Nanofluid bioconvection in water-based suspensions containing nanoparticles and oxytactic microorganisms: oscillatory instability

Similarity analysis of bioconvection of unsteady nonhomogeneous hybrid nanofluids influenced by motile microorganisms

Motile bacteria in hybrid nanofluids cause bioconvection. Bacillus cereus, Pseudomonas viscosa, Bacillus brevis, Salmonella typhimurium, and Pseudomonas fluorescens were used to evaluate their effect and dispersion in the hybrid nanofluid. Using similarity analysis, a two-phase model for mixed bioconvection magnetohydrodynamic flow was developed using hybrid nanoparticles of Al2O3 and Cu (Cu-Al2O3/water). The parametric investigation, covering the magnetic parameter, permeability coefficient, nanoparticle shape factor, temperature ratio, radiation parameter, nanoparticle fraction ratio, Brownian parameter, thermophoresis parameter, motile bacteria diffusivity, chemotaxis parameter, and Nusselt, Reynold, Prandtl, Sherwood numbers, as well as the number of motile microorganisms', showed significant outcomes. Velocity and shear stresses are sensitive to M, Pr, and [Formula: see text]. Magnetic, radiation, and chemotaxis factors impact bacterial density. The hybrid nanofluid velocity decreases when the magnetic parameter, M, Prandtl number Pr increases, while it increases with the increasing of porosity coefficient, [Formula: see text], and the hybrid nanoparticle ratio Nf. The temperature distribution decreases with the increasing of Prandtl number and Nf. Increasing temperature differential and bacterium diffusivity increases bacterial aggregation.

Thermal performance of Joule heating in radiative Eyring-Powell nanofluid with Arrhenius activation energy and gyrotactic motile microorganisms

Background

Bioconvection is the term for macroscopic convection of particles accompanied by a variable density gradient and a cluster of swimming microorganisms. The accumulation of gyrotactic microbes in the nanoparticles is important to exaggerate the thermal efficacy of various structures for instance, germs powered micro-churns, microbial fuel cubicles, micro-fluidics policies, and chip-designed micro plans like bio-microstructures.

Purpose

Here approach in the current effort is to present an innovative study of bio-convection owing to gyrotactic microbes in a nanofluid comprising non-uniform heat source/sink, space and temperature-dependent viscosity and Joule dissipation. The physical constraints such as convective-surface and new mass flux conditions are examined for 3D Eyring-Powell magneto-radiative nanofluid via porous stretched sheet.

Method

ology: Over suitable similarity alterations, the related non-linear flow, temperature, and concentration phenomena, equations are altered into non-linear equations. By combining the shooting methodology with the Runge-Kutta fourth-order technique is applied to get numerical solutions. A thorough investigation for the impact of important non-dimensional thermophysical parameters regulating flow characteristics is carried out.

Motivation

Lots of the studies on nanofluids realize their performance therefore that they can be exploited where conventional heat transport development is paramount as in numerous engineering uses, micro-electronics, transportation in addition to foodstuff and bio-medicine. The gyrotactic microbes flow in nanofluids has attained great devotion amongst researchers and the scientist community because of its works in numerous areas of bio-technology. The benefits of counting nanoparticles in mobile microbe's deferral can be established in micro-scale involvement and stability of nanofluid.

Significant results

For a few chosen parameters, the computed results for friction factor and transport for motile microorganism values are shown. The computed numerical results for parameters of engineering interest are given using tables. Furthermore, the recent solutions are stable with the former stated results and excellent association is found. The temperature of the fluid exaggerates for higher values of thermo-Biot and radiation parameter; however, Peclet and bio-convective Lewis's factor decay the motile microorganisms' field of Eyring-Powell fluid. The concentration field also enhances the activation energy parameter.

Incidence of Manifold Slip on Transport and Reaction Dynamics in Magneto-Bioconvective and Magnetic Nanoparticles Fe3O4 (Magnetite) Power-Law Flow Between Two Parallel Plates

The focus of this paper is based on the incidence of manifold slip on the transport and dynamics of magnetobioconvective and magnetic nanoparticles Fe3O4 (magnetite) power-law flow between two parallel plates. An interaction takes place between nanoparticles and the organism by inhalation routes, oral, dermal, and distributed to different tissue through the circulatory system The equations of motion are a set of partial differential equations (PDEs). The governing equations are transformed into ordinary differential equations (ODE) by utilizing similarity transformations. The transformed equations are solved by using the Runge-Kutta Gill method alongside the shooting techniques MATLAB software implementation. The velocity of fluid decreases when the magnetic parameter increases. The outcomes of this model find usefulness in controlling the turbulent flow of fluid due to the presence of a magnetic field and also helpful in reducing the dosage of anticancer drugs in the medical field because of the presence of the magnetic nanoparticles. The correctness of the present result is ascertained by comparing it with reported data.

