Density Of Motile Microorganisms Research Articles

Bioconvective flow of thermally radiative Casson nanofluid with aerobic microorganisms over a stretching surface

A mathematical model is proposed to analyze the flow characteristics of a thermally radiative, chemically reacting Casson nanofluid incorporating aerobic microorganisms over a stretching sheet. Nonlinear dimensionless ordinary differential equations are formulated through suitable similarity transformations. The resulting coupled system of nonlinear ordinary differential equations is numerically solved using the finite difference method with the bvp4c routine in MATLAB. The verification of the numerical solution’s accuracy is conducted by comparing it with previously established results under specific conditions pertinent to the present investigation. Skin friction coefficients, local Nusselt number, and Sherwood number are computed for various parameters and their implications for engineering applications are discussed. The investigation also explores the impact of different dimensionless parameters on velocity, temperature, mass concentration, motile microorganism density, and oxygen concentration profiles for both Casson and Newtonian nanofluids, offering a comprehensive analysis. The study highlights that suspending non-Newtonian nanofluids with fast-moving aerobic microorganisms and nanoparticles results in enhanced heat transfer rates, thus presenting potential benefits for practical applications such as the manufacturing of biofilms.

Nonlinear thermal radiation analysis for bioconvection peristaltic transport of fourth-grade nanofluid

Nanoparticles mixed with base liquids result in the formation of nanofluids, known for their exceptional thermal conductivity and their ability to enhance the performance of electrical and mechanical devices. Therefore, this study investigates the peristaltic activity of fourth-grade nanomaterial by taking the consideration of magnetic aspects. Analysis is carried out in the presence of motile gyrotactic microorganisms, Ohmic heating, and viscous dissipation. Thermal transport incorporated effects of nonlinear thermal radiation along with Brownian motion and thermophoresis. Thermal and mass convective conditions are imposed on elastic symmetric channels. The assumptions of low Reynolds number and long wavelength approximations have led to the simplification of the nonlinear partial differential equations system into ordinary differential equations. The governing system is solved numerically by NDSolve technique via Mathematica. Graphs are plotted and examined for velocity, thermal field, density of motile gyrotactic microorganisms, and heat transfer rate.

Darcy Forchhiemer imposed exponential heat source-sink and activation energy with the effects of bioconvection over radially stretching disc

The Darcy–Forchheimer model is a commonly used and accurate method for simulating flow in porous media, proving beneficial for fluid separation, heat exchange, subsurface fluid transfer, filtration, and purification. The current study aims to describe heat and mass transfer in ternary nanofluid flow on a radially stretched sheet with activation energy. The velocity equation includes Darcy–Fochheimer porous media effects. The novelty of this study is enhanced by incorporating gyrotactic microorganisms which are versatile and in nanofluid can greatly improve the thermal conductivity and heat transfer properties of the base fluid, resulting in more efficient heat transfer systems. Furthermore, the governing PDEs are reduced to ODEs via appropriate similarity transformations. The influence of numerous parameters is expanded and physically depicted through the graphical illustration. As the Forchheimer number escalates, so do the medium's porosity and drag coefficient, resulting in more resistive forces and, as a result, lowering fluid velocity. It has been discovered that increasing the exponential heat source/sink causes convective flows that are deficient to transport heat away efficiently, resulting in a slower heat transfer rate. The concentration profile accumulates when the activation energy is large, resulting in a drop in the mass transfer rate. It is observed that the density of motile microorganisms increases with a rise in the Peclet number. Further, the results of the major engineering coefficients Skin-friction, Nusselt number, Sherwood number, and Microorganism density number are numerically examined and tabulated. Also, the numerical outcomes were found to be identical to the previous study.

