass Transfer in a Micropolar Fluid with Soret and Dufour Effects

A mathematical model for the steady, mixed convection heat and mass transfer along a semi-infinite vertical plate embedded in a micropolar fluid in the presence of Soret and Dufour effects is presented. The non-linear governing equations and their associated boundary conditions are initially cast into dimensionless forms using local similarity transformations. The resulting system of equations is then solved numerically using the Keller-box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The non-dimensional velocity, microrotation, temperature and concentration profiles are displayed graphically for different values of coupling number, Soret and Dufour numbers. In addition, the skin-friction coefficient, the Nusselt number and Sherwood number are shown in a tabular form.     

Unsteady radiative nanofluid flow near a vertical heated wavy surface with temperature-dependent viscosity

In the present contribution, a numerical treatment is provided to describe unsteady nanofluid flow near a vertical heated wavy surface. A memorable feature of the present work is the investigation of nanofluid flow associated with thermal radiation that acts as a catalyst for heat transfer rates. Likewise, the effectiveness of variable viscosity is examined as it controls fluid flow as well as heat transfer. It is necessary to study heat and mass transfer for complex geometries because predicting heat and mass transfer for irregular surfaces is a topic of fundamental importance, and irregular surfaces frequently appear in many applications, such as flat-plate solar collectors and flat-plate condensers in refrigerators. A simple coordinate transformation from the wavy surface into a flat one is employed. The non-dimensional boundary layer equations that governing both heat transfer and nanofluid flow phenomena along the wavy surface are solved via a powerful numerical approach called the implicit Chebyshev pseudospectral (ICPS) method with Mathematica code. A comparison graph of the current numerical computation and the published data shows a perfect match. Figures depict the effect of various physical parameters on nanofluid velocities, temperature, salt concentration, nanoparticle concentration, skin friction, Sherwood, nanoparticle Sherwood, and Nusselt numbers. According to the numerical results, increasing the variable viscosity parameter value causes a drop in the local skin friction coefficient value and an increase in the steady-state axial nanofluid velocity profile near the wavy surface. Furthermore, as heat radiation is increased, the local Nusselt number decreases but the nanoparticle Sherwood number increases.     

The influence of heat radiation on mixed convection boundary layer flow of a viscoelastic fluid over a circular cylinder with constant surface temperature

The influence of mixed convection boundary layer flow of a viscoelastic fluid over an isothermal horizontal circular cylinder has been analyzed. The boundary layer equations governing the problem are reduced to dimensionless nonlinear partial differential equations and then solved numerically using Keller-box method. Skin friction coefficient and Nusselt number are emphasized specifically. These quantities are displayed against curvature parameter. Effects of mixed convection parameter and radiation-conduction parameter on skin friction coefficient and Nusselt number are illustrated through graphs and table. The boundary layer separation points along the surface of cylinder are also calculated with/without radiation, and a comparison is shown. The presence of radiation helps to reduce the skin friction coefficient in opposing flow case and enhances it for assisting flow case. The increase in value of radiation-conduction parameter helps increase the value of skin friction coefficient and Nusselt number for viscoelastic fluids. The boundary layer separation delays due to thermal radiation.     

Influence of bioconvection on Maxwell nanofluid flow with the swimming of motile microorganisms over a vertical rotating cylinder

