Motile Microorganisms Research Articles

Response surface optimization and sensitive analysis on biomagnetic blood Carreau nanofluid flow in stenotic artery with motile gyrotactic microorganisms

In this study, we investigate blood flow in a small artery with a constriction using gold nanoparticles (Au) in the presence of microorganisms, mass, and heat transfer. The non-Newtonian behavior of blood fluid in slight arteries is quantitatively inspected by simulating blood flow using the Carreau fluid model. Momentum equations incorporating magnetohydrodynamics (MHD) and Darcy–Forchheimer porous media are used to model the fluid flow. Heat transfer properties, including thermal radiation, joule dissipation, and bio-convective microorganisms, are investigated. Blood serves as the base fluid for the nanofluid, which contains gold nanoparticles. The system's nonlinear partial differential equations are transformed into nonlinear ODEs through suitable transformations. To obtain numerical solutions for these ODEs, the homotopy analysis method is used. The physical implications of flow restrictions are compared with fictitious fluid flow using physical interpretations. Additionally, investigations into the interpretations of blood flow based on drag force and heat transfer are being conducted. ANOVA, or analysis of variance, is a dependable statistical tool used to evaluate regression models and a variety of statistical tests. These investigations include error assessments, total error evaluations, F-values, p-values, and model fit assessments. These statistical investigations were applied to the dataset at hand, with the goal of achieving a robust 95% level of confidence. We investigate the effects of minute adjustments in parameters on both the heat transfer rate and the friction factor rate using these analyses. The study intends to dive deeper into the potential effects of minor changes in one or more factors on the overall effectiveness of surface friction rate and the larger domain of thermal energy transfer. This will be performed by employing sensitivity analysis approaches. This strategy allows us to obtain a better understanding of how minor changes to specific parameters might affect the speed of thermal energy conveyance and fluid flow management. Furthermore, it lays the framework for future studies aimed at optimising system designs.Article highlightsWe examined blood based MHD Au-nanofluid flow in the presence of microorganisms applying Carreau fluid model.To model the nanofluid flow we used, Darcy-Forchheimer porous media and heat transfer properties.Analysis of variance is a dependable statistical tool is used for the finding of regression models and a variety of statistical tests.

Cattaneo–Christov double diffusive non-Newtonian nanofluid flow over a rotating disk of variable thickness influenced by swimming microorganisms and velocity slip condition

This exploration examines the effects of the Cattaneo–Christov double diffusion in the Ostwald-de-Waele nanofluid flow on a rotating disk with varying thicknesses. The incorporation of the impacts of the bioconvection microorganisms increases the stability of the nanofluids. The slip boundary constraint is taken at the disk. The flow system is based on the Buongiorno nanofluid model. The envisioned fluid flow model incorporates heat transmission properties that are affected by nanoparticle volume fraction, Brownian motion, and thermophoresis. The numerical software bvp4c method is affianced. The presented diagrams portray the correlation of the protuberant parameters with the associated profiles given with cogent arguments. It is heeded that higher estimates of the thermal and solutal relaxation parameters dwindled the thermal and mass profiles. Furthermore, the motile microorganism distribution is diminished for larger counts of the Peclet number. A comparison table is also included to justify the truthfulness of the proposed model.

Triple-Diffusive Bioconvection Flow of Sutterby Nanofluid Over an Oscillatory Stretchable Surface Immersed in a Darcy-Forchheimer Porous Medium