Numerical comparison of nonlinear thermal radiation and chemically reactive bio-convection flow of Casson-Carreau nano-liquid with gyro-tactic microorganisms: Lie group theoretic approach

The current research presents a mathematical model to study the flow of a non-Newtonian magnetohydrodynamics (MHD) Casson-Carreau nanofluid (CCNF) over a stretching porous surface, considering mass and heat transport rates with Stefan blowing, non-linear thermal radiation, heat source-sink, chemical reaction, thermophoretic and Brownian motions, convective heating, Joule heating, motile microorganisms, and bio-convection. The presence of microorganisms is utilized to control the suspension of nanomaterials within the nanofluid. The current flow model has been rendered by the boundary layer approximation and we get the highly nonlinear partial differential equations (PDEs). These nonlinear PDEs are simplified by the novel Lie group theoretic method. The one-parameter Lie scaling method simplified the PDEs and convert it into the ordinary differential equations (ODEs). Numerical solutions for these ODEs are obtained using the bvp4c scheme built-in function in MATLAB, ensuring reliable outcomes for temperature, velocity, concentration, and motile microorganism density profiles. The numerical results are presented through graphs and compared with available data, showing good agreement. These numerical outcomes reveal several important flow characteristics. Rates of change for Nr are 0.0007 and 0.0005, and for Ω, they are −0.0754 and −0.0536, respectively. Similarly, the rate of change for Rb in both models is −0.002 and −0.0002. Analysis shows a positive impact of the bioconvection Rayleigh number in both models, notably higher for the Casson fluid compared to the Carreau fluid model. Buoyancy ratio parameter exhibits consistent rates of change, while the reduction in impact is more pronounced for the Casson fluid model in the case of the mixed bioconvection parameter. The mixed bio-convection parameter reduces momentum velocity for both Casson and Carreau fluids, whereas the Darcy parameter boosts fluid velocity. As the Newtonian heating parameter increases, the temperature velocity distribution of both fluids also increases. The concentration profile of both Casson-Carreau fluid phases declines as the heat source-sink parameter and Schmidt number increase. Microbial velocity shows a decrease with increasing R values, whereas the opposite trend is observed for the Peclet number Pe.

Numerical analysis of thermophoretic particle deposition in a magneto-Marangoni convective dusty tangent hyperbolic nanofluid flow – Thermal and magnetic features

Abstract In the current study, we focus on the Magneto-Marangoni convective flow of dusty tangent hyperbolic nanofluid (TiO2 – kerosene oil) over a sheet in the presence of thermophoresis particles deposition and gyrotactic microorganisms. Along with activation energy, heat source, variable viscosity, and thermal conductivity, the Dufour-Soret effects are taken into consideration. Variable surface tension gradients are used to identify Marangoni convection. Melting of drying wafers, coating flow technology, wielding, crystals, soap film stabilization, and microfluidics all depend on Marangoni driven flow. This study’s major objective is to ascertain the thermal mobility of nanoparticles in a fluid with a kerosene oil base. To improve mass transfer phenomena, we inserted microorganisms into the base fluid. By using similarity transformations, the resulting system of nonlinear partial differential equations is converted into nonlinear ordinary differential equations. Using a shooting technique based on RKF-45th order, the numerical answers are obtained. For various values of the physical parameters, the local density of motile microorganisms, Nusselt number, skin friction, and Sherwood number are calculated. The findings demonstrated that as the Marangoni convection parameter is raised, the velocity profiles of the dust and fluid phases increase, but the microorganisms, concentration, and temperature profiles degrade in both phases.

Magnetohydrodynamic thermo-bioconvective flow of 3D rotating Williamson nanofluid with Arrhenius activation energy in a Darcy–Forchheimer medium over an exponentially stretching Surface

