Influence of Gyrotactic Microorganisms on Bioconvection in Electromagnetohydrodynamic Hybrid Nanofluid through a Permeable Sheet

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. Since there are many formulas in Section 3, I suggest to add a nomenclature for all the definitions. 

2. In section 4, the results obtained associated with the verification and the sensitivity analyses of key parameters should be elaborated and linked with the theoretical analysis in Section 3. 

3. The discussions on the influences of prandtl number, magnetic diffusivity, brownian motion coefficient, thermophoresis diffusion coefficient,  microorganism diffusion coefficient, concentration difference and bioconvection peclet number should be elaborated in detail. 

4. Is there any coupling effect of the different factors?

5. The conclusions should be concise.

 

Author Response

Response to Reviewer #1

First, we would like to express our sincere gratitude to Reviewer #1 for his/her effort in revising this manuscript. The comments were very useful to enrich the significance of the paper. All corrections are given in red and highlighted.

1. Since there are many formulas in Section 3, I suggest to add a nomenclature for all the definitions. 

Thanks for this suggestion. Your comment has been considered.

2. In section 4, the results obtained associated with the verification and the sensitivity analyses of key parameters should be elaborated and linked with the theoretical analysis in Section 3. 

We found your comment very useful. Section 4 has been reconsidered and updated.

3. The discussions on the influences of prandtl number, magnetic diffusivity, brownian motion coefficient, thermophoresis diffusion coefficient,  microorganism diffusion coefficient, concentration difference and bioconvection peclet number should be elaborated in detail. 

Thanks for your comment. The discussion has been reconsidered and updated.

4. Is there any coupling effect of the different factors?

Yes, there is a strong possibility of coupling effects between the factors: Prandtl number (), magnetic diffusivity (), shape factor (n), microorganism diffusion coefficient (,), Brownian motion coefficient (), thermophoresis diffusion coefficient (), bioconvection Peclet number (), temperature difference (), and concentration difference (). These parameters can interact and influence each other in various ways, impacting the overall behavior of bioconvection in fluid flows.

Here are some potential coupling effects:

•  and : The interplay between  and controls the relative strength of thermal and magnetic diffusion in the system. High  compared to  leads to dominant thermal effects, while high η favors magnetic influences.
• n and Pe: The shape factor, through its influence on surface area, can affect the bioconvection Peclet number, which determines the relative importance of buoyancy-driven convection versus diffusion. Complex shapes (high n) generally enhance bioconvection due to increased surface area for microorganism activity.
• D_n and D_B: The combined effect of microorganism diffusion and Brownian motion determines the overall movement and distribution of microorganisms within the flow. Interactions between these two mechanisms can create complex patterns and influence heat and mass transfer rates.
• D_T and : Thermophoresis, driven by temperature gradients and influenced by D_T, can further enhance bioconvection by directing microorganisms towards warmer regions. This coupling strengthens the heat transfer process.
•  and : Depending on the bioconvection Peclet number and concentration difference, microorganisms can influence mass transfer rates and create concentration gradients within the flow. This coupling can be relevant in bioremediation or pollution dispersion problems.

These are just a few examples, and the specific interactions between these parameters will depend on the specific context and governing equations of the bioconvection phenomenon under study. Understanding and quantifying these coupling effects is crucial for accurately predicting and controlling bioconvection in various applications.

5. The conclusions should be concise.

Thanks. Your comment has been considered.

Reviewer 2 Report

Comments and Suggestions for Authors

computation-2812606

The paper titled "Influence of Gyrotactic Microorganisms on Bioconvection in Electromagnetohydrodynamic-Hybrid Nanofluid through a Permeable Sheet" explores the interaction between microorganisms' movement and physical forces like buoyancy and fluid flow in bioconvection.  It focuses on the laminar-mixed convection incompressible flow at the stagnation point with viscous and gyrotactic microorganisms in a stable electrically conducting hybrid nanofluid (Fe3O4-Cu/water).  The study uses group technique to reduce the governing system to ordinary differential equations (ODEs) and examines the impacts of multiple parameters like Prandtl number, magnetic diffusivity, and bioconvection Peclet number.  The research aims to understand the effects of temperature, magnetic field, velocity, motile microorganisms, and nanoparticles concentration.

