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The unsteady hydromagnetic free convection flow of rotating incompressible viscous fluids across an infinite moving plate with fractional thermal transportation is explored in the presence of heat source, Hall current and slip velocity effects. The Laplace transform method is used to convert the controlling PDEs corresponding to the temperature and velocity profiles into linear ODEs. To get the results, the classical model is modified to a fractional-order model using constitutive relations of the generalized Fourier’s law for heat flux. After making the equations dimensionless, solutions to the energy and velocity equations may be found. Graphs are plotted to check the insight of physical characteristics. Moreover, the Mittag-Leffler kernel is most affected. The memory of temperature improved by using generalized Mittag-Leffler kernel in comparison of exponential kernel. Some graphical representations of the temperature and velocity were created using the software application Mathcad. As a result, it is found that with the application of a generalized Mittag-Leffler kernel, the thermal and momentum boundary layers as well as the memory of fluid properties can be enhanced for larger values of the fractional parameter.

This research discusses the investigation of heat and mass transfer in a magnetohydrodynamic (MHD) Casson fluid (CF) flow over an exponentially porous stretching sheet. The analysis takes into account the existence of thermal radiation, viscous dissipation, chemical reactions, and the influence of velocity and thermal slips. A recognized Casson model is taken into account in order to distinguish the characteristics of Casson fluid from those of Newtonian fluids. Using the geometry under consideration, the current physical problem is modeled. Appropriate similarity conversions are implemented to reduce the resultant set of coupled nonlinear PDEs to a set of nonlinear ODEs. By implementing the Keller-Box technique, numerical solutions to these reduced non-dimensional governing flow field equations are obtained. Tables and diagrams are utilized to illustrate the physical behavior of various control parameters. The temperature profile is enhanced and velocity profile diminished as the CF parameter value increased, according to this study. An increase in the velocity slip factor resulted in a diminution in the velocity field, while a gain in the thermal and concentration contours. With growing amounts of the chemical reaction factor, the concentration profile exhibited a decline. Indeed, the similar outcomes elucidated in this paper exhibit a remarkable correspondence with solutions that have been previously documented in the academic literature. This research may be motivated by a desire to improve the comprehension of fluid flow in different engineering and environmental situations, where these conditions are common, such as geothermal energy extraction, thermal management, chemical processing industries, and environmental control technologies.

This study investigates the impact of variable permeability as well as chemical reactions on the oscillatory free convective flow that passes parallel porous flat plates with fluctuating temperature and concentration in the presence of a magnetic field. A vertical channel is assumed to be rotating at an angular velocity $\mathrm{\Omega }$. Periodic free stream velocity causes oscillations in one plate, while periodic suction velocity causes oscillations in the other plate. Complex variable notations are used to solve the governing equations. The perturbation technique is used to derive analytical expressions for the temperature, concentration, and velocity fields. In this study, various parameters were investigated in relation to mean velocity, mean temperature, mean concentration, amplitude, and phase difference. The study also examines the impact on secondary velocity, primary velocity, temperature, concentration, and heat transfer rate during transients. The outcomes are presented graphically for the physical parameters of the problem. The findings contribute to optimizing systems and improving efficiency in heat transfer, fluid dynamics, and environmental remediation.

The principal aim of the work is to investigate the flow of Williamson fluid on a power law extended lubrication surface with partial sliding under the Magnetohydrodynamic issue on account of alterable thickness lubricated film. Accounting for the influence of microbes, assumption of activation energy, Cattaneo–Christov mass and heat flux took place in the equations of concentration and also in the temperature. Our paper will provide remarkable help to the medical and industrial areas because of the inspection under electro osmosis along with MHD effects in the Williamson fluid flow. With the influence of boundary conditions, built-in equations were studied. The BVP4C technique adopted to solve numerically the transformed ordinary differential equations from nonlinear partial differential equations using innumerable variables. The significant outlines of microorganisms, temperature, concentration and velocity were discussed. Decreases in the velocity distribution were observed with magnetic parameters. Also, an increase in friction coefficient was noticed as 3.1069% for rising magnetic field strength.