This paper aims to analyze the heat and mass transfer characteristics of the 3D thermo-bioconvective flow of rotating Williamson nanofluid over an exponentially stretching vertical sheet. The flow distribution considers the influence of nonlinear thermal radiation, Hall and ion-slip currents, joule heating, coupled effects of Dufour and Soret diffusion, internal heat generation, Arrhenius activation energy, Brownian, and thermophoresis diffusion in a Darcy–Forchheimer porous medium. The modeled partial differential equations (PDE) in terms of continuity, momentum, energy, concentration, and density of motile microorganisms are reformed into ordinary differential equations (ODE) forms employing similarity variables. The resulting equations are solved numerically using the spectral local linearization method (SLLM). The successive over-relaxation technique is applied to accelerate and enhance the convergence of the method. The obtained results are graphically and tabularly represented and numerically explored for the effects of pertinent parameters on the velocity, temperature, nanoparticle concentration, and motile microorganism concentration profiles. The rotation and mixed convection parameters dropped the primary velocity curve, while the Williamson and heat source parameters uplifted the microbes density distributions. The temperature field rises with an increase in radiation and microbes Brownian motion and declines with an increase in Hall and ion-slip numbers. Furthermore, with the increase in activation energy from 0.5 to 2 and the mixed convection parameter from 0.6 to 1.3, we observe a respective 3.93% rise and 8.30% fall in mass transfer rates. The current investigation has broad applications, including MHD accelerators, biotechnology, the formation of elastic sheets, the production of polymer solutions, and the synthesis of nanoparticles through microbial processes.

A ROTATING WAVY CYLINDER ON BIOCONVECTION FLOW OF NANOENCAPSULATED PHASE CHANGE MATERIALS IN A FINNED CIRCULAR CYLINDER: ISPH SIMULATIONS

The originality of this study is the introduction of numerical investigations on the bioconvection flow of nano-encapsulated phase change materials (NEPCMs) with oxytactic microorganisms in a new configuration of a circular annulus with a rotating wavy inner cylinder. The incompressible smoothed particle hydrodynamics (ISPH) method was applied to solve the governing partial differential equations for the velocity, temperature, concentration, and density of motile microorganisms. Compared with the conventional mesh-based method, this mesh-free, particle-based approach offers strong advantages in the simulation of complex problems with free surfaces and moving boundaries with large displacements. The pertinent parameters are the undulation number (<i>N<sub>und</sub></i> = 2-36), bioconvection Rayleigh number (<i>Ra<sub>b</sub></i> = 1-1000), Darcy parameter (Da = 10<sup>-5</sup>-10<sup>-2</sup>), length of the inner fin (<i>L<sub>Fin</sub></i> = 0.05-0.15), radius of the inner wavy cylinder (<i>R<sub>c</sub></i> = 0.05-0.25), Rayleigh number (Ra = 10<sup>3</sup>-10<sup>5</sup>), undulation amplitude of the inner wavy cylinder surface (<i>A</i> = 0.1-0.4), and frequency parameter (<i>ω </i>= 1-5). The undulation number of the inner wavy cylinder enhanced the flow of the oxytactic microorganisms and isotherms, whereas it had the reverse effect on the velocity, decreasing the maximum velocity by 26.56%. In addition, the comparatively high undulation amplitude and frequency increased the average Nusselt and Sherwood numbers. It was found that the embedded wavy cylinder interacting with fins plays an important role in enhancing heat transfer and the bioconvection flow within a closed domain.

Sensitivity analysis for MHD bionanofluid slip flow model in fluid-permeable plate

Diagnostic and therapeutic purpose on human healthcare is moving to a trend of combined engineering principles and design concepts. It is therefore beneficial to refine the study on thermodynamic properties of bionanofluid towards a better state of diagnoses and treatments. This paper aims to determine the characteristics of a magnetohydrodynamics (MHD) bionanofluid slip flow model in a fluid-permeable plate. A Buongiorno mathematical model describing steady two-dimensional MHD bionanofluid slip flow across a permeable plate is constructed. Numerical analysis by shooting technique and sensitivity analysis under the principle of RSM is configured to determine the correlation between input parameters and output responses. The relationship between the four parameters of interest namely skin friction coefficient, local Nusselt number, local Sherwood number and local density of motile microorganism with respective velocity, temperature, nanoparticle concentration and microorganism density distributions to the selected input parameters are investigated. Skin friction coefficient and local density of motile microorganism increase with suction and Schmidt number respectively, signifying positive sensitivity. Local Sherwood number is conditionally more sensitive to Brownian motion parameter or else Lewis number. While, local Nusselt number is always gaining negative sensitivity from Lewis number, thermophoresis and Brownian motion parameters. Extensive numerical studies on boundary layer problem have been done; yet this is the first study invoking sensitivity analysis to discuss the sensitivity of parameters of interest to the input thermophysical parameters.

