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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.

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.

This study explores the effects of thermal and magnetohydrodynamics (MHD) on Powell–Eyring fluid with the Cattaneo–Christov heat flux over a curved surface. The mathematical framework regarding the physical problem turn out to a set of nonlinear partial differential equation. The set of governing equations are first reduced into nonlinear ordinary differential equations via appropriate transformations and then analytical solutions of resulting nonlinear differential equations have been obtained by optimal homotopy asymptotic method. The influence of involved parameters such as magnetic parameter, fluid parameter, thermal relaxation parameter, curvature parameter, relaxation parameter, Grashof number, material parameter and Prandtl number are discussed and analyzed in tabular as well as in pictorial form. Finally, a comparison with the existing literature is prepared and an excellent agreement is seen.

Gyrotactic microorganisms may be mobile ones that exist in surroundings, for instance oceans, pools, and reservoirs. The convective heat transfer due to the movement of these microorganisms in the base fluids is known as bio-convection. In this paper, the analysis of MHD bio-convection of nanofluid in the $\mathrm{\Gamma }$-shaped enclosure with gyrotactic microorganisms inside is conducted. The effect of thermal Rayleigh number Ra_t (10⁴–10⁵), bio-convection Rayleigh number (10–100), Lewis number (0.1–0.9), and Peclet number (10${}^{-3}$–10${}^{-1}$) on the natural convection (NC) and concentration of the micro-organisms (C) is investigated. The Navier–Stokes equations are used as the governing equations and are solved by Finite Element Method. The results reveal that Le may have a reverse impact on Nu_avg (upto 42%); however, Pe has a positive impact on both Nu_avg (upto 10%) and Sh_avg (upto 12%) and enhances heat transfer performance.

In most of practical situation multiple slips (velocity, temperature and concentration) has importance in manufacturing, medicinal, imaging processes and design of materials. In view of this, the present work considered the multiple slips on Magneto hydrodynamic (MHD) dissipative non-Newtonian fluid (Casson fluid) above a curved type of a stretching surface are studied. Multiple slips with Casson fluid have significance in controlling the blood flow distribution in human and animal bodies. The R–K fourth-order via shooting technique is used to convert the nonlinear governing equations. The impact of governing parameters is shown and explored graphically. The present investigation explores the multiple slip effects in governing equations under the influence of the magnetic field; the fluid’s temperature and velocity have reverse characteristics. In a few unique situations, the current findings have been in reasonable agreement with the current results. As opposed to when viscous dissipation is absent, the temperature distribution is higher when viscous dissipation is present. It helps us to decide depending on the industrial and manufacturing processes, whether dissipation has to be applied or not. The stretching parameter enhances the Skin friction coefficient and rate of heat transfer, while decreases the rate of mass transfer. Also, the fluid’s temperature decreases because an increase in Casson fluid parameter enhances the plastic dynamic viscosity, which creates resistance in the fluid motion.

In this paper, magnetohydrodynamics of a Casson fluid flow is inspected with the presence of thermal radiation and chemical reaction. Employing the perturbation procedure, the modeling equations are tenacious; the graphs are acquired to illustrate the results. The Casson fluid velocity increases as the perturbation parameter increases. Grashof values for heat and mass transport enhanced Casson fluid velocity. Increasing Casson, magnetic, heat source, and radiation parameters reduce the flow velocity. Prandtl number, heat source, and radiation parameter all reduced the temperature profiles. Chemical reaction parameters lowered the concentration profiles. The skin friction enhances with Casson parameter impact. However, the skin-friction coefficient, Sherwood and Nusselt numbers reduce with an increment in the perturbation parameter. In certain cases, this study’s answers agreed well with the previous literature. Casson liquid with a magnetic region using mixed convection by an exponential vertical boundary layer is the novelty of the work.

The use of heat transfers in heat exchangers, nuclear cooling, solar collectors, and electrical devices is crucial nowadays. Hybrid nanofluid can be used in these applications to get the best results because it encourages efficient heat transmission compared to conventional fluid. The effect of radiation and an unsteady Carreau hybrid fluid in addition to non-Fourier heat flux over a shrinking sheet is discussed in this paper. Using similarity transformations, the newly developed system of partial differential equations (PDEs) is converted into a set of ordinary differential equations (ODEs), that are next numerically addressed by utilizing shooting approach and the Runge–Kutta (RK) method. Tables and graphs are used to present utilizing the computational findings for nondimensional temperature, velocity, heat transfer rate, and friction between fluid and hybrid nanoparticles. Additionally, for certain physical factors, the physical quantities in numerical values were also presented (such as the friction factor and local Nusselt number). We made a restricted case comparison between the current findings and the body of prior research. Our finding confirms that the temperature profile is strengthened by the heat generation parameter and the effect of radiation. The porosity parameter decelerates the momentum boundary layer thickness near the plate.

The theme of this model is to examine the characteristics of heat and mass transfer flow through cone along with volumetric heat generation, variable viscosity, magnetic field and higher-order chemical reaction utilizing SWCNT–Ag/H₂O hybrid nanofluid. The transformed partial differential equations are solved by shooting scheme. The numerical outcomes of physical quantities are revealed by graphs and tables. The local Nusselt number and Sherwood number are displayed with the support of bar diagram. The study depicted that an increase in temperature-dependent viscosity parameter for a particular magnetic field induced an increase in the local Nusselt number and Sherwood number. Furthermore, there was a rise in the data of internal heat generation, temperature outlines of hybrid nanofluid escalated while concentration profiles of working fluid depreciated.

The topic of this study is the flow of a micro-polar liquid toward a nonlinear stretched surface using magnetohydrodynamics (MHDs). The analysis presents the effects of some important parameters on fluid flow. The mixed convection phenomena are used to examine the characteristics of heat transmission. By using the appropriate transformations, dimensional nonlinear equations can be transformed into dimensionless expressions. The governing dimensionless problems are solved using the modified Laplace decomposition approach by examining the effects of various boundary factors on flow and heat transfer.