Swirling flows are important in rheological devices, spin coatings and lubrication, so we set out to investigate what makes chemically reactive non-Newtonian spinning flows across a disk with a radially applied magnetic field so interesting. Nanofluids are thermally enhanced working fluids with many interesting physical properties. This study takes its inspiration from rotating disk oxidations used in the medical techno industry and builds a mathematical model of a continuous convective von Kármán swirling flow including Jeffrey, magnetic, Joule/ohmic and chemical reactions. The wall anisotropy slips and the concentration-induced blowing effects are included. By using the bvp4c approach, the transformed boundary conditions (BCs) are addressed. Graphical representations of the effects of involved parameters on the density distribution of motile microorganisms, concentration, temperature and dimensionless velocity components are shown. Supporting evidence from prior research is included. Novel bioreactors, membrane oxygenators, bio-chromatography and food processing should take note of the study’s findings. As Jeffrey’s parameter upsurges, there is a decrease in radial velocity. As the Jeffrey parameter increases, there is a decrease in the circumferential velocity. Radial flow is significantly enhanced near the wall as the radial slip parameter ($\delta u)$ increases. As the Eckert number grows, the quantity of temperature increases. Concentration distribution closer to the disk to grow as Le increases. The concentration and diffusivity of microorganisms drop as the number of motile microorganisms thickens.

This research utilizes the bvp4c method to conduct a detailed numerical analysis of the hydrothermal behavior of magnetized hybrid nanofluids flowing across a permeable curved surface. The study explores the impact of crucial parameters such as curvature, magnetic field strength, viscosity and suction/injection, alongside the heat absorption coefficient, on the transport properties of copper (Cu) and ferric oxide (Fe₃O₄) nanomaterial’s suspended in water. Results reveal that as the curvature parameter increases, velocity profiles exhibit a decrease under suction conditions and an increase under injection conditions for both conventional and hybrid nanofluids. Furthermore, higher magnetic parameters are found to decrease velocities in general. Hybrid nanofluids display enhanced velocity and thermal performance compared to conventional nanofluids, manifesting higher skin friction and heat transfer rates. Temperature profiles exhibit a complex interplay with curvature, magnetic parameters and the injection/suction scenario, where injection conditions intensify thermal effects. The incorporation of the heat absorption coefficient further amplifies the thermal efficiency of hybrid nanofluids. These findings, supported by previous research, offer valuable insights for optimizing industrial processes, especially in sectors like ceramics, plastics and polymers, where efficient heat management is paramount.

This paper investigates the influence of magneto-tangent hyperbolic nanofluid on the flow of a tri-hybrid nanoliquid consisting of ${\mathrm{\text{MoS}}}_2,\mathrm{\text{Si}}{\mathrm{\text{O}}}_2$, and $\mathrm{\text{GO}}$ particles suspended in $\mathrm{\text{EG}}$. The entropy production is encountered in this analysis. The fluid flows over a stretch sheet is considered. In addition, the energy equation also assumes the existence of a uniform heat source or sink and thermal radiation. Furthermore, the concentration equation emphasizes the chemical reaction. The current proposed model yields a set of nonlinear governing equations. The modeled formulation is transformed into a dimensionless system through the application of a suitable alteration. The complex nonlinear equation system was solved using the bvp4c through numerical methods. The main motive of this exploration is to emphasize the rate of heat and mass transfer in a flow of ${\mathrm{\text{MoS}}}_2,\mathrm{\text{Si}}{\mathrm{\text{O}}}_2$, and $\mathrm{\text{GO}}/\mathrm{\text{EG}}$-based hybrid nanofluid across a stretch sheet. The graphical study illustrates that Weissenberg number and magnetic field enhancement result in decreasing the velocity. But thermal layer, entropy production, and Bejan number are enhanced with larger values of Weissenberg number and magnetic field. This study focuses on different profiles with various flow parameters. Furthermore, we have compared the tri-hybrid nanofluid with the hybrid and mono nanofluid in all the figures and tabular format. Additionally, we have compared tri-hybrid, hybrid, and mono nanofluid using graphs for velocity, temperature, concentration, entropy production, and Bejan number.