A Numerical approach of activation energy and gyrotactic effects on MHD Carreau Nanofluid flow over plate, wedge and stagnation point

This study numerically investigates the steady two-dimensional flow of a Carreau nanofluid with activation energy and motile microorganisms over a plate, wedge and stagnation point. The effects of the magnetic field, the Brownian motion, the viscous dissipation and the thermophoresis examined for both shear-thinning and the shear-thickening fluids. The similarity transformations are implemented to convert the governing equations into a non-dimensional form for easier analysis. The Runge–Kutta Method and the shooting technique are employed for finding numerical solutions using MATLAB plot form. The obtained numerical results were analyzed for a broad spectrum of dimensionless parameters and are discussed through graphs. These encompass 0.1≤M≤0.4,0.2≤We≤0.8,0.1≤S≤0.4,0.1≤Ec≤0.4,5≤Sc≤20,0.01≤R≤0.04,1≤Nb≤4,0.1≤Nt≤0.4,0.1≤Pe≤0.4,0.01≤Pr≤2and 1≤Ec≤2.5. These ranges were explored concerning velocity, temperature, concentration, diffusion, wall frictional factor and heat transfer rate, both through numerical computations and graphical representations. A decreasing trend in profiles is observed except for velocity, as the magnetic field parameter increases. The flow over a plate exhibits lower skin friction, heat transfer, mass transfer and gyrotactic microorganism compared to other geometries. The Brownian motion leads to a decreased nanoparticle concentration and motile microorganism density, while increasing thermophoresis has the opposite effect. The suction/injection parameter increases fluid velocity but decreases the temperature, the concentration and the motile microorganism density. The shear-thinning nanofluids demonstrate higher rates of the heat transfer, the mass transfer and the motile microorganism compared to shear-thickening fluids. Furthermore, the present analysis demonstrates that as the Peclet number and bioconvective Schmidt number increase, there is a corresponding decrease in microorganism concentration. Additionally, the higher activation energy E is found to enhance the concentration field due to the reduced chemical reaction rates.

Impact of activation energy on magneto-bioconvection flow of oxytactic microorganisms with NePCM in complex shaped enclosure considering thermal radiations

This work explores the effect of activation energy on bioconvection flow of oxytactic microorganisms with nano-encapsulated phase change materials in complex shaped enclosure. The inner wavy wall is partially fixed at the constant high temperature. The proposed problem has been modeled first using the conservation laws and then simulated by utilizing finite element method. The discretized system of nonlinear algebraic equation is computed using the Newtons method. The obtained results have been analyzed for the several important controlling parameters. It has been observed that the vortex centers have been established near the adiabatic walls for lower values of Lewis number. The average Sherwood number and density of motile microorganism are the increasing functions of chemical reaction parameter. Moreover, the average Nusselt number declines with rising values of Peclet number.

Computational investigation for silica-molybdenum disulfide/water-based hybrid nanofluid over an exponential stretching sheet with spectral quasi-linearization method

The current research is focused on analyzing gyrotactic microorganisms within a hybridized nanofluid (NF) model by considering magnetohydrodynamics, electroosmosis, and radiation effects. Demarcated flow is mathematically modeled to yield coupled nonlinear partial differential equations, which are consequently transmuted into ordinary differential equations (ODEs) by adopting similarity transformations. The spectral quasilinearization method is used to generate the solutions of the transformed ODEs via MATLAB. The influence of various flow parameters on both mono NF and hybrid NF phases for velocity, thermal, concentration, and density of motile microorganism is depicted using graphs. The convergence and residual errors are demonstrated in tables for various influenced parameters on hybrid NF. Additionally, interested physical quantities like shear stress and rate of thermal diffusion at the wall have been tabulated by varying the controlling parameters. It is concluded from the current analysis that the higher velocities and temperatures are observed in hybrid NF model as compared with the mono NF model. Biot number and Hartmann number enhance the temperature profile. The velocity is an enhancing function of mixed convection parameter and bioconvection Rayleigh constant. NF flow over a stretching sheet finds applications in enhancing heat transfer for efficient cooling systems, such as electronics and solar collectors, as well as improving drug delivery in biomedicine, nanoparticle synthesis, and chemical processes.

