This study examines the behavior of a micropolar nanofluid flowing over a sheet in the presence of a transverse magnetic field and thermal effects. In addition, chemical (first-order homogeneous) reactions are taken into account. A similarity transformation is used to reduce the system of governing coupled non-linear partial differential equations (PDEs), which account for the transport of mass, momentum, angular momentum, energy and species, to a set of non-linear ordinary differential equations (ODEs). The Runge-Kutta method along with shooting method is used to solve them. The impact of several parameters is evaluated. It is shown that the micro-rotational velocity of the fluid rises with the micropolar factor. Moreover, the radiation parameter can have a remarkable influence on the flow and temperature profiles and on the angular momentum distribution.

Nanoparticles are particles with a size of less than 100 nanometers. They can be made through nanotechnology-based procedures. When nanoparticles are added to a base fluid, they can form a stable suspension and enhance the thermal properties of the fluid. This is because the nanoparticles increase the surface area of the fluid, which allows for more efficient heat transfer. Nanofluids have been shown to have much better heat absorbing and heat transfer properties than traditional working fluids. This makes them promising candidates for a variety of applications, such as electronics, communication, and computational systems, optical devices, and thermal management. In recent years, research into nanofluids has attracted considerable interest due to their extraordinary potential applications. The use of nanoparticles for heat transfer enhancement was first proposed by Choi et al. [

Micropolar fluids are a type of fluid characterized by their microstructure. They fall into the category of fluids with a non-symmetric stress tensor, which we will refer to as polar fluids. These micropolar fluids can also represent systems where rigid, randomly oriented (or spherical) particles are suspended within a viscous medium, with the deformation of these particles being disregarded. This extension of the concept constitutes a noteworthy expansion of the traditional Navier-Stokes model, offering new avenues for potential applications. The model of micropolar fluids particularly compelling and robust is that it serves as both a significant and straightforward extension of the classical Navier-Stokes model. This dual nature enhances its attractiveness and utility in various scientific and engineering contexts. The micropolar fluids were defined by Erignen [

The Fluid flow caused by stretching/shrinking sheet has become an extremely interesting topic over the past decade due to its many industrial uses. Numerous researchers have investigated the dynamics of boundary layer flow and heat transfer over sheet subjected to linear or non-linear stretching or shrinking. The study of micropolar nanofluid flow over these sheets has gained increasing attention in the realm of fluid mechanics. Micropolar nanofluids can be used to improve the quality of glass fibres by reducing defects and increasing strength. Miklavčič et al. [

MHD is the study of how fluids and magnetic fields can interact to produce a variety of phenomena, such as plasma confinement, magnetic propulsion, and dynamo action. The study of magnetohydrodynamic (MHD) flow on boundary layers over continuous stretching/shrinking sheets has gained significant attention in recent years due to its many applications in industrial manufacturing processes. This research is still ongoing, but it has the potential to make significant contributions to the efficiency and safety of these processes. The effects of MHD flow on different geometries have been investigated by many researchers [

Inspired by the previous studies and the importance of heat and mass transfer (HMT) over a stretching/shrinking sheet in various applications of magnetic micropolar-nanomaterials, we are currently working on a study that investigates a novel theoretical approach to the flow behavior of a micropolar nanofluid over a stretching or shrinking sheet in the presence of a transverse magnetic field and thermal effects. The study will take into account various physical aspects, such as chemical reactions, heat generation/absorption, thermal and mass convection. The findings will be well-analyzed using both graphical illustrations and tabular representations.

A review of the literature shows that no previous study has investigated the numerical treatment for creeping the flow through a stretching and shrinking sheet with a magnetic field of micropolar nanofluid model, taking into account the efficiency of thermal radiation, heat source/sink, and chemical reaction. This study aims to fill this gap by providing a comprehensive understanding of the non-Newtonian transport of magnetic field of nanofluid model.