In recent times, bioconvection phenomenon through the use of nanomaterials has encountered significant manufacturing and technical applications. Bioconvection has several applications in bio-micro-system, due to the enhancement in mass transformation and mixing, which are crucial problems in different micro-systems. The aim of current article is to scrutinize the bioconvection phenomenon in 3D Maxwell nanofluid flow with useful characteristics of mixed convection, activation energy, motile microorganisms and solutal boundary conditions. The flow problem focused on the related laws, outcomes in a series of PDEs which have also been delayed in ODE's structure. The numerical method based on a shooting technique is applied to implement a bvp4c solver using the computational software MATLAB. Shooting tactic is utilized to construct the numerical arrangement of subsequent problem. The mathematical division for the local Nusselt number, the motile microorganism's number, and the local Sherwood number is provided when applying different characteristics to the concerned parameters. The hypothetical simulations mentioned may be more successful in enhancing thermal extrusion mechanisms and solar energy structures. The numerical results regarding flow, thermal field, solutal field and concentration of microorganisms are revealed for growing values of interesting parameters. Furthermore, it is inspected that velocity field dwindles with enlarged variation of Maxwell fluid parameter. It is analyzed that radial velocity of Maxwell nanofluid reduces for larger magnitude of mixed convection parameter. Additionally, temperature profile of species upsurges for larger values of thermal stratification Biot number. Moreover, it is inspected that concentration of species decline for higher estimation of Lewis number while enhanced for activation energy parameter. Microorganisms concentration field of Maxwell nanofluid is detected to be an declining function of Peclet number and bioconvection Lewis number. Angorgeous concurrence is obtained when our accomplished numerical results are compared with an already existed magnitudes in limiting condition; hence dependable results are being eliminated.     

Three-Dimensional Hybrid Nanofluid Flow and Heat Transfer past a Permeable Stretching/Shrinking Sheet with Velocity Slip and Convective Condition

The present work deals with the three-dimensional hybrid Cu-Al₂O₃/water nanofluid flow towards a stretching/shrinking sheet with the presence of velocity slip and convective conditions. A permeable sheet is considered to maintain the shrinking flow through an adequate wall mass suction. The nonlinear governing boundary layer coupled with energy equations are transformed into the ordinary differential equations using similarity transformation. Numerical computations are performed with the aid of boundary value problem solver (bvp4c) in the Matlab software and the results are presented in the tables and graphs. The boundary layer separation occurs in the shrinking flow region. An upsurge of slip and copper nanoparticle volume fraction parameters can increase the range of first and second solutions whereas Biot parameter give zero impact on delaying the boundary layer separation. However, an increase of Biot and slip parameters can boost the heat transfer rate while opposite result is obtained with the augmentation of the copper solid volume fraction. The stability of both solutions are examined, and it is validated that the first (upper branch) solution is more stable than second solution.     

Advanced Study of Unsteady Heat and Chemical Reaction with Ramped Wall and Slip Effect on a Viscous Fluid

This paper investigate the effect of slip boundary condition, thermal radiation, heat source, Dufour number,chemical reaction and viscous dissipation on heat and mass transfer of unsteady free convective MHD flow of a viscous fluid past through a vertical plate embedded in a porous media. Numerical results are obtained for solving the nonlinear governing momentum, energy and concentration equations with slip boundary condition, ramped wall temperature and ramped wall concentration on the surface of the vertical plate. The influence of emerging parameters on velocity,temperature and concentration fields are shown graphically.     

MHD mixed convection stagnation point flow of a hybrid nanofluid past a vertical flat plate with convective boundary condition

The steady magnetohydrodynamics (MHD) mixed convection stagnation point flow of a hybrid nanofluid past a vertical flat plate with convective boundary condition is investigated in this study. By choosing appropriate similarity variables, the partial differential equations are transformed into a system of linear equations which are solved afterwards by using the boundary value problem solver, namely bvp4c in Matlab software. The solutions of the ordinary differential equations are proven to have two branches which are upper and lower solutions in a certain range of the mixed convection parameter. This leads to the execution of a stability analysis that verifies the achievable solution of the upper branch which is considered stable while the lower branch is unstable. The findings exposed that the fluid velocity increases with the increasing value of the magnetic parameter while the fluid temperature is decreased contradictory.     

Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H2O nanofluid on a flat surface in a porous medium: A stability analysis

The nanofluid and porous medium together are able to fulfill the requirement of high cooling rate in many engineering problems. So, here the impact of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H₂O nanofluid on a flat surface in a porous medium is examined. Moreover, the thermal radiation and viscous dissipation effects are considered. The problem governing partial differential equations are converted into self-similar coupled ordinary differential equations and those are numerically solved by the shooting method. The computed results can reveal many vital findings of practical importance. Firstly, dual solutions exist for decelerating unsteady flow and for accelerating unsteady and steady flows, the solution is unique. The presence of nanoparticles affects the existence of dual solution in decelerating unsteady flow only when the medium of the flow is a porous medium. But different shapes of nanoparticles are not disturbing the dual solution existence range, though it has a considerable impact on thermal conductivity of the mixture. Different shapes of nanoparticles act differently to enhance the heat transfer characteristics of the base fluid, i.e., the water here. On the other hand, the existence range of dual solutions becomes wider for a larger permeability parameter related to the porous medium. Regarding the cooling rate of the heated surface, it rises with the permeability parameter, shape factor (related to various shapes of Cu-nanoparticles), and radiation parameter. The surface drag force becomes stronger with the permeability parameter. Also, with growing values of nanoparticle volume fraction, the boundary layer thickness (BLT) increases and the thermal BLT becomes thicker with larger values of shape factor. For decelerating unsteady flow, the nanofluid velocity rises with permeability parameter in the case of upper branch solution and an opposite trend for the lower branch is witnessed. The thermal BLT is thicker with radiation parameter. Due to the existence of dual solutions, a linear stability analysis is made and it is concluded that the upper branch and unique solutions are stable solutions.     

Three-dimensional flow of Powell–Eyring nanofluid with heat and mass flux boundary conditions

This article investigates the three-dimensional flow of Powell–Eyring nanofluid with thermophoresis and Brownian motion effects. The energy equation is considered in the presence of thermal radiation. The heat and mass flux conditions are taken into account. Mathematical formulation is carried out through the boundary layer approach. The governing partial differential equations are transformed into the nonlinear ordinary differential equations through suitable variables. The resulting nonlinear ordinary differential equations have been solved for the series solutions. Effects of emerging physical parameters on the temperature and nanoparticles concentration are plotted and discussed. Numerical values of local Nusselt and Sherwood numbers are computed and examined.     

Numerical simulation of Electrokinetically Driven Peristaltic Pumping of Silver-Water Nanofluids in an asymmetric microchannel

This article intends to focus on the theoretical and numerical investigation of the peristaltic pumping of water-based silver nanofluid in the presence of electroosmotic forces. The investigation is carried out in an asymmetric microchannel subject to the influence of mixed convection and viscous dissipation. No-slip boundary conditions for velocity, temperature, and nanoparticle volume fraction are imposed on channel walls. The lubrication approach is utilized to simplify the normalized constitutive equations. The distribution of electric potential in the electric double layer is characterized by Poisson-Boltzmann ionic distribution which is further linearized by Debye-Hückel approximation. Nanofluid properties are predicted by a combination of the Buongiorno two-phase mixture model and homogeneous flow model. Additionally, the effective thermal conductivity and dynamic viscosity of silver-water nanofluid are characterized by the Corcione model. Silver nanoparticles of 20nm diameter are utilized in this suspension. The transformed set of nonlinear and coupled equations is numerically executed for axial velocity, temperature, and nanoparticle volume fraction by employing the mathematical software Maple 17. Pumping and trapping phenomena are also investigated. A comparison between the thermal conductivity of nanofluid predicted by the Corcione model and the Maxwell model is further presented. The influence of various flow parameters is outlined through graphical results. It has been observed that the thermal conductivity of silver-water nanofluid enhances with increasing nanoparticle volume fraction and temperature but decreases for larger sized nanoparticles. Moreover, the heat transfer rate rises significantly when smaller silver nanoparticles are suspended in water. Furthermore, the temperature of nanofluid is directly related to the Debye length parameter and the Helmholtz- Smoluchowski velocity parameter.     