To respond to the demands of modern technological processes, the employment of nanofluids to maximize energy efficiency has been a topic of interest to many scientists. The stability of such nanofluids can be appropriately enhanced with the use of gyrotactic microorganisms. In the current framework, we inspect the triple-diffusive bioconvection flow of electro-magnetized Sutterby nanofluid via an oscillatory stretchable surface with Brownian diffusion of both nanoparticles and microorganisms, thermophoresis, buoyancy, and inertial forces. With the utilization of acceptable dimensionless variables, the governed flow equations are first metamorphosed into non-dimensional form, and solutions of the resulting equations are computed using the overlapping grid spectral collocation scheme. The rationale for choosing this numerical approach is provided by computing residual errors and condition numbers. The significance of physical parameters on the quantities of engineering interest and flow profiles is discussed. The main results include that reduced surface shear stress and minimal oscillatory nature of velocity are achieved with the inclusion of porous media, inertial forces, bioconvection, and nanofluid buoyancy forces. Temperature and rate of heat transfer are upsurged with the existence of variable thermal conductivity, nonlinear radiation, and convective heat conditions, which advocate that such features promote superior heat transport within the Sutterby working fluid. Growth in solutal Dufour Lewis number increases solutal concentration while reducing solutal-mass transfer rate. Improvement in microbial Brownian diffusion parameter causes enhancement in the rate of motile microorganisms transfer and reduction in the concentration of gyrotactic microorganisms. This implies that the random motion of motile microorganisms plays a prominent role in the dynamics of microorganisms.

Consequences of an inclined magnetic field and variable viscosity on Williamson blood nanomaterial with bioconvection phenomena passing through peristalsis geometry

The current study presents a novel mathematical model to analyze the peristaltic motion of a blood flow along a vertical tube with Williamson nano fluid; specifically, such geometry is more applicable for medical purposes like esophagus movement. The study includes the solar mimetic system, Rosseland’s estimations, inclined MHD effect, variable conductivity and viscosity. The numerical results of modelled equations were launched using the Bvp4c approach. Important velocity-related discoveries show that viscosity and the Williamson variable lower the blood flow. The temperature is upgraded by the inclusion of Brownian as well as thermophoresis factors and is retarded by the Prandtl number. Although the Brownian motion parameter results in a higher density of motile microorganisms and the activation energy follows the low concentration distribution. The inclined magnetic field decreases the velocity of blood. The consequences of pertinent parameters on the Nusselt number, local skin friction, and Sherwood number are elaborated through graphs.

Sisko nanofluid flow through exponential stretching sheet with swimming of motile gyrotactic microorganisms: An application to nanoengineering

Abstract The swimming of motile gyrotactic microorganism’s phenomenon has recently become one of the most important topics in research due to its applicability in biotechnology, many biological systems, and numerous engineering fields. The gyrotactic microorganisms improve the stability of the nanofluids and enhance the mass/heat transmission. This research investigates the MHD fluid flow of a dissipative Sisko nanofluid containing microorganisms moving along an exponentially stretched sheet in the current framework. The mathematical model comprises equations that encompass the preservation of mass, momentum, energy, nanoparticle concentration, and microorganisms. The equations that govern are more complicated because of nonlinearity, and therefore to obtain the combination of ordinary differential equations, similarity transformations are utilized. The numerical results for the converted mathematical model are carried out with the help of the bvp4c solver. The resulting findings are compared to other studies that have already been published, and a high level of precision is found. The graphical explanations for velocity, temperature, and nanoparticles volume fraction distribution are shown with physical importance. Physical characteristics like Peclet number, Sisko fluid parameter, thermophoresis and Brownian motion parameter, and Hartmann number are taken into consideration for their effects. Based on the numerical outcomes, the bioconvection Peclet number enhances the density of mobile microorganisms, whereas thermal radiation contributes to an elevation in temperature. The velocity field decreases with the enhancement of magnetic parameter; however, the temperature field increases with increased magnetic parameter and thermophoresis parameter augmentation. Our numerical findings are ground breaking and distinctive, and they are used in microfluidic devices including micro instruments, sleeve electrodes, and nerve development electrodes. This study has various applications in nanoengineering, including nanomaterial synthesis, drug delivery systems, bioengineering, nanoscale heat transfer, environmental engineering.

Heat generation (absorption) in 3D bioconvection flow of Casson nanofluid via a convective heated stretchable surface

In the past few years, the bioconvection phenomenon has become increasingly important in various fields such as genetic systems, manufacturing, biotechnology, and ecological sciences. Bioconvection refers to the large-scale movement of fluid driven by a density gradient resulting from the collective spinning of microorganisms, like bacteria and algae. These self-propelled motile microorganisms increase the fluid's density as they swim in a coordinated direction, giving rise to the bioconvection phenomenon. The current study's goals are to investigate the characteristics of heat generation and absorption in a three-dimensional mixed bioconvection flow of Casson nanofluid inside a stretching cylinder. To analyze the system, a set of transformed nonlinear equations is numerically solved using the Runge-Kutta algorithm. The graphical representation helps explain the impact of different variables on physical properties. Notably, higher values of the Casson parameter are associated with increased viscosity and flow resistance, while a higher bioconvection Rayleigh number leads to elevated skin friction and motile density. Also, Skin friction is decreased by increasing the stretching and mixed convection characteristics. Heat generating processes achieve higher motile densities, Nusselt, and Sherwood amounts than heat absorbing processes.