Entropy Optimization and Heat Transfer Analysis of Magneto-Bioconvective Powell Eyring Nanofluid with Nonlinear Thermal Radiation and Chemical Reaction Over a Stretching Sheet

This paper investigates the entropy generation in the bioconvection of Powell Eyring nanofluid containing motile gyrotactic microorganisms over a convectively stretching sheet. The influences of magnetohydrodynamic forces, nonlinear thermal radiation effects, chemical reactions of species in a Powell Eyring nanofluid flow are analyzed. Motile microorganisms are added along with nanoparticles in the Powell Eyring base fluid for the prevention of nanoparticles agglomeration and to stabilize the nanoparticles in the suspension. The governing nonlinear partial differential equations along with boundary conditions are solved numerically after these equations are transformed into a system of nonlinear ordinary differential equations by using the similarity transformation. The results are compared with previously published research papers. The impact of significant physical and bioconvection parameters on the profile of nanofluid velocity, temperature, nanoparticles concentration, the density of motile microorganisms, and entropy generation are analyzed graphically. It is noticed that the velocity profile increases by increasing the values of the Powell Eyring fluid parameter. The incidence of nanoparticles in Powell Eyring nanofluid decreases the nanoparticle concentration due to an increase in the value of the chemical reaction parameter and Lewis number. Also, the profile of entropy generation increases as the values of Br, γ1, and γ2 are increased.

Numerical Study of the Electromagnetohydrodynamic Bioconvection Flow of Micropolar Nanofluid through a Stretching Sheet with Thermal Radiation and Stratification

The current work explores the bioconvection micropolar nanofluid through a stretching surface subjected to thermal radiation, stratification, and heat and mass transmission. Bioconvection contains the gyrotactic (random movement of microorganism in the direction of gravity with weak horizontal verticity) unicellular microorganism in aqueous environments. Heat and mass transfer assists the bioconvection to occur. The aim of this research is to evaluate the heat transfer rate of nanofluid in the presence of a unicellular microorganism. Self-similar variables are induced to reduce the governing equations into a non-linear differential system which is further solved via the bvp4c algorithm to tackle the fluid problem. Using visual representations, the effects of a number of dimensional less factors arising from the dimensional less differential system are determined. For a range of limiting conditions, the obtained results of this model correspond precisely to those in the literature. This study's findings are highly regarded in the evaluation of the impact of key design factors on heat transfer and, therefore, in the optimization of industrial processes. Skin friction, local Nusselt number, Sherwood number, and density of microorganism concentrations are also studied for various parameters. Buoyancy ratio factor supports skin friction and density of microorganism profile to increase. Local Nusselt number drops due to the thermal radiation factor. Brownian motion speeds up the Sherwood number.

Effects of Hall Current and Viscous Dissipation on Bioconvection Transport of Nanofluid over a Rotating Disk with Motile Microorganisms

The study of rotating-disk heat-flow problems is relevant to computer storage devices, rotating machineries, heat-storage devices, MHD rotators, lubrication, and food-processing devices. Therefore, this study investigated the effects of a Hall current and motile microorganisms on nanofluid flow generated by the spinning of a disk under multiple slip and thermal radiation conditions. The Buongiorno model of a nonhomogeneous nanofluid under Brownian diffusion and thermophoresis was applied. Using the Taylor series, the effect of Resseland radiation was linearized and included in the energy equation. By implementing the appropriate transformations, the governing partial differential equations (PDEs) were simplified into a two-point ordinary boundary value problem. The classical Runge-Kutta dependent shooting method was used to find the numerical solutions, which were validated using the data available in the literature. The velocity, motile microorganism distribution, temperature, and concentration of nanoparticles were plotted and comprehensively analyzed. Moreover, the density number, Sherwood number, shear stresses, and Nusselt number were calculated. The radial and tangential velocity declined with varying values of magnetic numbers, while the concentration of nanoparticles, motile microorganism distribution, and temperature increased. There was a significant reduction in heat transfer, velocities, and motile microorganism distribution under the multiple slip conditions. The Hall current magnified the velocities and reduced the heat transfer. Thermal radiation improved the Nusselt number, while the thermal slip conditions reduced the Nusselt number.