The study uses a group technique to reduce the governing system to ordinary differential equations.  This approach, while simplifying the model, might oversimplify the complex interactions in electromagnetohydrodynamic flows and bioconvection processes.  A more detailed computational fluid dynamics model could provide more accurate insights.

The paper makes several assumptions for the sake of analysis.  For instance, the assumption of laminar flow and the neglect of turbulent effects might limit the applicability of the findings to real-world scenarios where turbulence is common.

The paper rely heavily on theoretical models and simulations.  Experimental validation of the results with actual physical systems involving gyrotactic microorganisms and hybrid nanofluids would strengthen the findings.

While the paper discusses the impact of various parameters like the Prandtl number and bioconvection Peclet number, it might benefit from a broader exploration of these parameters.  Understanding how the results vary across a wider range of conditions could provide more comprehensive insights.

The main quantitative results are to be presented on the abstract.

The introduction is relatively short and is to be extended,

The novelty of the paper is to be clearly stated.

To which fluids corresponds the used Prandtl values?  Is there any fluid with Pr = 3?

Is there any direct practical application of the studied configuration?

The following papers may be added to the literature review:

10.1080/17455030.2022.2063989

10.18280/ijht.370209

10.1142/S0217979224502023

10.1142/S0217979223502983

The paper is to be checked for misprints and grammatical errors.

The paper could enhance its contribution by integrating more interdisciplinary perspectives, particularly from biology, to better understand the behavior of microorganisms in such complex flows.

Author Response

Response to Reviewer #2

First, we would like to express our sincere gratitude to Reviewer #2 for his/her effort in revising this manuscript. The comments were very useful to enrich the significance of the paper. All corrections are given in red and highlighted.

The main quantitative results are to be presented on the abstract.

Thanks for your comment. The abstract has been updated.

The introduction is relatively short and is to be extended,

We appreciate your comment. The introduction has been extended.

The novelty of the paper is to be clearly stated.

Thanks for your suggestion. A paragraph has been added at the end of the introduction.

To which fluids corresponds the used Prandtl values?  Is there any fluid with Pr = 3?

The Prandtl number ( ) is a dimensionless quantity that characterizes the relative importance of momentum diffusivity (kinematic viscosity) to thermal diffusivity in a fluid. It is defined as the ratio of the kinematic viscosity to the thermal diffusivity:

 

where  is the kinematic viscosity and  is the thermal diffusivity.

there can indeed be fluids with a Prandtl number of approximately 3. For example, chloromethane, methanol and water liquids can have Prandtl numbers in the range of 2 to 7. However, it's important to note that the Prandtl number can vary depending on factors such as temperature and pressure, so specific fluids may have slightly different Prandtl numbers under different conditions. Moreover, at higher temperatures, water may have Pr of 3. Typically, water may have Pr of 3 to 13 between 0 ^oC and 100 ^oC

 

Is there any direct practical application of the studied configuration?

The study of hybrid nanofluid flow over a horizontal porous stretched sheet, considering external and induced magnetic field effects, has potential applications in various domains, including biological areas such as drug delivery and microcirculatory system flow dynamics. Here are some potential applications:

1. Drug delivery: The use of nanofluids in drug delivery systems has gained considerable attention due to their unique properties. By studying the behavior of hybrid nanofluid flow over a porous stretched sheet, researchers can gain insights into the transport phenomena involved in drug delivery. The external and induced magnetic fields can further enhance the control and targeting of drug-loaded nanoparticles within the fluid flow, allowing for precise delivery to specific locations in the body.
2. Microcirculatory system flow dynamics: Understanding the flow dynamics in the microcirculatory system is crucial for studying various physiological processes and diseases. The application of hybrid nanofluid flow analysis can provide insights into the behavior of blood flow through microvessels. The inclusion of external and induced magnetic fields can help investigate the effects of magnetic nanoparticles on blood flow behavior, such as altering viscosity or inducing targeted flow patterns.
3. Hyperthermia treatment: Hyperthermia is a therapeutic approach that involves raising the temperature of specific body tissues to treat conditions like cancer. The application of external magnetic fields to hybrid nanofluids can induce heat generation through magnetic hyperthermia. By studying the flow characteristics of these nanofluids over a porous stretched sheet, researchers can optimize the heat transfer process, leading to improved hyperthermia treatments.
4. Biomedical diagnostic techniques: The behavior of nanofluids in the presence of external and induced magnetic fields can be exploited for biomedical diagnostic techniques. For example, magnetic resonance imaging (MRI) relies on the interaction between magnetic fields and nanoparticles to create detailed images of internal body structures. The knowledge gained from studying hybrid nanofluid flow in the presence of magnetic fields can contribute to the development of more efficient and accurate diagnostic techniques.