Effect of electrostatic force and thermal radiation of viscoelastic nanofluid flow with motile microorganisms surrounded by PST and PHF: Bacillus anthracis in biological applications

Current studies have a significant application in various fields; motile microorganism, such as bacteria, can be used for targeted drug delivery. This is because they can be engineered to carry drugs to specific locations in the body. For example, bacteria can be modified to express genes that code for targeting ligands, which are molecules that bind to specific receptors on cells. This could help to prevent the bacteria from multiplying and causing disease. The main aim of the current work is to perform the numerical analysis of three-dimensional radiative, steady viscoelastic nanofluids flow towards an exponentially stretchable porous surface. The impact of nth-order chemical reaction and motile microbes are also disclosed looks at how multiple slips affect the Buongiorno model for magnetohydrodynamic viscoelastic nanofluids with radiation across a permeable stretched sheet. The appropriate suitable are used to transform nonlinear partial differential equations into ordinary differential equations. The numerical solution of the resulting system of equations is handled numerically by employing the bvp4c algorithm built-in MATLAB Software which comes of three-stage Lobatto IIIa formula. Dimensionless values such as temperature, concentration, velocity, and the non-Newtonian nano-fluid density profile are explored, as are non-dimensional numbers such as the local Nusselt, local friction coefficient, Sherwood, and motile microbe. Present results signifies enhancement in the temperature profiles as well as the thickness of the thermal boundary layer by increasing Brownian motion (Nb) and thermophoresis parameters (Nt), whereas decrement is noted against the viscoelastic parameter (K). As the value of the magnetic parameter ranges 0.0≤M≤ 0.2 the relative increment noted in skin friction coefficient is about 1.9 %, while decrement is found in curves of velocity field. Our findings are compared with the data available in the literature and found to be in good consensus.

Ternary Hybrid Nanofluids Containing Gyrotactic Microorganisms with Magnetohydrodynamics Effect over a Shrinking/Stretching of the Horizontal Plate

Nowadays, ternary hybrid nanofluids have been discovered by the researchers to play an important role in heat transfer systems. This study focuses on the study of heat and mass transfer of ternary hybrid nanofluids over a shrinking/stretching horizontal plate induced by gyrotactic microorganisms with the effects of magnetohydrodynamics (MHD). Motile microorganisms were added to a suspension of nanoparticles in a base fluid and mixed in most microsystems to the enhance the convectional properties of the nanofluids. This research uses water as the base fluid to investigate the effects of silver (Ag), Aluminium Oxide (AI203) and Copper (Cu) nanoparticles. The similarity transformation was used to reduce the partial differential governing equations into ordinary differential equations. The transformed nonlinear ordinary differential equations with appropriate transformed boundary conditions were solved numerically using the bvp4c procedure in the MATLAB software. The combination of the Tiwari and Das with Buongiorno model used in this mathematical equation. The results of the research are illustrated graphically and presented via tables to show the behaviour of velocity, temperature, concentration of nanoparticles, and microorganism density as well as the coefficients of skin friction, Nusselt number, Sherwood numbers, and motile microorganism density for the nanoparticles of the THNF. The results show that, for the shrinking case, the magnetic field parameter increases for skin friction and Sherwood number, while it decreases for the Nusselt number and density of motile microorganisms. The Brownian motion parameter and bioconvection Péclet number are shown to significantly increase the Sherwood Number and density motile microorganisms. Thermophoresis, however, has been proven to lower the Sherwood number and density of motile microorganisms. Then, THNF (water/Ag-AI2O3-Cu) is shown to better compared to nanofluids (water/AI2O3) and hybrid nanofluids (water/Ag-AI2O3) in both cases.