The aim of this study is to analyze heat transfer over two horizontal concentric cylinders in the influence of MHD, internal heat source containing porous nanofluids and thermal radiation are considered. The novelty of this work is internal heat source and porous media of H₂O–Cu nanofluids with the Lorentz effect are investigated and its applications are cooling systems, and heat exchangers. In addition, transformation for the momentum and energy equation is applied to obtain a set of ODEs for governing equations in the heat transfer flows. Further, the numerical technique BVP4C is used to solve the resulting system of nonlinear, coupled equations with boundary conditions. The influence of Hartmann number, volume fraction, radiation parameter, internal heat source parameter, Darcy number and different nanoparticles are examined in velocity and temperature profiles. The results show good agreement with the existing work of velocity and temperature graphs. Moreover, they reveal that thermal radiation significantly influences temperature distribution within the annulus, leading to a higher heat transfer rate. Furthermore, the presence of a porous medium and internal heat source modulates the flow patterns. This study provides optimizing MHD nanofluid systems for engineering applications such as thermal management systems, hyperthermia treatment in cancer therapy, food processing, rotating machinery and cooling systems.

In the present paper a one-dimensional mathematical model of a cerebral aneurysm is considered. The model combines the interaction between the arterial wall structure, blood pressure and the cerebral spinal fluid (CSF) that is around the aneurysm. CSF is considered electrically conducting in the presence of a uniform magnetic field. Therefore, it may be possible to control pressure and its flow behavior by using an appropriate magnetic field. Hence, such studies have potential for the treatment of Cerebral aneurysms, diseases of heart and blood vessels. The modeled mathematical equations are solved algebraically and the displacement of the arterial wall is plotted to visualize the wall movement. It is evident from the graphs the inclusion of magnetic field reduce the movement of the arterial wall and in turn prevent the rupture of the cerebral aneurysm. The solution is also investigated using computational tools for various other parameters involve in the model.

This work examines the magnetohydrodynamic (MHD) three-dimensional (3D) flow comprising Cu and Al₂O₃ water-based nanofluids. The effects of heat and mass transfer with the effects of nanoparticles are carried out in the existence of thermal radiation and convective heat and mass transfer boundary conditions. By applying the proper similarity transformations the partial differential equations describing velocity, temperature and nanoparticle volume fraction (NVF) are transformed to a system of nonlinear ordinary differential equations (NODE). An optimal homotopy analysis technique is applied to evaluate the analytical solutions. The influences of pertinent parameters on the velocity, temperature and NVF are displayed in graphical and tabular forms. Calculations of Nusselt number, skin friction coefficients and the local Sherwood number are evaluated via tables. An excellent comparison has also been made with the previously-published literature.

The flow of non-Newtonian liquids and their heat transfer characteristic gained more importance due to their technological, industrial and in many engineering applications. Inspired by these applications, the magnetohydrodynamic (MHD) flow of non-Newtonian liquid characterized by a power-law model is scrutinized. Further, viscous dissipation, Marangoni convection and thermal radiation are taken into the account. In addition, the production of entropy is investigated as a function of temperature, velocity and concentration. For different flow parameters, the total entropy production (EP) rate is examined. The appropriate similarity transformations are used to reduce the modeled equations reduced into ordinary differential equations (ODEs). The Runge–Kutta–Fehlberg 45-order procedure is then used to solve these reduced equations numerically using the shooting technique. Results reveal that the escalating values of radiation parameter escalate the heat transference, but the contrary trend is portrayed for escalating values of power-law index. The augmented values of thermal Marangoni number decline the heat transference. The gain in values of radiation parameter progresses the entropy generation.

