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The purpose of this paper is to study the two-dimensional micropolar fluid flow with conjugate heat transfer and mass transpiration. The considered nanofluid has graphene nanoparticles.

Governing nonlinear partial differential equations are converted to nonlinear ordinary differential equations by similarity transformation. Then, to analyze the flow, the authors derive the dual solutions to the flow problem. Biot number and radiation effect are included in the energy equation. The momentum equation was solved by using boundary conditions, and the temperature equation solved by using hypergeometric series solutions. Nusselt numbers and skin friction coefficients are calculated as functions of the Reynolds number. Further, the problem is governed by other parameters, namely, the magnetic parameter, radiation parameter, Prandtl number and mass transpiration. Graphene nanofluids have shown promising thermal conductivity enhancements due to the high thermal conductivity of graphene and have a wide range of applications affecting the thermal boundary layer and serve as coolants and thermal management systems in electronics or as heat transfer fluids in various industrial processes.

Results show that increasing the magnetic field decreases the momentum and increases thermal radiation. The heat source/sink parameter increases the thermal boundary layer. Increasing the volume fraction decreases the velocity profile and increases the temperature. Increasing the Eringen parameter increases the momentum of the fluid flow. Applications are found in the extrusion of polymer sheets, films and sheets, the manufacturing of plastic wires, the fabrication of fibers and the growth of crystals, among others. Heat sources/sinks are commonly used in electronic devices to transfer the heat generated by high-power semiconductor devices such as power transistors and optoelectronics such as lasers and light-emitting diodes to a fluid medium, thermal radiation on the fluid flow used in spectroscopy to study the properties of materials and also used in thermal imaging to capture and display the infrared radiation emitted by objects.

Micropolar fluid flow across stretching/shrinking surfaces is examined. Biot number and radiation effects are included in the energy equation. An increase in the volume fraction decreases the momentum boundary layer thickness. Nusselt numbers and skin friction coefficients are presented versus Reynolds numbers. A dual solution is obtained for a shrinking surface.

The purpose of this study is to analyze the impact of inclined magnetohydrodynamics (MHD) and thermal radiation on the flow of a ternary micropolar nanofluid on a sheet that is expanding and contracting while applying mass transpiration and velocity slip conditions to the flow. The nanofluid, which is composed of Au, Ag and Cu nanoparticles dispersed in water as the base fluid, possesses critical properties for increasing the heat transfer rate and is frequently used in manufacturing and industrial establishments.

The set of governing nonlinear partial differential equations is transformed into a set of nonlinear ordinary differential equations. The outcome of this differential equation is solved and obtained the closed-form solution and energy equation in the form of hypergeometric functions.

The velocity, micro-rotation and temperature field are investigated versus a parametric variation. The physical domains of mass suction or injection and micropolar characteristics play an important role in specifying the presence, singleness and multiplanes of exact solutions. In addition, many nondimensional characteristics of the profiles of temperature, angular velocity and velocity profiles are graphically shown with substantial consequences. Furthermore, adding nanoparticles increases the heat transfer rate of the fluid used in manufacturing and industrial establishments. The current findings may be used for better oil recovery procedures, smart materials such as magnetorheological fluids, targeted medicine administration and increased heat transmission. Concerning environmental cleanup, nanomaterial fabrication and biomedical devices, demonstrate their potential influence in a variety of disciplines.

The originality of this paper is to analyze the impact of inclined MHD at an angle with the ternary nanofluid on a micropolar fluid over an expanding and contracting sheet with thermal radiation effect.

In this communication, a theoretical simulation is aimed to characterize the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching sheet. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. Two different kinds of thermal boundary conditions, namely, the prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux, are considered in the heat transfer analysis. Joule heating (Ohmic dissipation), viscous dissipation and heat source/sink impacts are also included in the energy equation because these phenomena arise frequently in magnetic materials processing.

The governing partial differential equations are transformed into nonlinear ordinary differential equations (ODEs) by adopting suitable similar transformations. The resulting system of nonlinear ODEs is tackled numerically by using the Runge–Kutta fourth (RK4)-order numerical integration scheme based on the shooting technique. The impacts of sundry parameters on stream function, velocity and temperature profiles are viewed with the help of graphical illustrations. For engineering interests, the physical implication of the said parameters on skin friction coefficient, Nussult number and surface temperature are discussed numerically through tables.

As a key outcome, it is noted that the augmented Chandrasekhar number, porosity parameter and Forchhemeir parameter diminish the stream function as well as the velocity profile. The behavior of the Darcian drag force is similar to the magnetic field on fluid flow. Temperature profiles are generally upsurged with the greater magnetic field, couple stress parameter and porosity parameter, and are consistently higher for the PEST case.

The findings obtained from this analysis can be applied in magnetic material processing, metallurgy, casting, filtration of liquid metals, gas-cleaning filtration, cooling of metallic sheets, petroleum industries, geothermal operations, boundary layer resistors in aerodynamics, etc.