The following papers may be added to the literature review:

10.1080/17455030.2022.2063989

10.18280/ijht.370209

10.1142/S0217979224502023

10.1142/S0217979223502983

Thanks for these interesting papers. They have been added.

The paper is to be checked for misprints and grammatical errors.

Thanks for your comment. The paper has been checked.

The paper could enhance its contribution by integrating more interdisciplinary perspectives, particularly from biology, to better understand the behavior of microorganisms in such complex flows.

Thanks for your suggestion. The results have been updated and interpreted from biological point of view. 

Reviewer 3 Report

Comments and Suggestions for Authors

What is bioconvection, and how is it defined in the context of the organized movement of microorganisms in fluid media?

What are the distinctive patterns produced by microorganisms participating in bioconvection, and what drives the formation of these patterns?

How does the interaction between the swimming behavior of microorganisms and physical forces, such as buoyancy and fluid flow, contribute to the development of bioconvection patterns?

What is the focus of the current research on bioconvection, and how does it relate to the laminar-mixed convection incompressible flow at the stagnation-point with viscous and gyrotactic microorganisms in a stable electrically conducting hybrid nanofluid (Fe3O4-Cu/water)?

What are the potential applications of the hybrid nanofluid flow over a horizontal porous stretched sheet, as well as external and induced magnetic field effects, in biological domains such as drug delivery and microcirculatory system flow dynamics?

Modified introduction “Extension of the Optimal Auxiliary Function Method to Solve the System of a Fractional-Order Whitham–Broer–Kaup Equation” “Solitary Waves Propagation Analysis in Nonlinear Dynamical System of Fractional Coupled Boussinesq-Whitham-Broer-Kaup Equation” “Unraveling the Dynamics of Singular Stochastic Solitons in Stochastic Fractional Kuramoto–Sivashinsky Equation”

How has the governing system been reduced in the current research, and what are the implications of this reduction to a set of ordinary differential equations (ODEs) through the use of the group technique?

What are the key parameters examined in the study, and how do they impact the physical characteristics of the system, including the effects of temperature, magnetic field, velocity, motile microorganisms, and nanoparticles concentration?

What are the potential implications of the research findings for understanding and potentially controlling bioconvection phenomena in fluid dynamics and related fields?

Author Response

Response to Reviewer #3

First, we would like to express our sincere gratitude to Reviewer #3 for his/her effort in revising this manuscript. The comments were very useful to enrich the significance of the paper. All corrections are given in red and highlighted.

What is bioconvection, and how is it defined in the context of the organized movement of microorganisms in fluid media?

The term "bioconvection" describes the structured migration of microorganisms in fluid media, which is usually caused by the interaction of physical and biological elements. The genesis of directed motion and the production of spatial patterns are results of the collective activity of microorganisms, a phenomenon that is seen in many microbial systems.

When microorganisms like bacteria, algae, or protozoa engage in bioconvection, their self-organizing nature causes the cells in the fluid medium to redistribute. Many variables, such as gradients in temperature, light intensity, dissolved gasses, or nutrient concentrations, might cause this redistribution.

Individual motility and cell-to-cell contacts work together to drive the movement of microorganisms during bioconvection. Microorganisms have the ability to move by gliding or swarming, as well as by employing appendages like cilia or flagella. Physical factors like hydrodynamic contacts or chemotactic reactions to chemical signals generated by nearby cells can cause connections between cells.