Confined run-and-tumble model with boundary aggregation: Long-time behavior and convergence to the confined Fokker–Planck model

The motile micro-organisms such as Escherichia coli, sperm, or some seaweed are usually modeled by self-propelled particles that move with the run-and-tumble process. Individual-based stochastic models are usually employed to model the aggregation phenomenon at the boundary, which is an active research field that has attracted a lot of biologists and biophysicists. Self-propelled particles at the microscale have complex behaviors, while characteristics at the population level are more important for practical applications but rely on individual behaviors. Kinetic PDE models that describe the time evolution of the probability density distribution of the motile micro-organisms are widely used. However, how to impose the appropriate boundary conditions that take into account the boundary aggregation phenomena is rarely studied. In this paper, we propose the boundary conditions for a 2D confined run-and-tumble model (CRTM) for self-propelled particle populations moving between two parallel plates with a run-and-tumble process. The proposed model satisfies the relative entropy inequality and thus long-time convergence. We establish the relation between CRTM and the confined Fokker–Planck model (CFPM) studied in [J. Fu, B. Perthame and M. Tang, Fokker–Plank system for movement of micro-organism population in confined environment, J. Statist. Phys. 184 (2021) 1–25]. We prove theoretically that when the tumble is highly forward peaked and frequent enough, CRTM converges asymptotically to the CFPM. A numerical comparison of the CRTM with aggregation and CFPM is given. The time evolution of both the deterministic PDE model and individual-based stochastic simulations are displayed, which match each other well.

Numerical assessment of bioconvection in MHD Prandtl nanofluid with gyrotactic motile microorganisms with bio-fuel applications

Due to the importance of bio-convection in biotechnology and various biological systems, scientists have made significant contributions in the current decade. This study intends to elaborate the investigation of the bio-convection flow in MHD Prandlt nanofluid with gyrotactic motile microorganism. Owing to engineering and industrial applications, the augmentation of dynamism by the insertion of nanoparticles is a prominent issue in the twenty-first period. The Arrhenius law and activation energy are also considered. The boundary layer approximations developed the governing flow equations such as momentum, energy, concentration and microorganisms equations. The non-linear coupled PDEs are converted to non-linear ODES with the help of similarity transformations. A couple of transmuted equations with modified boundary conditions are elucidated with the employ of the BVP4C via Matlab software. The behavior of different parameters on fluid motion, energy equation, concentration, and motile microorganisms are also discussed through graphical illustrations. It is analyzed that the heat transfer is improved by magnetic field while velocity field is diclines. Concentration and density performance improvises on thermophoretic and Brownian motion impact. Microorganisms field is decline with increasing the Peclet number and bioconvection Lewis number.

Permeation Dynamics of Active Swimmers Through Anisotropic Porous Walls

AbstractNatural habitats of most living microorganisms are distinguished by a complex structure often formed by a porous medium such as soil. The dynamics and transport properties of motile microorganisms are strongly affected by crowded and locally anisotropic environments. Using Chlamydomonas reinhardtii as a model system, we explore the permeation of active colloids through a structured wall of obstacles by tracking microswimmers' trajectories and analyzing their statistical properties. Employing micro‐labyrinths formed by cylindrical or elongated pillars, we demonstrate that the anisotropy of the pillar's form and orientation strongly affects the microswimmers' dynamics on different time scales. Furthermore, we discuss the kinetics of the microswimmer exchange between two compartments separated by an array of pillars.

Development of an intelligent computing system using neural networks for modeling bioconvection flow of second-grade nanofluid with gyrotactic microorganisms