The findings of this study are also relevant to electromagnetic micro-scale pumps that mimic real working fluids and use non-Newtonian micropolar mechanisms. These pumps have the potential to be used in bio-inspired transportable intravenous dripping systems for medical procedures in the 21^{st} century, as they avoid contamination problems, require less maintenance, and have better longevity and efficiency. The current study is discussed in the following sections:

The continuation of a transverse magnetic field in a two-dimensional (2D) flow of a micropolar fluid of nanoparticles with heat and mass transfer over a stretching or shrinking surface was investigated. Both chemical (first-order homogeneous) reactions and thermal radiation were considered. The flow was restricted to the section (y > 0) of the coordinate system, as shown in _{0}, was applied perpendicular to the flow. The induced magnetic field was ignored because the magnetic Reynolds number was relatively constant. The velocity distribution was assumed to be parabolic, as shown in _{w}, C_{w},

(i) Continuity equation:

(ii) Momentum equation:

(iii) Angular momentum equation:

(iv) Energy equation:

(v) Nanoparticle volume fraction equation:

The term can be expressed clearly as follows, using the Roseland approximation (Brewster [

The coefficient of mean absorption is here represented by

Assuming that the temperature difference within the flow can be expressed as a linear combination of the temperature, we can expand

Here neglecting higher order terms beyond the first degree. Using

The equivalent boundary conditions are defined as follows, based on the requirements of the problem [

Here,

The spin gradient viscosity (γ) is proposed to be defined as follows (Fauzi et al. [

In the above context, the material constraint is represented by

Based on the premises outlined by Fauzi et al. [

Here, a > 0 denotes the initial stretching rate,

To non-dimensionalize the governing equations, we make the following suitable substitutions (Fauzi et al. [

It is clear that

The boundary conditions at the transformed domain are as follows:

To provide a comprehensive analysis of the flow, this study not only provides solutions for velocity, microrotation, temperature, and concentration, but also solutions for shear stress at the plates. Additionally, it includes dimensional coefficients for mass and heat transfer rates at the plates, which are quantified by the local Sherwood and local Nusselt numbers.

The skin resistance (friction)

_{w}

Substituting

It is difficult to obtain an analytical solution to the reduced set of coupled similarity

In this study, we assumed that the solution approaches a specific value as

Fauzi et al. [ |
Gangadhar et al. [ |
Present | Fauzi et al. [ |
Gangadhar et al. [ |
Present | |
---|---|---|---|---|---|---|

0 | −1.00000 | −1.000008 | −1.00000 | −1.0000 | −1.000008 | −1.00000 |

1 | −1.3680 | −1.367996 | −1.367999 | −1.2248 | −1.224820 | −1.22483 |

2 | −1.6225 | −1.621575 | −1.621562 | −1.4159 | −1.414479 | −1.414480 |

4 | −2.0075 | −2.005420 | −2.005120 | −1.7381 | −1.733292 | −1.733292 |

0.5 | 1.0 | 0.1 | 0.1 | 2.657307 | 0.258052 | 0.585318 | 0.652472 |

1.0 | -- | -- | -- | 2.579934 | 0.199724 | 0.437316 | 0.658314 |

2 | -- | -- | -- | 2.423979 | 0.162103 | 0.362930 | 0.663776 |

-- | 0.0 | -- | -- | 2.548865 | 0.027702 | 0.641012 | 0.690123 |

-- | 1.0 | -- | -- | 2.657307 | 0.258052 | 0.585318 | 0.652472 |

-- | 2.0 | -- | -- | 2.777827 | 0.448992 | 0.538902 | 0.618085 |

-- | -- | 0.1 | -- | 2.657307 | 0.258052 | 0.585318 | 0.652472 |

-- | -- | 1.0 | -- | 2.418373 | 0.244180 | 0.431765 | 0.734672 |

-- | -- | 2.0 | -- | 2.218373 | 0.236847 | 0.354763 | 0.775956 |

-- | -- | -- | 0.1 | 2.657307 | 0.258052 | 0.585318 | 0.652472 |

-- | -- | -- | 0.3 | 2.954563 | 0.251534 | 0.502983 | 0.698677 |

-- | -- | -- | 0.5 | 3.227309 | 0.242829 | 0.402503 | 0.751802 |

A mathematical framework has been developed to investigate the combined effects of thermal and mass convection, as well as variable electrical conductivity, on a two-dimensional stretching/shrinking MHD micropolar nanofluid flow. The flow variables in

The calculated values are used in

The impact of the field of magnetic parameter

The influences of the Brownian motion parameter

As shown in

The flow (velocity), microrotation, and temperature summaries for several values of the heat absorption/generation parameter

The patterns of translational flow (velocity), microrotation, and nanoparticle concentration change for deviating values of the

To validate the accuracy of the numerical method used in this study, we compare our results with the available studies of Fauzi et al. [