In bioconvection, the arranged migration of microorganisms frequently results in the creation of discrete configurations, such rolls, vortices, or bands, in the fluid medium. These patterns result from the interaction between population-level feedback systems and the motility of individual cells. The particular patterns that are created are determined by the fluid medium's qualities, the environment, and the microorganisms' traits.

Numerous systems, such as microbial mats, biofilms, and suspensions of microorganisms, have been used to study bioconvection. It affects a wide range of disciplines, including environmental science, microbiology, ecology, and biotechnology. Gaining knowledge about the dynamics and mechanisms of bioconvection might help us understand how microorganisms behave collectively and how that affects ecosystem processes.

What are the distinctive patterns produced by microorganisms participating in bioconvection, and what drives the formation of these patterns?

Different patterns can emerge in the fluid medium as a result of microorganisms engaged in bioconvection. The particular patterns that arise are determined by a number of variables, such as the fluid medium's qualities, the ambient circumstances, and the microorganisms' attributes. The following are a few typical bioconvection patterns that are seen:

1. Bands: Perpendicular to the direction of gravity, bands consist of high cell density or parallel stripes. These bands can cover the whole height of the fluid container and are frequently evenly spaced. A combination of downward sinking owing to gravity and upward fluid movement brought on by the motility of microorganisms drives the creation of bands.
2. Vortices: Microorganisms that rotate produce circular or spiral patterns known as vortices. Regions of high and low cell density are produced by the fluid flow that is caused by moving and rotating cells. These areas come together to create vortices. Both two- and three-dimensional fluid environments can include vortices, which are controlled by variables including fluid viscosity and cell motility.
3. Rolls: Parallel to the direction of fluid flow, rolls are elongated formations or rolls of cells. They are frequently seen in systems like channels or flow chambers that have significant fluid flow. The interaction of cell motility and fluid shear pressures is what causes rolls to occur. Longitudinal structures are formed when cells align and aggregate along the direction of flow.
4. Aggregates and clumps: Cells inside microorganisms can group together in aggregates or clumps as a result of chemotactic or adhesion factors. These aggregates come in a range of sizes and shapes, from tiny clusters to massive clumps with strange shapes. Different environmental cues, such as nutritional gradients or chemical signals emitted by nearby cells, might cause aggregates to form.

The interaction between individual cell motility and population-level feedback processes is what drives the creation of these patterns. These patterns occur as a result of several factors, including fluid movement, gravity, cell motility, chemotaxis, and physical interactions between cells. Research on the precise mechanisms behind pattern generation in bioconvection is currently ongoing, and our knowledge of these processes is always changing.

How does the interaction between the swimming behavior of microorganisms and physical forces, such as buoyancy and fluid flow, contribute to the development of bioconvection patterns?

A key factor in the formation of bioconvection patterns is the interplay between physical forces and the swimming behavior of microorganisms. Microorganisms can cause cell redistribution and the formation of ordered patterns due to their swimming habit, buoyancy, and fluid movement. These elements influence pattern development in the following ways:

1. Swimming behavior: Microorganisms can swim in a variety of ways, including by utilizing cilia, flagella, or other processes like gliding or swarming. The ability to swim lets bacteria navigate their surroundings. The geographical distribution and response to environmental stimuli of individual cells are influenced by their motility.
2. Gravity and buoyancy: Because of variations in cell density and the surrounding fluid, microorganisms in fluid media are subject to buoyancy forces. Cells in the fluid may rise or sink due to buoyancy forces. When subjected to gravity, microorganisms with greater buoyancy than the fluid have a tendency to rise, whereas those with less buoyancy tend to sink. This vertical movement propelled by buoyancy aids in the creation of patterns in bioconvection, such bands.
3. Fluid flow: The creation of bioconvection patterns is greatly influenced by fluid flow, which can be produced by the motility of microorganisms or propelled by outside influences. Microorganism motion causes fluid to move, which affects how cells are distributed. Shear forces, gradients in cell density, and advecting of cells can all be produced by the fluid flow. Microorganisms' swimming behavior is influenced by these flow-induced forces, which can also result in the creation of patterns like rolls or vortices.
4. Hydrodynamic interactions: These happen when the fluid flow surrounding a microbe has an impact on nearby cells. The cells may align, cluster, or redistribute as a result of these interactions. For instance, hydrodynamic attraction or repulsion between nearby swimming cells might result in the development of clusters or the dispersion of cells, respectively. Hydrodynamic interactions affect the formation of bioconvection patterns and are involved in the spatial organization of microorganisms.