Numerical simulation of unsteady MHD bio-convective flow of viscous nanofluid through a stretching surface

The current flow model is prepared to explore the characteristics of heat and mass transfer through a time-dependent bio-convection slip flow of viscous nanofluid moving over a porous radiative stretched surface model. The outset of bio-thermal convection in a suspension comprising gyrotactic microorganisms and nanoparticles is considered along with radiation and velocity slip. The presence of these nanoparticles and their motion within the nanofluid gives rise to thermophoresis as well as the Brownian motion phenomena and the consideration of these aspects in the model gives realistic results. Moreover, the present model includes the collective influence of the aligned magnetic field, heat source, and mass suction on the boundary. The similarity analysis has been carried out to transform the basic model equations into nonlinear dimensionless ordinary differential equations (ODEs) which are solved numerically using the bvp4c technique in MATLAB. Some reasonable values have been assigned to the flow parameters based on the above different conditions which provide various graphical results. Certain finding states that velocity and temperature respectively decrease and increase as the aligned magnetic field angle is scaled up, whereas the nano particles concentration strengthens with the amplifying values of convection diffusion and thermophoresis parameter and slumps with the rising values of Brownian motion parameter and Schmidt number respectively. Moreover, the concentration of microorganism and nano particles diminishes with the rising values of Schmidt number, as well as the improvement of convection diffusion parameter and Schmidt number magnifies the Sherwood number. The local density of motile microorganisms reduces with the improvement of stretching parameter and bio-convection Schmidt respectively. The obtained results have been validated by comparing them with the published literature.

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.

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.

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.

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.

Bio-Convective Hartmann Flow of Couple Stress Hybrid Nanofluid Between Two Dilating Parallel Walls with Heat and Mass Transfer

The study of bio-convective flow of hybrid nanofluid attracted many researchers because of tremendous applications in the fields of biofuel biotechnology, enzyme-based biosensors and biomedical science. The present work addresses a comparative study of CuO/Al2O3-water and CuO-water nanoparticles on heat and mass transfer characteristics of the squeezing flow of MHD couple stress fluid between two parallel plates by suspending motile micro-organisms. An approximated numerical technique (Shooting method along with Runge-Kutta 4th order scheme) have been employed to analyse the system of coupled nonlinear ordinary differential equations. The above numerical investigations were carried out for various governing parameters such as couple stress parameter, Hartmann number, bioconvection Peclet number, squeezing parameter etc. The effects of these physical parameters are illustrated graphically over velocity components, temperature distribution, diffusion of concentration and density of motile microorganisms. In addition to this the numerical values of skin friction, the local Nusselt number and local Sherwood number are tabulated at the upper plate for CuO-water and CuO–Al2O3-water at the expanding and squeezing cases. The numerical results for temperature profiles are in good consistency with earlier research.

Comparative Numerical Analysis for the Error Estimation of the Fluid Flow over an Inclined Axisymmetric Cylinder with a Gyrotactic Microbe

The numerical investigation of bioconvective nanofluid (NF) flow, which involves gyrotactic microbes and heat and mass transmission analysis above an inclined extending axisymmetric cylinder, is presented in this study. The study aims to investigate the bioconvection flow of nanofluid under the influence of heat sources/sinks. Through proper transformation, all partial differential equations are transformed into a non-linear ODE scheme. A new set of variables is presented in the directive to get the first-order convectional equations and then solved numerically using bvp4c MATLAB, embedded in the function. The proposed model is validated after calculating the error estimation and obtaining the residual error. The influence of various factors on the velocity, energy, concentration, and density of motile microorganisms is examined and studied. The analysis describes and addresses all physical measures of concentration such as Skin Friction (SF), Sherwood number, the density of motile microorganisms, and Nusselt number. To validate the present study, a comparison is conducted with previous studies, and excellent correspondence is found. In addition, the ND-Solve approach is utilized to confirm the bvp4c. The mathematical model is confirmed through error analysis. This study provides the platform for industrial applications such as cooling capacity polymers, heat exchange, and chemical production sectors.