Rheological Analysis of CNT Suspended Nanofluid with Variable Viscosity: Numerical Solution

In this article, we discuss the two-dimensional stagnation-point flow of carbon nanotubes towards a stretching sheet with water as the base fluid under the influence temperature dependent viscosity. Similarity transformations are used to simplify the governing boundary layer equations for nanofluid. This is the first article on the stagnation point flow of CNTs over a stretching sheet with variable viscosity. A well known Reynold's model of viscosity is used. Single wall CNTs are used with water as a base fluid. The resulting nonlinear coupled equations with the relevant boundary conditions are solved numerically using shooting method. The influence of the flow parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are explored and presented in forms of graphs and interpreted physically.     

Cubic Auto-Catalysis Reactions in Three-Dimensional Nanofluid Flow Considering Viscous and Joule Dissipations Under Thermal Jump

In this problem, simultaneous effects of Joule and viscous dissipationin three-dimensional flow of nanoliquid have been addressed in slip flow regime under timedependent rotational oscillations. Silver nanoparticles are submerged in the base fluid (water)due to their chemical and biological features. To increment the novelty, effects of cubicautocatalysis chemical reactions and radiative heat transfer have been incorporated in therelated boundary layer equations. Dimensionless partial differential system is solved byemploying the proposed implicit finite difference approach. Convergence conditions andstability criteria are obtained to ensure the convergence and accuracy of solutions.A comparative analysis is proposed for no-slip nanofluid flow (NSNF) and slip nanofluid flow(SNF). Variations in skin-friction coefficients, Sherwood and Nusselt numbers against physicalparameters are tabulated. It is investigated that velocity slip and temperature jump significantlycontrol drag forces and rate of heat transfer.     

Magnetohydrodynamics (MHD) axisymmetric flow and heat transfer of a hybrid nanofluid past a radially permeable stretching/shrinking sheet with Joule heating

The main interest of the present work is to fundamentally investigate the flow characteristics and heat transfer of a hybrid Cu-Al₂O₃/water nanofluid due to a radially stretching/shrinking surface with the mutual effects of MHD, suction and Joule heating. The surface is permeable to physically allow the wall mass fluid suction. Tiwari and Das model of nanofluid is used with the new thermophysical properties of hybrid nanofluid to represent the problem. A similarity transformation is adopted to convert the governing model (PDEs) into a nonlinear set of ordinary differential equations (ODEs). A bvp4c solver in MATLAB software is employed to numerically compute the transformed system. The numerical results are discussed and graphically manifested in velocity and temperature profiles, as well as the skin friction coefficient and heat transfer rate with the pertinent values of the dimensionless parameters namely magnetic, Cu volume fraction, suction and Eckert number. The Eckert number has no impact on the boundary layer separation while the higher value of the suction parameter may affect the heat transfer performance. The presence of dual solutions (first and second) is seen on all the profiles within a limited range of the physical parameters. The stability analysis is executed, and it is validated that the first solution is the real solution.     

MHD squeezed flow of water functionalized metallic nanoparticles over a sensor surface

Present study is devoted to analyze the magnetohydrodynamics (MHD) squeezed flow of nanofluid over a sensor surface. Modeling of the problem is based on the geometry and the interaction of three different kinds of metallic nanoparticles namely: copper (Cu), alumina (Al₂O₃) and titanium dioxide (TiO₂) with the homogeneous mixture of base fluid (water). The self-similar numerical solutions are presented for the reduced form of the system of coupled ordinary differential equations. The effects of nanoparticles volume friction, permeable velocity and squeezing parameter for the flow and heat transfer within the boundary layer are presented through graphs. Comparison among the solvent are constructed for both skin friction and Nusselt number. Flow behavior of the working nanofluid according to the present geometry has analyzed through Stream lines. Conclusion is drawn on the basis of entire investigation and it is found that in squeezing flow phenomena Cu–water gives the better heat transfer performance as compare with the rest of mixtures.     

MHD mixed convection flow near the stagnation-point on a vertical permeable surface

The steady magnetohydrodynamic (MHD) mixed convection boundary layer flow of a viscous and electrically conducting fluid near the stagnation-point on a vertical permeable surface is investigated in this study. The velocity of the external flow and the temperature of the plate surface are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for both cases, and the range of the mixed convection parameter for which the solution exists increases with suction.