Electromagnetohydrodynamic bioconvective flow of binary fluid containing nanoparticles and gyrotactic microorganisms through a stratified stretching sheet

Bioconvection has recently been the subject of dispute in a number of biotechnological fields that depend on fluids and their physical properties. When mixed nanofluids are subjected to heat and mass transmission, the process of bioconvection occurs. This attempt conveys the theoretical analysis of two-dimensional electrically conducting and magnetically susceptible binary fluid containing nanoparticles and gyrotactic microorganisms past a stratified stretching surface. Furthermore binary chemical reaction, thermal radiation, and activation energy are taken into assumptions. The analytical solution based on HAM has been performed. The convergence of HAM is presented with the help of figures. The present study is compared with previously published results and has established an excessive agreement which validate the present study. It is perceived that the presence and absence of an electric field influences the variations in fluid velocities due to presence of magnetic field. The micropolar constant heightens the velocity and microrotation of the fluid flow. The buoyancy parameter and bioconvection Rayleigh number diminish the velocity function while these parameters show dual impact on microrotation function. The skin friction and couple stress escalates with the increasing buoyancy ratio parameter and bioconvection Rayleigh number.

Statistical modeling for bioconvective tangent hyperbolic nanofluid towards stretching surface with zero mass flux condition

This article presents the implementation of a numerical solution of bioconvective nanofluid flow. The boundary layer flow (BLF) towards a vertical exponentially stretching plate with combination of heat and mass transfer rate in tangent hyperbolic nanofluid containing microorganisms. We have introduced zero mass flux condition to achieve physically realistic outcomes. Analysis is conducted with magnetic field phenomenon. By using similarity variables, the partial differential equation which governs the said model was converted into a nonlinear ordinary differential equation, and numerical results are achieved by applying the shooting technique. The paper describes and addresses all numerical outcomes, such as for the Skin friction coefficients (SFC), local density of motile microorganisams (LDMM) and the local number Nusselt (LNN). Furthermore, the effects of the buoyancy force number, bioconvection Lewis parameter, bioconvection Rayleigh number, bioconvection Pecelt parameter, thermophoresis and Brownian motion are discussed. The outcomes of the study ensure that the stretched surface has a unique solution: as Nr (Lb) and Rb (Pe) increase, the drag force (mass transfer rate) increases respectively. Furthermore, for least values of Nb and all the values of Nt under consideration the rate of heat transfer upsurges. The data of SFC, LNN, and LDMM have been tested utilizing various statistical models, and it is noted that data sets for SFC and LDMM fit the Weibull model for different values of Nr and Lb respectively. On the other hand, Frechet distribution fits well for LNN data set for various values of Nt.

Bio-convective and chemically reactive hybrid nanofluid flow upon a thin stirring needle with viscous dissipation

In this work, the thermal analysis for bio-convective hybrid nanofluid flowing upon a thin horizontally moving needle is carried out. The chemical reaction and viscous dissipation has also considered for flow system in the presence of microorganism. The hybrid nanoparticles comprising of Copper \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {Cu} \right)$$\end{document}Cu and Alumina \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {Al_{2} O_{3} } \right)$$\end{document}Al2O3 are considered for current flow problem. Mathematically the flow problem is formulated by employing the famous Buongiorno’s model that will also investigate the consequences of thermophoretic forces and Brownian motion upon flow system. Group of similar variables is used to transform the model equations into dimensionless form and have then solved analytically by homotopy analysis method (HAM). It has established in this work that, flow of fluid declines due to increase in bioconvection Rayleigh number, buoyancy ratio and volume fractions of nanoparticles. Thermal flow grows due to rise in Eckert number, Brownian, thermophoresis parameters and volume fraction of nanoparticles. Concentration profiles increase due to growth in Brownian motion parameter and reduces due to increase in thermophoresis parameter and Lewis number. Motile microorganism profile declines due to augmentation in Peclet and bioconvection Lewis numbers. Moreover, the percentage enhancement in the drag force and rate of heat transfer using conventional nanofluid and hybrid nanofluid are observed and discussed. The hybrid nanofluid increases the skin friction and heat transfer rate more rapidly and efficiently as compared to other traditional fluids. A comparison of the present study with the existing literature is also conducted with a closed agreement between both results for variations in thickness of the needle.