Nanoparticles are carried in bioconvective fluid flow by convective motion caused by living tissues. This flow has important applications in cell and tissue engineering because it demonstrates the mechanics of particle transfer between cells and fluids. This type of flow is used in medicine delivery systems that particularly target cancer cells in real life. Nanofluids are crucial suspensions that allow nanomaterials to disperse and behave in a homogeneous and stable environment. The bioconvective second-grade nanofluid flow, on the other hand, is distinguished by a more complex process that permits nanoparticle motion to be controlled by external fields and pressures. This type of flow has numerous applications, including biology, the environment, and energy. It is particularly useful in medical imaging, cancer hyperthermia treatment, and nanodrug delivery systems. The primary purpose of this research is to use an artificial neural network to examine the rate of heat, mass, and motile microbe movement in the convective flow of magnetohydrodynamic second-grade nanofluid toward vertical surface. Suspended nanoparticles are effectively stabilized by the action of microorganisms, facilitated through bioconvection. This process is influenced by both nanoparticle attributes and buoyancy forces. In addition to thermophoretic dynamics and Brownian motion, the model considers radiation and Newtonian heating effects. Nonlinear equation systems are obtained using appropriate transformations. The non-linear simplified equations underwent numerical calculations utilizing the fourth-order Runge-Kutta shooting method. The Sherwood number, Nusselt number, and density of motile microorganism coefficient were determined using various parameters, and three distinct artificial neural networks were built employing the findings.

Peristaltic flow of bioconvective Ree–Eyring nanofluid through an inclined elastic channel with partial slip effects

Pharmaceutical fluid processing is a procedure of medication manufacturing, utilizing a particular kind of heat transfer in a biofluid designed to maintain the desired temperature for extended periods. Choosing a suitable fluid can have a positive effect on the operating efficacy of the system and lengthen the fluid’s and system’s life spans. As an outcome of this development, we investigate the influence of the partial slip and gyrotactic microorganisms on the peristaltic transport of a magnetohydrodynamic Ree–Eyring nanofluid via an aligned porous conduit with thermal radiation, energy generation, along with cross and double diffusion effects. By invoking suitable nondimensional parameters, the proposed dimensional governing equations are transformed into a system of dimensionless partial differential equations. The analytical solutions for the system of partial differential equations are obtained by incorporating the homotopy perturbation method. Further, tabular and graphical presentations are used to examine the characteristics of the various sundry parameters on the temperature, concentration, motile microorganism density, axial velocity, trapping, and other relevant flow quantities. The observations of this study indicate that the Darcy number and thermal Grashof number have the capability to enhance the velocity distribution of the Ree–Eyring nanofluid in the presence of bioconvection. The trapped bolus size and the skin friction coefficient increase noticeably because of an enhancement in the Ree–Eyring fluid parameter. Also, the Darcy number and the Hall current parameter increase the skin friction coefficient. Furthermore, validation of the results is carried out to examine the consistency between the current and the previous findings for some special cases and excellent agreements are found.

Multilayer neural networks for studying three-dimensional flow of non-Newtonian fluid flow with the impact of magnetic dipole and gyrotactic microorganisms

The current paper explores the three-dimensional flow of an Oldroyd-B liquid with the impact of a magnetic dipole that occurred by stretching a flat surface placed in the plane with a linear velocity variation in two directions containing motile gyrotactic microorganisms. Using proper similarity transformations, the governing equations are reduced into nonlinear coupled ordinary differential equations (ODEs). The ODEs are then solved using Runge–Kutta-Fehlberg (RKF) method. The training, testing, and validation processes are carried out in parallel to adapt neural networks and calculate an approximate solution for the considered model. This helps to reduce the mean square error (MSE) function by Levenberg–Marquardt backpropagation. The efficiency of the suggested backpropagated neural networks methodology has been demonstrated by utilizing outcomes such as MSE, error histograms, correlation and regression. Results reveal that the heat transport augments for increased Biot number values. The mass transport declines for improved chemical reaction rate parameter values. A higher Peclet number will result in a lower motile diffusivity and result in a decline in the micro-organism’s density profile. For the least value of Mu and gradient, better convergence of the findings can be achieved with better network testing and training.