0.1 | 0.3 | 1.5 | 0.1 | 0.687542 | 0.268807 |

0.3 | -- | -- | -- | 0.640553 | 0.474842 |

0.5 | -- | -- | -- | 0.585310 | 0.632471 |

-- | 0.5 | -- | -- | 0.617305 | 0.703832 |

-- | 1.0 | -- | -- | 0.585318 | 0.632471 |

-- | 1.5 | -- | -- | 0.567705 | 0.535068 |

-- | -- | 2.0 | -- | 0.585318 | 0.632471 |

-- | -- | 2.5 | -- | 0.554265 | 0.859145 |

-- | -- | 3.0 | -- | 0.527618 | 1.122960 |

-- | -- | -- | 0.1 | 0.585318 | 0.632471 |

-- | -- | -- | 0.3 | 0.561812 | 0.888751 |

-- | -- | -- | 0.5 | 0.542468 | 1.140132 |

We used a similarity function to investigate the effects of thermal radiation and chemical reaction on MHD free convection flow of micropolar nanofluid across a stretching/shrinking sheet in the presence of a heat source. We obtained the features of the flow, heat transfer, and mass transfer, as well as their rate of flow (skin-friction), rate of heat transfer (local Nusselt number), and rate of mass transfer (local Sherwood number). Here are some of the most significant findings of our study:

The Brownian motion parameter

As the nonlinear stretching sheet/shrinking sheet parameter

The concentration of the fluid decreased as the Lewis number

The fluid concentration and temperature profiles both increased as the thermophoretic parameter

The study opens up new avenues for future research. By examining the effects of hybrid nanoparticles and other physical parameters on the flow and thermal behavior of fluids, we can better understand how to control and optimize these processes. This knowledge could be used to develop new and improved technologies in a variety of fields.

The investigation of the flow mechanics throughout an exponential stretching/shrinking regime provides a framework for scientific and practical applications utilizing electric fluids as they may shed more light on how oil and gas move through a reservoir in an oil or gas field, the movement of subsurface water, and the effectiveness of deviating filtration and purification processes. Possible applications in nuclear engineering include advances in heat shifter design, glass fiber outlining, and combined reactor cooling.

_{0}

Magnetic’s field strength

Volume friction of nanoparticle

_{w}

Volume friction of nanoparticles at sheet

_{f}

Coefficient of friction skin factor

_{p}

Specific heat at constant pressure

_{p})

Fluid’s heat capacitance (^{−1}^{−3})

_{T}

Coefficient of thermophoretic diffusion

_{B}

Diffusion of Brownian motion

Volume fraction of nanoparticle

Dimensionless flow function

Acceleration due to gravity (^{2})

Grashof parameter

Lewis parameter

Fluid’s thermal conductivity

Brownian motion parameter

Thermophoresis parameter

Buoyancy ratio parameter

Convective heat parameter

Magnetic field parameter

_{w}

Wall heat flux

_{x}

Local Nusselt number

Dimensional pressure (

Prandtl number

_{w}

Surface heat flux (^{−2})

Radiation parameter

_{x}

Local Reynolds number

Mass flux parameter

Schmidt number

Local Sherwood number

GFuid temperature (

_{w}

Surface temperature (

Ambient temperature (

Time (

Constant free flow velocity (^{−1})

Velocity components in the ^{−1})

_{w}

Velocity of the wall mass transfer (^{−1})

Cartesian coordinates (

Thermal diffusivity (^{2}/

Similarity variable

Flow function

Dimensionless temperature

Heat generation/absorption parameter

Moving parameter

Dynamic viscosity of the fluid (^{−1}^{−1})

Kinematic viscosity of the fluid (^{2}^{−1})

Density of the fluid (^{−3})

Stefan–Boltzmann constant

The electrical conductivity (^{−1})

Dimensionless time variable

_{w}

Skin friction or wall shear stress

Base fluid

Nanofluid

Wall boundary condition

Free-flow condition

Differentiation with respect to

We are very much thankful to learned reviewers for their useful suggestions for the improvement in the quality of our manuscript.

The authors received no specific funding for this study.

The majority of the article was prepared by P. Roja, and T. Sankar Reddy, however, S.M. Ibrahim, and G. Lorenzini developed the model, provided computational suggestions, and proofread it. The final manuscript was read and approved by all authors.

All code and materials used in the study are available from the corresponding author upon reasonable request.

The authors declare that they have no conflicts of interest to report regarding the present study.

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