Microorganisms and their surroundings interact intricately due to the combined effects of buoyancy, fluid flow, hydrodynamic interactions, and swimming behavior. By influencing the geographical distribution of cells and dictating their collective activity, this interaction results in the formation of bioconvection patterns. Determining the processes behind bioconvection and its consequences in many biological and ecological environments requires an understanding of these interactions.

What is the focus of the current research on bioconvection, and how does it relate to the laminar-mixed convection incompressible flow at the stagnation-point with viscous and gyrotactic microorganisms in a stable electrically conducting hybrid nanofluid (Fe3O4-Cu/water)?

As bacteria are self-organizing entities, their bioconvection process results in the redistribution of fluid medium cells. There are several factors that might lead to this redistribution, including gradients in temperature, heat flux, velocity, or nutrient concentrations.

Laminar-mixed convection incompressible flow: Laminar flow is defined as a turbulence-free, smooth, orderly flow, whereas mixed convection is a mixture of forced (externally driven) and natural (buoyancy-driven) convection. In this instance, buoyancy effects (caused by temperature or density gradients) as well as external forces (such pumps or fans) have an impact on the fluid flow. The precise properties of the flow, such as velocity patterns and pressure distributions, will impact how microorganisms interact with the fluid and each other.

Stagnation point: The surface of an item facing the incoming flow is usually the location of the stagnation point, which is reached when the fluid velocity is zero. The flow is diverted at the stagnation point, creating an area of high pressure. Microorganisms at the stagnation point can modify flow patterns and cause localized variations in shear and pressure forces, all of which can have an impact on fluid dynamics.

Effects of viscosity: The resistance of a fluid to flow is measured by its viscosity. Viscosity has an impact on the mobility and dispersion of cells in the setting of microorganisms in a fluid. Increased viscosity can hinder an organism's motility by lessening its capacity to swim and adding more resistance to its movement. This may have an impact on the bacteria' behavior and dispersal throughout the fluid.

The term "gyrotactic microorganisms" describes the phenomena in which some microorganisms move or align themselves preferentially in response to a gravitational field. The orientation or swimming motion of gyrotactic microorganisms is usually towards the uphill or downward direction of the gravitational field. Gyrotactic microorganisms can segregate or collect in certain flow zones when stable density gradients are present (such as those caused by temperature changes in the fluid), which can help produce localized patterns or aggregations.

Electrically conducting hybrid nanofluid: The system becomes more complicated when an electrically conducting hybrid nanofluid is included. The fluid's electrical conductivity has the ability to interact and change the behavior of microorganisms. Microorganisms' motility, orientation, or aggregation, for instance, can be influenced by electric fields or electrically generated flows, which may result in altered bioconvection patterns.

 

In conclusion, gyrotactic microorganisms, laminar-mixed convective incompressible flow, viscous effects, and an electrically conducting hybrid nanofluid combine to form a complicated system in which the behavior of microorganisms and fluid dynamics are linked.

 

What are the potential applications of the hybrid nanofluid flow over a horizontal porous stretched sheet, as well as external and induced magnetic field effects, in biological domains such as drug delivery and microcirculatory system flow dynamics?

The study of hybrid nanofluid flow over a horizontal porous stretched sheet, considering external and induced magnetic field effects, has potential applications in various domains, including biological areas such as drug delivery and microcirculatory system flow dynamics. Here are some potential applications:

1. Drug delivery: The use of nanofluids in drug delivery systems has gained considerable attention due to their unique properties. By studying the behavior of hybrid nanofluid flow over a porous stretched sheet, researchers can gain insights into the transport phenomena involved in drug delivery. The external and induced magnetic fields can further enhance the control and targeting of drug-loaded nanoparticles within the fluid flow, allowing for precise delivery to specific locations in the body.