Biological transmission in a magnetized reactive Casson–Maxwell nanofluid over a tilted stretchy cylinder in an entropy framework

Biological transmission (or bioconvection) offers a huge room for studying the interplay between microorganisms and fluid dynamics. The understanding of bioconvection is relevant for studying microbial ecology, population dynamics and exploring the behaviour of microorganisms in complex environments. The objective of this research work is to delve into the physical and biochemical aspects of bioconvection in a magnetized Casson–Maxwell nanofluid containing gyrotactic microorganisms. The investigation is conducted on a tilted elongated cylindrical surface, taking into account the presence of entropy generation. Arrhenius activation energy and slip and convective boundary conditions are novel aspects of this research. The current model invokes the impacts of thermophoresis diffusion, and Brownian motion impacts using the Buongiorno model. The Casson–Maxwell fluid model is employed to expound the rheological behaviour of non-Newtonian nanofluids with the migration of gyrotactic microorganisms. The similarity functions are used to convert the model equations and the related boundary conditions into dimensionless form. The insightful numerical results are developed by implementing the ND Solver in Mathematica, providing valuable insights into the velocity, thermal, concentration, and microorganism fields, as well as the rate of entropy generation and other engineering quantities. Outcomes are presented as graphs and tables for further analysis and discussion. The computational findings unravel several significant contributions of influential model parameters. The Lorentz force and porosity are found to create a drag force that deters the fluid pace, while the reverse trend holds for the fluid temperature. Higher activation energy results in a growth in the concentration field. A larger Peclet number leads to a decline in microorganism density. Furthermore, motile microorganisms’ density and swimming speed significantly influence entropy inflation. A 10% increase in magnetic strength results in a 1.47% increase in skin friction for the Casson fluid model and a 1.32% increase in skin friction for the Casson–Maxwell fluid model. This study contributes to understanding bioconvection in reactive Casson–Maxwell nanofluids with gyrotactic microorganisms and sheds light on entropy production in biological systems.

A hybrid machine learning algorithm for studying magnetized nanofluid flow containing gyrotactic microorganisms via a vertically inclined stretching surface.

The novelty of the present work is to acquire continuous functions as solutions rather than the discrete ones that traditional numerical methods generally produce and to minimize simulation times and higher computation costs that are the fundamental barriers to employing any numerical method. In this study, a novel hybrid finite element-based machine learning algorithm utilizing the Levenberg-Marquardt scheme with backpropagation in a neural network (LMBNN) is presented to analyze the nanofluid flow in the presence of magnetohydrodynamics and gyrotactic microorganisms through a vertically inclined stretching surface in a porous medium. Finite Element Method is used to generate the minimum reference dataset for LMBNN by varying six flow parameters in the form of six scenarios. Surface plots are utilized to understand how these scenarios affect velocity, temperature, concentration of nanoparticles, and density of motile microorganisms. Regression analysis, error histogram analysis, and fitness curves based on mean square error all support the LMBNN's effectiveness and dependability. Results reveal that temperature increases with the rise in Brownian motion and thermophoresis parameter, whereas the reverse trend has been noticed for Prandtl number. The motile microorganism density number decreases with the rise in Prandtl numbers but improves with the porosity parameter.

Role of nanolayer on the dynamics of tri-hybrid nanofluid subject to gyrotactic microorganisms and nanoparticles morphology vis two porous disks

This paper investigates the simultaneous heat and mass transfer phenomena in nanolayers induced by morphology, motile microorganisms, and magnetohydrodynamics (MHD). The study also discusses the crucial role of viscous dissipation resulting from joule heating effects in the flow of ternary hybrid nanofluids, considering both model thermal conductivity and nanolayer thermal conductivity. The influence of various types of nanoparticles on thermal conductivity (TC) and nanolayer thermal conductivity (NTC) is examined, with a focus on the significance of chemical reactions and concentration equations. To solve the nonlinear system of ordinary differential equations, a stable and accurate numerical method is employed. The study provides valuable engineering insights, summarizing key parameters such as skin friction coefficient, Nusselt number, Sherwood number, and motile number. Several nondimensional parameter effects like Re, Pr, β, Pe,α,h,r,γ, and Sc are shown in graphical and tabulation form for both porous disks. The addition of nanolayer thermal conductivity of ternary nanoparticles at a level of 5% enhances the heat transfer rate. When the values of the radius of nanoparticles and nanolayer thickness increase, the flow of tri-hybrid nanofluid's nanolayer thermal conductivity behaves oppositely.