From the literature review, it has been found that the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching surface with heat flux conditions is still scarce. The numerical data of the present results are validated with the already existing studies under limited cases and inferred to have good concord.

In recent times, ternary hybrid nanofluid has garnered attention from scientist and researchers due to its improved thermal efficiency. This study aims to delve into the examination of ternary hybrid nanofluid (Al₂O₃–Cu–TiO₂/water), particularly concerning axisymmetric flow over a nonlinearly permeable stretching/shrinking disk. In addition, the investigation of convective boundary conditions and thermal radiation effects is also considered within the context of the described flow problem.

Mathematical formulations representing this problem are reduced into a set of ordinary differential equations (ODEs) using similarity transformation. The MATLAB boundary value problem solver is then used to solve the obtained set of ODEs. The impact of considered physical parameters such as suction parameter, radiation parameter, nonlinear parameter, nanoparticle volumetric concentration and Biot number on the flow profiles as well as the physical quantities is illustrated in graphical form.

The findings revealed the thermal flux for the nonlinearly shrinking disk is approximately 1.33%, significantly higher when compared to the linearly shrinking disk. Moreover, the existence of dual solutions attributed to the nonlinear stretching/shrinking disk is unveiled, with the first solution being identified as the stable and reliable solution through temporal stability analysis.

Understanding ternary hybrid nanofluid behavior and flow has applications in engineering, energy systems and materials research. This study may help develop and optimize nanofluid systems like heat exchangers and cooling systems.

The study of flow dynamics across nonlinear stretching/shrinking disk gains less attention compared to linear stretching/shrinking geometries. Many natural and industrial processes involve nonlinear changes in boundary shapes or sizes. Understanding flow dynamics over nonlinear shrinking/stretching disks is therefore essential for applications in various fields such as materials processing, biomedical engineering and environmental sciences. Hence, this study highlights the axisymmetric flow over a nonlinear stretching/shrinking disk using ternary hybrid nanofluid composed of alumina (Al₂O₃), copper (Cu) and titania (TiO₂). Besides, this study tackles a complex problem involving multiple factors such as suction, radiation and convective boundary conditions. Analyzing such complex systems can provide valuable insights into real-world phenomena where multiple factors interact.

The main focus is to provide a non-similar solution for the magnetohydrodynamic (MHD) flow of Casson fluid over a curved stretching surface through the novel technique of the artificial intelligence (AI)-based Lavenberg–Marquardt scheme of an artificial neural network (ANN). The effects of joule heating, viscous dissipation and non-linear thermal radiation are discussed in relation to the thermal behavior of Casson fluid.

The non-linear coupled boundary layer equations are transformed into a non-linear dimensionless Partial Differential Equation (PDE) by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ordinary differential equations (ODEs). The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

The results indicate that the non-linear radiation parameter increases the fluid temperature. The Casson parameter reduces the fluid velocity as well as the temperature. The mean squared error (MSE), regression plot, error histogram, error analysis of skin friction, and local Nusselt number are presented. Furthermore, the regression values of skin friction and local Nusselt number are obtained as 0.99993 and 0.99997, respectively. The ANN predicted values of skin friction and the local Nusselt number show stability and convergence with high accuracy.

AI-based ANNs have not been applied to non-similar solutions of curved stretching surfaces with Casson fluid model, with viscous dissipation. Moreover, the authors of this study employed Levenberg–Marquardt supervised learning to investigate the non-similar solution of the MHD Casson fluid model over a curved stretching surface with non-linear thermal radiation and joule heating. The governing boundary layer equations are transformed into a non-linear, dimensionless PDE by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ODEs. The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

The purpose of this paper is to present an analytical study on an unsteady magnetohydrodynamic (MHD) boundary layer flow of a rotating viscoelastic fluid over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream taking Hall and ion-slip currents into account. The unsteady MHD flow in the rotating fluid system is generated due to the buoyancy forces arising from temperature and concentration differences in the field of gravity and oscillatory movement of the free-stream.

The resulting partial differential equations governing the fluid motion are solved analytically using the regular perturbation method by assuming a very small viscoelastic parameter. In order to note the influences of various system parameters and to discuss the important flow features, the numerical results for fluid velocity, temperature and species concentration are computed and depicted graphically vs boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form.

An interesting observation is recorded that there occurs a reversal flow in the secondary flow direction due to the movement of the free stream. It is also noted that a decrease in the suction parameter gives a rise in momentum, thermal and concentration boundary layer thicknesses.

Very little research work is reported in the literature on non-Newtonian fluid dynamics where unsteady flow in the system arises due to time-dependent movement of the plate. The motive of the present analytical study is to analyse the influences of Hall and ion-slip currents on unsteady MHD natural convection flow of a rotating viscoelastic fluid (non-Newtonian fluid) over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream.

As transferring biological fluid through an artery is nowadays a pivotal subject, the purpose of this paper is to study the mathematical model of hybrid nanofluid flow comprising pure blood as base fluid and TiO₂ and Ag as nanoparticles through the porous channel, which can be an applicable model for drug delivery.