Hybrid nanofluid gains attention of scientists due to its dynamic properties in various fields, and thus, hybrid nanofluids can be taken as an innovative form of nanofluids. Even though analysts acquire tremendous results in the field of hybrid nanofluids but yet no study has been carried out to predict magnetohydrodynamic effects in such fluid models. In this present analysis, influence of MHD has been investigated for the micro hybrid nanofluid over a stretched surface under convective conditions. Combine boundary layer equations for the flow have been altered into a suitable form via boundary layer approximations. Further, complete nonlinear system of equations has been numerically solved via BVP-4C method. Interesting results have been demonstrated for an exponentially stretched surface and expressed in the form of shear stress and rate of heat transfer. Results have also been visualized in the form of streamlines and isotherms. This study reveals after observing the numeric values of skin friction and Nusselt number that micropolar hybrid nanofluid models have greater heat transfer rate as compared to nanofluids.

This paper presents the finitely extensible nonlinear elastic-Peterlin (FENE-P) fluid model to analyze how polymeric fluid affects drag and heat transfer over a magnetized stretching surface. The FENE-P is one of the viscosity models used to study the behavior of polymeric fluids. The governing boundary layer equations based on physical laws are transformed into a similar form using appropriated transformation. To discuss the impacts of polymers and magnetic fields on flow and heat transfer, the resulting equations are numerically solved using the shooting method, and the outcomes are presented graphically. The role of magnetic fields and polymers as drag-reducing and heat transfer enhancing agents is also thoroughly discussed.

This analysis inspects an unsteady and incompressible Casson-type fluid moving on a poured inclined oscillating plane with a ramped thermal profile. The physical effects of flow parameters cannot be investigated and studied using a memory effect, just like with regular PDEs. In this study, we have confabulated the solution of magnetised Casson-type fluid with the help of the best and most modified fractional definition, known as the Prabhakar-like thermal fractional derivative. An integral transforms scheme, namely Laplace transformation (LT) solves the dimensionless governed equations. The physical impacts of significant and fractional constraints are examined graphically and mathematically. As a result, we have confabulated that both thermal and momentum dynamics of flowing Casson fluid slow down with the increment in fractional constraint. Additionally, because of the thickness of the boundary layer, the Casson fluid parameter emphasises the dual character of flowing fluid dynamics.

Recent advancements in nanotechnology have created a tremendous platform for the development of the improved performance of ultrahigh coolants known as nanofluids for several industrial and engineering technologies. The present research peruses an inspection of irreversibility analysis of mixed convective flow near a stagnation point provoked by ternary hybrid nanoparticles through a vertical heated flat plate with the Hall effects. Water conveying alumina (Al₂O₃), silver (Ag) and titanium oxide (TiO₂) nanoparticles experiencing convectively heated as appropriate in the engineering or industry are investigated. The leading equations are non-dimensionalized using relevant similarity variables and then numerically cracked via utilizing the bvp4c solver. The impressions of different pertinent parameters on the axial velocity, transverse velocity and temperature profile along with heat transfer and drag force are discussed carefully. Double solutions are observed in the opposing flow; however, a single solution is obtained for the assisting flow. Also, the results indicate that due to nanofluid, the velocity boundary layer thicknesses decrease and the thermal boundary layer width upsurges. Further, the flow and the characteristics of heat transfer can be controlled using a magnetic field.

The heat conversation medium temperately regulates the heat exploitation effectiveness of solar energy. Nanofluids, a kind of functioning fluids with extraordinary thermal conductivity and strong light concentration, have been scrutinized and functionalized to progress the exploitation of solar energy. In recent times the current progress examines the nanofluids with the consideration of thermal sources as it can raise the heat transportation amount. Here, the purpose is to explore the thermal properties of Joule heating and thermal conductivity in magnetite Maxwell nanofluid. The concept of heat sink/source and chemical reaction are also studied. The achieved ordinary differential equations have been solved via homotopic algorithm. The enactment of functioning variables is examined. For Eckert number and variable conductivity factors, the Maxwell temperature field has analogous tendencies. The fluid concentration inflates for thermophoretic factor; however, slows down for the Brownian motion factor. The Brownian and thermophoretic factors decay for Nusselt number. Additionally, the excellent results have been achieved accompanied with possible existing prose precisely.