Numerical simulation of squeezing flow Jeffrey nanofluid confined by two parallel disks with the help of chemical reaction: effects of activation energy and microorganisms

The utilization of nano-materials in a base fluid is a new dynamic technique to improve the thermal conductivity of base fluids. The suspension of tiny nanoparticles in base fluids is referred to the nano-materials. Nanofluids play a beneficial contribution in the field of nanotechnology, heat treatment enhancement, cooling facilities, biomedicine, bioengineering, radiation therapy and in military fields. The analysis of bioconvection characteristics for unsteady squeezing flow of non-Newtonian Jeffery nanofluid with swimming microorganisms over parallel disks with thermal radiation and activation energy has been studied in this continuation. The motivations for performing current analysis are to inspect the heat transfer enhancement in Jeffrey nanofluid in presence of multiple thermal features. The Jeffrey nanofluid contains motile microorganisms which convey dynamic applications in bio-technology and medical sciences and agricultural engineering. The system comprising differential equations of derivative is restricted to an ordinary one by means of a sufficient dimensionless similarity vector, and then implemented numerically by means of a famous shooting scheme with MATLAB tools. The effect of the significant parameters over the fluid flow is investigated from a physical point of view. The numerical findings of the modeled system are explored in detail using tabular data.

Bioconvection flow in accelerated couple stress nanoparticles with activation energy: bio-fuel applications

On the account of significance of bioconvection in biotechnology and several biological systems, valuable contributions have been performed by scientists in current decade. In current framework, a theoretical bioconvection model is constituted to examine the analyzed the thermally developed magnetized couple stress nanoparticles flow by involving narrative flow characteristics namely activation energy, chemical reaction and radiation features. The accelerated flow is organized on the periodically porous stretched configuration. The heat performances are evaluated via famous Buongiorno’s model which successfully reflects the important features of thermophoretic and Brownian motion. The composed fluid model is based on the governing equations of momentum, energy, nanoparticles concentration and motile microorganisms. The dimensionless problem has been solved analytically via homotopic procedure where the convergence of results is carefully examined. The interesting graphical description for the distribution of velocity, heat transfer of nanoparticles, concentration pattern and gyrotactic microorganism significance are presented with relevant physical significance. The variation in wall shear stress is also graphically underlined which shows an interesting periodic oscillation near the flow domain. The numerical interpretation for examining the heat mass and motile density transfer rate is presented in tubular form.

Modulated Viscosity-Dependent Parameters for MHD Blood Flow in Microvessels Containing Oxytactic Microorganisms and Nanoparticles

This work’s primary purpose is to implement a numerical study that simulates blood flow through a microvessel involving oxytactic microorganisms and nanoparticles. The oxytactic microorganisms exhibit negative chemotaxis to gradients of oxygen (oxygen repellents). These microorganisms are to batter infected hypoxic tumor cells as drug-carriers. The viscosity of blood is to vary with temperature, shear-thinning, and nanoparticle concentration. We have formulated a mathematical model then simplified it under assumptions of long wavelength and low Reynold’s number. The resulting non-linear coupled differential equation system is solved numerically with the MATHEMATICA software aid using the built-in command (ParametricNDSolve). This study treated all non-dimensional parameters defined in terms of viscosity to be variables (VP-Model), unlike some previous literature attempts that have considered these parameters mentioned above as constants (CP-Model). The achieved results assured the reliability of the (VP-Model) over the (CP-Model). Our results reveal that temperature and microorganism density increase with the thermophoresis parameter. The impact of increasing the Brownian motion parameter is to increase temperature and lessen microorganism density. Outcomes also indicate an enhancement in the microorganism density towards the hypoxic tumor regions located aside the microvessel walls by boosting oxygen concentrations in the streamflow. The current study is believed to provide further opportunities to improve drug-carrier applications in hypoxic tumor regions by better recognizing the flow features, heat, and mass transfer in such zones.