 

2. Microcirculatory system flow dynamics: Understanding the flow dynamics in the microcirculatory system is crucial for studying various physiological processes and diseases. The application of hybrid nanofluid flow analysis can provide insights into the behavior of blood flow through microvessels. The inclusion of external and induced magnetic fields can help investigate the effects of magnetic nanoparticles on blood flow behavior, such as altering viscosity or inducing targeted flow patterns.

 

3. Hyperthermia treatment: Hyperthermia is a therapeutic approach that involves raising the temperature of specific body tissues to treat conditions like cancer. The application of external magnetic fields to hybrid nanofluids can induce heat generation through magnetic hyperthermia. By studying the flow characteristics of these nanofluids over a porous stretched sheet, researchers can optimize the heat transfer process, leading to improved hyperthermia treatments.

 

4. Biomedical diagnostic techniques: The behavior of nanofluids in the presence of external and induced magnetic fields can be exploited for biomedical diagnostic techniques. For example, magnetic resonance imaging (MRI) relies on the interaction between magnetic fields and nanoparticles to create detailed images of internal body structures. The knowledge gained from studying hybrid nanofluid flow in the presence of magnetic fields can contribute to the development of more efficient and accurate diagnostic techniques.

Modified introduction “Extension of the Optimal Auxiliary Function Method to Solve the System of a Fractional-Order Whitham–Broer–Kaup Equation” “Solitary Waves Propagation Analysis in Nonlinear Dynamical System of Fractional Coupled Boussinesq-Whitham-Broer-Kaup Equation” “Unraveling the Dynamics of Singular Stochastic Solitons in Stochastic Fractional Kuramoto–Sivashinsky Equation”

Done

How has the governing system been reduced in the current research, and what are the implications of this reduction to a set of ordinary differential equations (ODEs) through the use of the group technique?

• Normalization for equations and B.C.
• Assume group structure

Assume the following structure for the group hierarchy:

           

The differential coefficient functions are represented as  and real values, respectively, with S denoting the system variables. Typically, partial derivatives are shown as:

 

• Substitution in equations
• Try to find
• Use Morgan theorem to find new independent and dependent variables
• Reduce to ODEs
• Find new B.C. corresponding to
• Solve numerically the new ODEs.

More details can be found in [42-48]

What are the key parameters examined in the study, and how do they impact the physical characteristics of the system, including the effects of temperature, magnetic field, velocity, motile microorganisms, and nanoparticles concentration?

Prandtl number, , magnetic diffusivity, , shape factor, microorganism diffusion coefficient, , Brownian motion coefficient, , thermophoresis diffusion coefficient,, bioconvection Peclet number,  , temperature difference, ,and concentration difference,.