This paper examines the influence of magnetized Casson nanofluid flow and heat transport phenomena towards a boundary layer flow over a nonlinear stretchable surface. The characteristics of the nanofluid are illustrated by considering Brownian motion and thermophoresis effects due to which the fluid is electrically conducting. The nonlinear Casson model is very useful to describe the fluid behavior and the flow curves of suspensions of pigments in lithographic varnishes intended for the preparation of printing inks. A uniform magnetic field, along with suction and chemical reaction are taken into account. Similarity transformations are employed to convert the PDEs into ODEs, and then solved numerically (Bvp4c) using MATLAB. This scheme consists of a finite difference scheme that implements three-stage Lobatto IIIa collocation formula which provides continuous solution upto fifth-order accuracy. Excellent correctness of the present results has been acquired which is compared with the previous one. The outcomes of various parameters on heat transfer rate, skin friction coefficient, nanoparticle concentration, Sherwood number, velocity and temperature profiles are demonstrated via tabular forms and pictorially. The most important fact is that an increase in the thermophoresis parameter, radiation and magnetic parameter boosts up the fluid temperature, resulting in an improvement in the thermal boundary layer.

A study has been carried for an incompressible electrically conducting, viscous fluid past a continuously stretching surface in the presence of thermal radiation, viscous dissipation and first-order chemical reaction with thermophoresis and Brownian motion. An inclined uniform magnetic field is applied to the fluid flow region. The governing coupled partial differential equations (PDEs) that describe the model are transformed into a set of nonlinear ordinary differential equations (ODEs) by applying similarity analysis. The resultant nonlinear coupled ODEs are computed numerically in MATLAB software using the boundary value problem solver (BVP4C). The effects of various physical parameters have been examined graphically on velocity, concentration and temperature distribution. The comparison has been made from the previously published work, and there is a good agreement with that. These results can be helpful in geothermal engineering, energy conversation and disposal of nuclear waste material. Moreover, this combined effect can also help biologists to study biological macromolecules such as genomic-length DNA and HIV in the microchannel.

This paper discusses the impacts of velocity, temperature, and solutal slip on the mass and heat transfer characterization of MHD mixed convection Casson fluid flow along an exponential permeable stretching surface with chemical reaction, Dufour and Soret effects. The Casson fluid is supposed to flow across an exponentially stretched sheet, together with the exponential temperature and concentration fluctuations of the fluid. As governing equations, the momentum, energy and species concentration equations are constructed and represented as PDEs. Following that, these equations were converted via the similarity transformation into ODEs. Finally, the ODEs are numerically solved using the Keller-box method with MATLAB software’s algorithm. Expressions are produced for the fluid flow, temperature and concentration gradients. We also determined the physical variables from which the friction factor, rate of mass and heat transfer are attained for engineering purposes. Using graphs and tables, the impacts of altered physical characteristics on flow amounts are explored. The consistency and validity of our outcomes revealed a significant degree of agreement when comparing them to previously published studies. The findings reveal that raising the Soret and Dufour parameter enhances the velocity profile at the wall, but the converse is true for increasing the velocity slip factor.

This research aims to study the 3D magnetohydrodynamics stagnation-point flow (SPF) over a horizontal plane surface (HPS) carrying water-based graphene oxide (GO) nanoparticles caused by an irregular heat source/sink used in heat transfer procedures. In addition, a Tiwari–Das model is used to inspect the dynamics of fluid flow behavior and heat transmission features of the nanoparticles with experiencing the impacts of thermal radiation. The acquired nonlinear set of partial differential equations (PDEs) is transfigured to a system of ordinary differential equations (ODEs) using similarity transformations. The accumulative dimensionless ODEs are then further tackled in MATLAB using the bvp4c solver. Tables and figures are prepared for the execution of several relevant constraints along with nodal/saddle indicative parameter, internal heat source/sink parameter, radiation parameter and nanoparticles volume fraction which divulges and clarify more accurately the posited quantitative data and graphical findings. Also, the velocity profile decelerated in the axial and transverse coordinate axes for a higher value of the nanoparticle volume fraction but the dimensionless temperature distribution is augmented. Additionally, thermal boundary layer thickness and profile of temperature enriches with higher impressions of radiation constraint. However, the internal heat sink factor declines the profiles of temperature while escalating with the superior value of the internal heat source parameter.