Significance of Hall effect and Ion slip in a three-dimensional bioconvective Tangent hyperbolic nanofluid flow subject to Arrhenius activation energy

The dynamics of partially ionized fluid flow subjected to the magnetic field are altogether distinct in comparison to the flow of natural fluids. Fewer studies are available in the literature discussing the alluring characteristics of the Hall effect and the Ion slip in nanofluid flows. Nevertheless, the flow of nanofluid flow with Hall and Ion slip effect integrated with activation energy, gyrotactic microorganisms, and Cattaneo-Christov heat flux is still scarce. To fill in this gap, our aim here is to examine the three dimensional electrically conducting Tangent hyperbolic bioconvective nanofluid flow with Hall and Ion slip under the influence of magnetic field and heat transmission phenomenon past a stretching sheet. Impacts of Cattaneo-Christov heat flux, Arrhenius activation energy, and chemical reaction are also considered here. For the conversion of a non-linear system to an ordinary one, pertinent transformations procedure is implemented. By using the bvp4c MATLAB function, these equations with the boundary conditions are worked out numerically. The significant impacts of prominent parameters on velocity, temperature, and concentration profiles are investigated through graphical illustrations. The results show that the velocity of the fluid is enhanced once the Ion slip and Hall parameters values are improved. Furthermore, the concentration is improved when the values of the activation energy parameter are enhanced.

Stability theory of nano-fluid over an exponentially stretching cylindrical surface containing microorganisms

This research is emphasized to describe the stability analysis in the form of dual solution of the flow and heat analysis on nanofluid over an exponential stretching cylindrical surface containing microorganisms. The research is also implemented to manifest the dual profiles of velocity, temperature and nanoparticle concentration in the effect of velocity ratio parameter (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s = \frac{{U_{w} }}{{U_{\infty } }}$$\end{document}s=UwU∞). Living microorganisms’ cell are mixed into the nanofluid to neglect the unstable condition of nano type particles. The governing equations are transformed to non-linear ordinary differential equations with respect to pertinent boundary conditions by using similarity transformation. The significant differential equations are solved using build in function bvp4c in MATLAB. It is seen that the solution is not unique for vertical stretching sheet. This research is reached to excellent argument when found results are compared with available result. It is noticed that dual results are obtained demanding on critical value (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s_{c}$$\end{document}sc), the meanings are indicated at these critical values both solutions are connected and behind these critical value boundary layer separates thus the solution are not stable.

Thermal Aspects of Casson Nanoliquid with Gyrotactic Microorganisms, Temperature-Dependent Viscosity, and Variable Thermal Conductivity: Bio-Technology and Thermal Applications

Owing to the expensive applications of nanoparticles in engineering sciences, an admirable attention has been intended by researchers on this topic in recent years. The utilization of nanoparticles as asource of energy is intended much attention of investigators in recent decade. This novel attempt investigates the thermal properties of Casson nanofluid containing microorganisms induced by an oscillatory moving surface. The fundamental features of heat and mass phenomenon are inspected by utilizing the temperature-dependent viscosity. Buongiorno’s mathematical model is used to report the famous Brownian motion and thermophoretic diffusion consequences. The flow problem characterizes the partial differential equations for which analytical solution has been computed with a convincible accuracy. The insight physical features are inspected with help of various curves. The physical significances of flow parameters is studied via various graphs.

Bioconvection in Cross Nano-Materials with Magnetic Dipole Impacted by Activation Energy, Thermal Radiation, and Second Order Slip

Ferro liquids derive their magneto–viscous behavior from the suspended magnetic nanomaterial that enables tunable changes in temperature, as well as nano-structured fluid characteristics. A theoretical model that depicts the bioconvection flow of cross nanofluid with a magnetic dipole subjected to a cylindrical surface was developed and numerically solved. The model encountered nonlinear thermal radiation, activation energy, and second order slip. The flow equations were reduced and are presented in dimensionless forms, and they were solved numerically using the shooting technique, which is a built-in feature of MatLab. The model encountered symmetrical constraints for predicting velocity, temperature, concentration, and gyrotactic microorganism distribution and profiles. Moreover, the numerical values were computed for local Nusselt number, local Sherwood number, and motile density number against each physical parameter.