Non‐similar analysis of chemically reactive bioconvective Casson nanofluid flow over an inclined stretching surface

AbstractBioconvection in non‐Newtonian nanofluids has a wide range of contemporary applications in biotech, biomechanics, microbiology, computational biology, medical science, etc. Considering the Casson fluid model and inclined stretching geometry a mathematical model is developed to investigate the influence of chemical reactions on bioconvection characteristics of self‐propelled microbes in a non‐Newtonian nanofluid. Nanoparticles that can be dissolved in the blood (base fluid) include titanium oxide () and aluminium oxide (). The impacts of heat generation, magnetic field, and dissipation of viscosity are also included. To simplify the governing system of partial differential equations (PDEs), boundary layer assumptions are used. By using the proper transformations, the governing PDEs and the boundary conditions that correspond with them are further changed to a dimensionless form. Utilizing a local non‐similarity technique up to the second degree of truncation in conjunction with MATLAB's (bvp4c) built‐in finite difference code, the results of the altered model are gathered. Additionally, after achieving good alignment between calculated findings and published results, the influence of changing factors on the flow of fluids and heat transfer features of the envisioned flow problems is shown and examined in graphical configuration. Tables are designed to establish numerical variants of the drag coefficient and Nusselt number. The Outcome of this study is to highlight the important role that chemical reactions play in the bioconvection of Casson nanofluids, and how manipulating the chemical reaction parameter can impact the transport and heat/mass transfer properties of the fluid. It is noted that increasing the chemical reaction parameter leads to a fall in the concentration profile of the bioconvection Casson nanofluid. Enhancing the Casson fluid parameter enhances the velocity and temperature profile. When the Peclet number is altered, the propagation of microorganisms is constrained. Moreover, it was observed that the density of motile microorganisms increased as the bioconvective Lewis numbers became higher. The coefficient of friction on the inclined stretched surface is increased significantly by the porosity parameter and Lorentz forces, as they act as amplifiers.

Significance of binary chemical reaction with activation energy in magneto-bioconvection flow of a Powell Eyring nanofluid past an inclined stretching sheet by considering temperature-dependent viscosity and thermal conductivity

ABSTRACT In this paper, an unsteady magneto-bioconvection flow of Powell Eyring nanofluid over an inclined stretching sheet in the presence of variable viscosity and thermal conductivity with multiple slip effects has been investigated numerically. The binary chemical reaction with activation energy, viscous dissipation and nonlinear thermal radiation effects are included in this study. The fluid viscosity and the thermal conductivity are assumed to be a linear function of temperature. The basic governing equations are solved numerically by the Runge-Kutta Felhberg method after using similarity transformation. The impact of bioconvection and important physical parameters on profiles of velocity and temperature of nanofluid and nanoparticles concentration, the density of motile microorganisms are analyzed graphically. Findings reveal that the velocity profile decreased by increasing the Powell Eyring fluid parameter values, whereas the temperature distribution depicts the opposite trend. The temperature profile increased with an increment of thermal conductivity parameter, whereas the opposite trends are found for Eckert number. The trend of the graph of temperature profile and nanoparticle concentration profile declined with an increment of the temperature slip parameter. Also, the nanoparticle concentration profile and density of microorganism profile decreased with an increment of activation energy parameter and chemical reaction parameter. The scope of the present investigation can be related to the advanced nanomechanical bioconvection energy conversion devices and bio-nanocoolant systems, among other relevant things.