• The temperature, heat flow, nanoparticles, and bacterial density all drop when values rise, according to research on the impact of Prandtl number. This is a result of increased fluid viscosity, which makes nanofluid flow more challenging. However, because of the increased viscosity, as  values increase, so does the pressure.
• By analyzing the effect of magnetic diffusivity, it is demonstrated that a drop in the magnetic field and nanofluid velocity is caused by an increase in This is because the rate at which magnetic fields penetrate a conducting fluid is regulated by magnetic diffusivity. Stronger magnetic interactions with the medium are the consequence of the fluid's ability to transfer and retain magnetic fields at low magnetic diffusivity with efficiency. When the magnetic field interacts with the generated electric currents in the fluid, Lorentz forces are created that may have an impact on the fluid's velocity.
• The temperature, heat flow, and bacterial density all reduce as values grow, according to research on the influence of the Brownian motion coefficient. Although the quantity of nanoparticles increases as values climb. Because of this, the random motion of particles floating in a fluid as a result of collisions with fluid molecules is described by the Brownian motion coefficient, which is inversely proportional to temperature. The result of fluid molecules' more energetic random motion as temperature rises is enhanced Brownian motion.
• Research on the effect of thermophoresis diffusion coefficient shows that when values grow, so do the temperature, heat flow, and nanoparticle numbers. However, when values increase, bacterial density decreases. This is because the term "thermophoresis" which is defined by the thermophoresis diffusion coefficient refers to temperature gradient-induced particle mobility in a fluid. It computes how quickly particles react to changes in temperature. The thermophoresis diffusion coefficient may be affected by the fluid's particle concentration. Increased particle concentrations may give rise to particle interactions and collective effects that impact the overall behavior of thermophoresis.
• An analysis of the effects of the microbe diffusion coefficient reveals that the density of bacteria increases with This is because the pace at which bacteria multiply and mix within the fluid is determined by the diffusion coefficient. Bacteria can proliferate across the fluid volume more rapidly and evenly when their diffusion coefficient is higher. The increased likelihood of contacts and interactions may lead to an overall higher density of bacteria in the fluid.
• Analyzing the impact of concentration difference, we see that temperature, heat flow, bacterial density, and nanoparticles all decrease as values increase. This is because changes in concentration lead to a phenomenon called diffusion, which is the net migration of particles from higher concentration areas to lower concentration areas. The diffusion of the nanoparticles generally expands out and equalizes the concentration distribution when there is a concentration gradient (). The characteristics of the fluid medium, concentration, and particle size are a few of the variables affecting the diffusion rate. With increasing diffusion over time, the concentration difference decreases.
• An analysis of the effects of temperature changes reveals that when values climb, the number of nanoparticles rises and the bacterial density falls. This is because the behavior of nanoparticles floating in a fluid can be affected by changes in temperature. A temperature differential can cause thermophoretic mobility, or thermophorophoresis, in nanoparticles. Particles undergoing thermophoresis move due to temperature gradients. Particles often go from hotter to colder regions. The parameters of the nanoparticles (such as size and surface charge) and the fluid (such as viscosity and heat conductivity) govern the amplitude and direction of the thermophoretic motion.
• Analyzing the effect of the nanoparticle shape factor shows that the density of bacteria and nanoparticles increases with n values. On the other hand, the temperature and heat flow increase as n values rise. Because of its greater surface area, the shape factor n = 5.7 platelets nanoparticles take up a higher temperature.
• Analyzing bioconvection's impacts Peclet number shows that bacterial density decreases with increasing Pe values. Motile bacteria rapidly lose thickness when their Peclet number increases. Stated differently, the Peclet number was unquestionably reinforced to compensate for the decreased dispersion of the microorganisms, but the thickness of the motile bacteria dropped. An increase in the value of Pe causes the thickness and limit layer thickness for motile bacteria to drop.

What are the potential implications of the research findings for understanding and potentially controlling bioconvection phenomena in fluid dynamics and related fields?

The study of hybrid nanofluid flow over a horizontal porous stretched sheet, considering external and induced magnetic field effects, has potential applications in various domains, including biological areas such as drug delivery and microcirculatory system flow dynamics. Here are some potential applications:

1. Drug delivery: The use of nanofluids in drug delivery systems has gained considerable attention due to their unique properties. By studying the behavior of hybrid nanofluid flow over a porous stretched sheet, researchers can gain insights into the transport phenomena involved in drug delivery. The external and induced magnetic fields can further enhance the control and targeting of drug-loaded nanoparticles within the fluid flow, allowing for precise delivery to specific locations in the body.
2. Microcirculatory system flow dynamics: Understanding the flow dynamics in the microcirculatory system is crucial for studying various physiological processes and diseases. The application of hybrid nanofluid flow analysis can provide insights into the behavior of blood flow through microvessels. The inclusion of external and induced magnetic fields can help investigate the effects of magnetic nanoparticles on blood flow behavior, such as altering viscosity or inducing targeted flow patterns.
3. Hyperthermia treatment: Hyperthermia is a therapeutic approach that involves raising the temperature of specific body tissues to treat conditions like cancer. The application of external magnetic fields to hybrid nanofluids can induce heat generation through magnetic hyperthermia. By studying the flow characteristics of these nanofluids over a porous stretched sheet, researchers can optimize the heat transfer process, leading to improved hyperthermia treatments.
4. Biomedical diagnostic techniques: The behavior of nanofluids in the presence of external and induced magnetic fields can be exploited for biomedical diagnostic techniques. For example, magnetic resonance imaging (MRI) relies on the interaction between magnetic fields and nanoparticles to create detailed images of internal body structures. The knowledge gained from studying hybrid nanofluid flow in the presence of magnetic fields can contribute to the development of more efficient and accurate diagnostic techniques.

 

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Accept