Both walls of the channel have different permeability, which enables the fluid to enter and exit, and variable height, which dilates and squeezes at the uniform rate. By taking advantage of the similarity transformation technique, governing equations have been converted into a system of the non-linear ordinary differential equation. This problem is solved numerically by utilizing BVP4C built-in function in MATLAB software to explore the impacts of pertinent parameters.

The plots of velocity and temperature profile, normal pressure distribution and wall shear stress, as well as Nusselt number for involved parameters, are presented and the logic and physical reasons beyond them are highlighted. It has been observed that the asymmetry of the channel, caused by different permeability at walls, affects the nature of flow significantly.

To the best of the authors’ knowledge, no one has ever attempted to study the flow through a deformable porous channel with blood as a base fluid and as hybrid nanoparticles to describe medical phenomena and treatment applications. Indeed, the achievements of this paper are purely original and the numerical results were never published by any researcher.

The purpose of this study is two-fold. First, it aims to differentiate the response of a stretching jet encountering a quadratic air resistance from the classical jet shape formed in a frictionless medium. Second, it investigates how the resulting jet forms with and without air resistance, seeking evidence that supports the similarity flows frequently studied for stretching/moving thin bodies under the boundary layer approximation.

This study extends the established electrohydrodynamic stretching jet theory, used to model electrospinning or jet printing in the absence of air resistance, to encompass the impact of the retarding force on the jet stretching in both the cone and final regimes before it impinges on a substrate.

A close examination of the nonlinear governing equations reveals that the jet rapidly thins near the nozzle because of the combined action of viscous and electrical forces. In this region, the exponentially decaying jet receives further support from the air resistance, resulting in a closer alignment with the observed experimental jet. This exponential decay, accelerated by the inversely quadratic speed of the liquid particles, serves as clear evidence for the existence of a similarity flow over an exponentially stretching sheet. Furthermore, in the final regime, the jet stretching exhibits an algebraic decay in the absence of air friction, while with air resistance, it decays exponentially to reach a limiting speed. In the former case, a square root dependence of the stretching jet speed leads to the emergence of a similarity flow over a thin stretching jet, while in the latter case, a Sakiadis’ similarity flow appears over a continuously moving flat surface.

The analysis goes beyond jet hydrodynamics, delving into the interplay of electrostatic forces (including Coulomb’s law) and quadratic air drag, drawing upon experimental data on glycerol liquid presented in earlier publications.

Finally, the asymptotic behavior of the stretching jet under the combined influence of electrostatic pull and its electric currents because of bulk conduction and surface convection is validated through a comprehensive numerical simulation of the nonlinear system.

The fluid flow and heat transfer between a rotating cone above a stretching disk is the prime purpose of the current work. Making use of suitable similarity transformations, it is shown that the physical phenomenon is represented by a system of similarity equations, which is compatible with that of literature in the absence of wall expansion.

Numerical simulation of the system enables us to seize the physical character of fluid filling the conical section as well as of the heat transfer, from small to adequately large gap sizes. How the surface expansion will contribute to the momentum and thermal layers; moreover, to the swirl angle from the disk wall, and heat transports from the cone and disk surfaces is studied in detail.

The results are clear evidences that the wall stretching completely changes the flow and heat behaviors within the conical gap. For instance, the centripetal/centrifugal flow properties of disk/cone are completely altered and the flow swirling angles are increased by means of the wall deformation.

The original value is that at small gap angles faster expansion of the wall overall leads to near-disk surface cooling, while causing the heated region near the cone surface, which has physical implications in practical applications.

A novel type of heat transfer fluid known as hybrid nanofluids is used to improve the efficiency of heat exchangers. It is observed from literature evidence that hybrid nanofluids outperform single nanofluids in terms of thermal performance. This study aims to address the stagnation point flow induced by Williamson hybrid nanofluids across a vertical plate. This fluid is drenched under the influence of mixed convection in a Darcy–Forchheimer porous medium with heat source/sink and entropy generation.

By applying the proper similarity transformation, the partial differential equations that represent the leading model of the flow problem are reduced to ordinary differential equations. For the boundary value problem of the fourth-order code (bvp4c), a built-in MATLAB finite difference code is used to tackle the flow problem and carry out the dual numerical solutions.

The shear stress decreases, but the rate of heat transfer increases because of their greater influence on the permeability parameter and Weissenberg number for both solutions. The ability of hybrid nanofluids to strengthen heat transfer with the incorporation of a porous medium is demonstrated in this study.

The findings may be highly beneficial in raising the energy efficiency of thermal systems.

The originality of the research lies in the investigation of the Darcy–Forchheimer stagnation point flow of a Williamson hybrid nanofluid across a vertical plate, considering buoyancy forces, which introduces another layer of complexity to the flow problem. This aspect has not been extensively studied before. The results are verified and offer a very favorable balance with the acknowledged papers.