Second Grade Bioconvective Nanofluid Flow with Buoyancy Effect and Chemical Reaction

This study mainly concerns with the examination of heat transfer rate, mass and motile micro-organisms for convective second grade nanofluid flow. The considered model comprises of both nanoparticles as well as gyrotactic micro-organisms. Microorganisms stabilize the suspension of nanoparticles by bio-convective flow which is generated by the combined effects of nanoparticles and buoyancy forces. The Brownian motion and thermophoretic mechanisms along with Newtonian heating are also considered. Appropriately modified transformations are invoked to get a non-linear system of differential equations. The resulting problems are solved using a numerical scheme. Velocity field, thermal and solute distributions and motile micro-organism density are discussed graphically. Wall-drag (skin-friction) coefficient, Nusselt, Sherwood and motile micro-organisms are numerically examined for various parameters. The outcomes indicate that for a larger Rayleigh number, the bio-convection restricts the upward movement of nanoparticles that are involved in nanofluid for the given buoyancy effect. Furthermore, larger buoyancy is instigated which certainly opposes the fluid flow and affects the concentration. For a larger values of fluid parameter, the fluid viscosity faces a decline and certainly less restriction is faced by the fluid. In both assisting and opposing cases, we notice a certain rise in fluid motion. Thermal layer receives enhancement for larger values of Brownian diffusion parameter. The random motion for stronger Brownian impact suddenly raises which improves the heat convection and consequently thermal distribution receives enhancement. Thermal distribution receives enhancement for a larger Lewis number whereas the decline is noticed in concentration distribution. The larger Rayleigh number results in a strong buoyancy force that effectively increases the fluid temperature. This also increases the concentration difference, thus more nanoparticles transport between surface and micro-organisms. Furthermore, for larger (Nb), the thermal state of fluid receives enhancement while a decline in motile density is observed. Numerical results show that mass flux is an enhancing function of both the (Le) and (Nb).

Utilization of Second Order Slip, Activation Energy and Viscous Dissipation Consequences in Thermally Developed Flow of Third Grade Nanofluid with Gyrotactic Microorganisms

In recent decades, an interest has been developed towards the thermal consequences of nanofluid because of utilization of nano-materials to improve the thermal conductivity of traditional liquid and subsequently enhance the heat transportation phenomenon. Following this primarily concept, this current work investigates the thermal developed flow of third-grade nanofluid configured by a stretched surface with additional features of activation energy, viscous dissipation and second-order slip. Buongiorno’s nanofluid model is used to explore the thermophoresis and Brownian motion features based on symmetry fundamentals. It is further assumed that the nanoparticles contain gyrotactic microorganisms, which are associated with the most fascination bioconvection phenomenon. The flow problem owing to the partial differential equations is renovated into dimensional form, which is numerically simulated with the help of bvp4c, by using MATLAB software. The aspects of various physical parameters associated to the current analysis are graphically examined against nanoparticles’ velocity, temperature, concentration and gyrotactic microorganisms’ density distributions. Further, the objective of local Nusselt number, local Sherwood number and motile density number are achieved numerically with variation of various parameters. The results presented here may find valuable engineering applications, like cooling liquid metals, solar systems, power production, solar energy, thermal extrusion systems cooling of machine equipment, transformer oil and microelectronics. Further, flow of nanoparticles containing gyrotactic microorganisms has interesting applications in microbial fuel cells, microfluidic devices, bio-technology and enzyme biosensors.

Significance of Bioconvective and Thermally Dissipation Flow of Viscoelastic Nanoparticles with Activation Energy Features: Novel Biofuels Significance

The analysis of bioconvection flow nanofluids is the topic of concern in recent decades as it involves a variety of physical significance in biotechnology. Bioconvection has many applications in the interdisciplinary field of sciences such as in biomedical science, biofuel biotechnology, and enzyme-based biosensors, among others. The aim of the current work is to analyze the bioconvection phenomenon in the two-dimensional steady flow of viscoelastic nanofluid over a vertical surface. Here, the effects of activation energy, second-order slip, and nanoparticles zero mass flux conditions are considered to investigate the flow problem. Based on dimensionless variables, the governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) which are further solved numerically by using a built-in BVP4C approach in MATLAB software. Various controlling parameters like Hartman number, viscoelastic parameter, first and second-order slip factors, buoyancy ratio parameter, thermophoresis parameter, Brownian motion constant, bioconvection Lewis number and Peclet number are graphically illustrated for the distributions of velocity, temperature, concentration, and motile microorganism. Moreover, the variation of local Nusselt number, local Sherwood number, and motile density number are numerically investigated for the involved parameters.