Radiative ternary nanoliquid flow over an exponentially stretching sheet with motile oxytactic microorganisms

This article examines the mixed convection ternary nanoliquid flow containing a suspension of oxytactic microorganisms under the impact of nonlinear thermal radiation. The potential applications include microbiology, biotechnology, biosensors, cell therapy, medication release system, and protein expression. The governing equations that handle the problem are partial differential equations, they are dimensional, nonlinear in nature, and are nondimensionalized by using nonsimilar transformations. Further, for the computation of mathematical analysis, the Quasilinearization technique and numerical method such as the implicit finite difference scheme are used. The impacts of varying relevant factors on velocity, temperature, and microbe density are thoroughly examined. Results designate that the radiation factor favorably affects the velocity and temperature profiles. The rate of mass transport of liquid oxygen rises by about 45% when the Schmidt number grows from 1 to 2. The coefficient of skin friction is found to be more for ternary nanofluid than hybrid nanoliquid and nanoliquid. The current analysis compares the solution to earlier literature and finds that there is a good agreement.

Homotopic simulation of MHD bioconvective flow of water-based hybrid nanofluid over a thermal convective exponential stretching surface

PurposeWhilst a modest number of investigations have been undertaken concerning nanofluids (NFs), the exploration of fluid flow under exponentially stretching velocities using NFs remains comparatively uncharted territory. This work presents a distinctive contribution through the comprehensive examination of heat and mass transfer phenomena in the NF ND–Cu/H2O under the influence of an exponentially stretching velocity. Moreover, the investigation delves into the intriguing interplay of gyrotactic microorganisms and convective boundary conditions within the system.Design/methodology/approachSimilarity transformations have been used on PDEs to convert them into dimensionless ODEs. The solution is derived by using the homotopy analysis method (HAM). The pictorial notations have been prepared for sundry flow parameters. Furthermore, some engineering quantities are calculated in terms of the density of motile microbes, Nusselt and Sherwood numbers and skin friction, which are presented in tabular form.FindingsThe mixed convection effect associated with the combined effect of the buoyancy ratio, bioconvection Rayleigh constant and the resistivity due to the magnetization property gives rise to attenuating the velocity distribution significantly in the case of hybrid nanoliquid. The parameters involved in the profile of motile microorganisms attenuate the profile significantly.Practical implicationsThe current simulations have uncovered fascinating discoveries about how metallic NFs behave near a stretched surface. These insights give us valuable information about the characteristics of the boundary layer close to the surface under exponential stretching.Originality/valueThe novelty of the current investigation is the analysis of NF ND–Cu/H2O along with an exponentially stretching velocity in a system with gyrotactic microorganisms. The investigation of fluid flow at an exponentially stretching velocity using NFs is still relatively unexplored.

Enhanced thermal and mass transfer of harnessing microbial mediation in electrically conducting Oldroyd-B nanofluid flow: Eukaryotes microorganisms in biological applications

In bioremediation, pollutants are broken down or detached from an atmosphere using microorganisms like bacteria or fungus. These bacteria can either ingest contaminants or be enzymatically converted into innocuous molecules. Bioremediation can be enhanced by several techniques, such as bioaugmentation (the introduction of specific microorganisms), biostimulator (the provision of nutrients to stimulate microbial activity), and bioventing (the provision of air or oxygen to encourage microbial growth). The creation and dissipation of heat in a convective non-Newtonian Oldroyd-B fluid flow across a nonlinear stretching sheet in a three-dimensional boundary layer is examined in this study. The boundary layer flow's highly nonlinear partial differential equations are transformed into ordinary differential equations in the study via similarity transformations. The bvp4c technique of MATLAB is then used to resolve these equations. The study looks at some variables, including as temperature, concentration, the presence of microorganisms, velocity, heat transfer rate, and shear stress. These parameters are evaluated graphically and presented in tabular form, with a focus on the local Deborah numbers (β₁ and β₂), the local buoyancy parameters (λ₁ and λ₂), the Prandtl number (Pr), the Schmidt number (Sc), the Bio-convection Schmidt number (Sb), and the Peclet number (Pe). The results show that raising the local buoyancy parameter improves the boundary layer flow's velocity field and rate of heat transfer. Visual representations of the effects of non-dimensional factors on non-dimensional velocity, concentration, motile microorganism, and temperature profiles help to comprehend the underlying physical properties clearly.