Activation Energy and Second Order Slip in Bioconvection of Oldroyd-B Nanofluid over a Stretching Cylinder: A Proposed Mathematical Model

The thermal performances based on the interaction of nanoparticles are the topic of great interest in recent years. In the current continuation, we have utilized the activation energy and thermal radiation consequences in the bioconvection flow of magnetized Oldroyd-B nanoparticles over a stretching cylinder. As a novelty, the second order slip features (Wu’s slip) and convective Nield boundary assumptions are also introduced for the flow situation. The heat performances of nanofluids are captured with an evaluation of the famous Buongiorno’s model which enables us to determine the attractive features of Brownian motion and thermophoretic diffusion. The suggested thermal system is based on the flow velocity, nanoparticles temperature, nanoparticles volume fraction and motile microorganisms. The governing flow equations for the flow problem are constituted with relevant references for which numerically solution is developed via shooting algorithm. A detailed graphically analysis for the assisted flow problem is performed in view of the involved parameters. Although some studies are available in the literature which deals with the flow of various fluids over-stretching cylinder, the phenomenon of bioconvection and other interesting features are not reported yet. Therefore, present scientific computations are performed to fill this gap and the reported results can be more useful for the enhancement of thermal extrusion processes, solar energy systems, and biofuels.

Interaction of Wu’s Slip Features in Bioconvection of Eyring Powell Nanoparticles with Activation Energy

The current continuation aim is to explore the rheological consequences of Eyring Powell nanofluid over a moving surface in the presence of activation energy and thermal radiation. The bioconvection of magnetized nanoparticles is executed with the evaluation of motile microorganism. The most interesting Wu’s slip effects are also assumed near the surface. The evaluation of nanoparticles for current flow problems has been examined by using Buongiorno’s model. The governing equations for the assumed flow problem are constituted under the boundary layer assumptions. After converting these equations in dimensionless form, the famous shooting technique is executed. A detailed physical significance is searched out in the presence of slip features. The variation of physical quantities, namely velocity, nanoparticles temperature, nano particles concentration, motile microorganism density, skin friction coefficient, local Nusselt number and motile organism density number are observed with detailed physical aspects for various flow controlling parameters.

A numerical treatment of radiative nanofluid 3D flow containing gyrotactic microorganism with anisotropic slip, binary chemical reaction and activation energy

A numerical investigation of steady three dimensional nanofluid flow carrying effects of gyrotactic microorganism with anisotropic slip condition along a moving plate near a stagnation point is conducted. Additionally, influences of Arrhenius activation energy, joule heating accompanying binary chemical reaction and viscous dissipation are also taken into account. A system of nonlinear differential equations obtained from boundary layer partial differential equations is found by utilization of apposite transformations. RK fourth and fifth order technique of Maple software is engaged to acquire the solution of the mathematical model governing the presented fluid flow. A Comparison with previously done study is also made and a good agreement is achieved with existing results; hence reliable results are being presented. Evaluations are carried out for involved parameters graphically against velocity, temperature, concentration fields, microorganism distribution, density number, local Nusselt and Sherwood numbers. It is detected that microorganism distribution exhibit diminishing behavior for rising values of bio-convection Lewis and Peclet numbers.

Fluid Flow and Heat Transfer Analysis of a Nanofluid Containing Motile Gyrotactic Micro-Organisms Passing a Nonlinear Stretching Vertical Sheet in the Presence of a Non-Uniform Magnetic Field; Numerical Approach

The behavior of a water-based nanofluid containing motile gyrotactic micro-organisms passing an isothermal nonlinear stretching sheet in the presence of a non-uniform magnetic field is studied numerically. The governing partial differential equations including continuity, momentums, energy, concentration of the nanoparticles, and density of motile micro-organisms are converted into a system of the ordinary differential equations via a set of similarity transformations. New set of equations are discretized using the finite difference method and have been linearized by employing the Newton’s linearization technique. The tri-diagonal system of algebraic equations from discretization is solved using the well-known Thomas algorithm. The numerical results for profiles of velocity, temperature, nanoparticles concentration and density of motile micro-organisms as well as the local skin friction coefficient C_fx, the local Nusselt number Nu_x, the local Sherwood number Sh_x and the local density number of the motile microorganism Nn_x are expressed graphically and described in detail. This investigation shows the density number of the motile micro-organisms enhances with rise of M, Gr/Re², Pe and Ω but it decreases with augment of Rb and n. Also, Sherwood number augments with an increase of M and Gr/Re², while decreases with n, Rb, Nb and Nr. To show the validity of the current results, a comparison between the present results and the existing literature has been carried out.