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This study is carried out to scrutinize the Hiemenz flow for ternary hybrid nanofluid flow across a stretching/shrinking sheet. This study aims to inspect the impacts of variations in the stretching/shrinking parameter and the volume fraction of nanoparticles on key aspects of the ternary hybrid nanofluid flow, specifically the skin friction, Nusselt number (which relates to heat transfer), velocity profiles, and the temperature profiles. The flow equations transform into a system of ordinary differential equations (ODEs) using a similarity transformation. Subsequently, the system is numerically solved using the MATLAB software's 4th-order accuracy boundary value problem solver, known as "bvp4c". Numeric findings reveal that skin friction values exhibit variations based on the magnitude of the stretching/shrinking parameter. Moreover, in the specific context of the flow problem being studied, the heat conduction efficiency of the hybrid (ternary) nanofluid surpasses that of the hybrid nanofluid. The system yields two distinct solutions within a specific shrinking/stretching parameter interval. Through an examination of the temporal stability of the solutions, it was determined that only one remained stable over an extended period. Remember that these current findings hold solely for the combination of copper, alumina, and titania. [ABSTRACT FROM AUTHOR]

New formulations are produced for problems associated with multiple cracks in the upper part of thermoelectric-bonded materials subjected to remote stress using hypersingular integral equations (HSIEs). The modified complex stress potential function method with the continuity conditions of the resultant electric force and displacement electric function, and temperature and resultant heat flux being continuous across the bonded materials' interface, is used to develop these HSIEs. The unknown crack opening displacement function, electric current density, and energy flux load are mapped into the square root singularity function using the curved length coordinate method. The new HSIEs for multiple cracks in the upper part of thermoelectric-bonded materials can be obtained by applying the superposition principle. The appropriate quadrature formulas are then used to find stress intensity factors, with the traction along the crack as the right-hand term with the help of the curved length coordinate method. The general solutions of HSIEs for crack problems in thermoelectric-bonded materials are demonstrated with two substitutions and it is strictly confirmed with rigorous proof that: (i) the general solutions of HSIEs reduce to infinite materials if G 1 = G 2 , K 1 = K 2 , and E 1 = E 2 , and the values of the electric parts are α 1 = α 2 = 0 and λ 1 = λ 2 = 0 ; (ii) the general solutions of HSIEs reduce to half-plane materials if G 2 = 0 , and the values of α 1 = α 2 = 0 , λ 1 = λ 2 = 0 and κ 2 = 0 . These substitutions also partially validate the general solution derived from this study. [ABSTRACT FROM AUTHOR]

The boundary layer flows exhibit symmetrical characteristics. In such cases, the flow patterns and variables are symmetrical with respect to a particular axis or plane. This symmetry simplifies the analysis and enables the use of symmetry-based boundary conditions or simplifications in mathematical models. Therefore, by using these concepts, the governing equations of the radiative flow of a hybrid nanofluid past a stretched and shrunken surface with the effect of a magnetic dipole are examined in this paper. Here, we consider copper (Cu) and alumina (Al2O3) as hybrid nanoparticles and use water as a base fluid. The heat transfer rate is enhanced in the presence of hybrid nanoparticles. It is observed that the heat transfer rate is increased by 10.92% for the nanofluid, while it has a 15.13% increment for the hybrid nanofluid compared to the base fluid. Also, the results reveal that the non-uniqueness of the solutions exists for a certain suction and shrinking strength. Additionally, the ferrohydrodynamic interaction has the tendency to reduce the skin friction and the heat transfer coefficients for both solution branches. For the upper branch solutions, the heat transfer rate increased over a stretching sheet but decreased for the shrinking sheet in the presence of the radiation. It is confirmed by the temporal stability analysis that one of the solutions is stable and acceptable as time evolves. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The goal of this study is to examine the significant parameter of unsteady Fe3O4‐CoFe2O4/H2O with heat generation flowing on a rotating disk using numerical and statistical approaches. The mathematical model respected to time‐dependent is first transformed into a set of ordinary differential equations (ODEs) by using similarity variables. The computation is done by employing bvp4c method utilizing MATLAB software. The validation of present model and the output is done by direct comparison with the established report in literature and found to be in a very good agreement. It is worth to mention the presence computation produces up to third solutions. The variations of skin friction coefficient for radial and azimuthal directions including Nusselt number for different value of magnetic parameter, suction parameter, and heat generation parameter are plotted graphically. A Response Surface Methodology (RSM) is applied to scrutinize the physical parameters that affect the response functions under a given set of assumptions. It is revealed the values of skin friction coefficients significantly affected by the magnetic and suction parameters whereas the values of thermal rate are influenced by magnetic, suction, and heat generation parameters. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids may exhibit higher thermal conductivity, chemical stability, mechanical resistance and physical strength compared to regular nanofluids. Our aim in this study is to investigate the flow of a water-based alumina-copper hybrid nanofluid in an inclined cylinder with the impact of buoyancy force and a magnetic field. The governing partial differential equations (PDEs) are transformed into a set of similarity ordinary differential equations (ODEs) using a dimensionless set of variables, and then solved numerically using the bvp4c package from MATLAB software. Two solutions exist for both buoyancy opposing (λ < 0) and assisting (λ > 0) flows, whereas a unique solution is found when the buoyancy force is absent (λ = 0). In addition, the impacts of the dimensionless parameters, such as curvature parameter, volume fraction of nanoparticles, inclination angle, mixed convention parameter, and magnetic parameter are analyzed. The results of this study compare well with previously published results. Compared to pure base fluid and regular nanofluid, hybrid nanofluid reduces drag and transfers heat more efficiently. [ABSTRACT FROM AUTHOR]

Nanofluid is a novel heat transfer fluid with the ability to significantly improve the heat transfer efficiency of regular fluids. Many efforts have been made to study its viscosity and thermal conductivity, both of which are crucial thermophysical properties. This work reports the significance of nanofluid along with thermophoretic and Brownian motion phenomena on the Agrawal flow towards a stagnation point past a permeable moving disk. The impacts of the Maxwell velocity slip and Smoluchowski temperature conditions are also incorporated. The leading equations in form of PDEs (Partial differential equations) are simplified into ODEs (Ordinary differential equations) by employing similarity theory. Then these simplified equations are solved numerically by utilizing a bvp4c solver (fourth‐order boundary value problem).The phenomenal effects of the relevant embedded distinguished parameters on the shear stress, rate of mass, and heat transfer are demonstrated through different graphs and tables. Graphical results indicate that double solutions are detected for stretching/shrinking parameter in a certain range. The heat transport and the wall drag force ascend with the suction aspect, while the mass transfer rate drops with suction in both solutions. [ABSTRACT FROM AUTHOR]

This study aims to investigate the magnetohydrodynamic flow induced by a moving surface in a nanofluid and the occurrence of suction and solar radiation effects using the Buongiorno model. The numerical findings are obtained using MATLAB software. The effects of various governing parameters on the rates of heat and mass transfer along with the nanoparticles concentration and temperature profiles are elucidated graphically. Non-unique solutions are discovered for a specific variation of the shrinking strength. The temporal stability analysis shows that only one of them is stable as time passes. Furthermore, raising the Brownian motion parameter reduces both the local Sherwood number and the local Nusselt number for both solutions. It is also observed that increasing the thermophoresis parameter reduces the rate of heat transfer, whereas the opposite trend is observed for the rate of mass transfer. [ABSTRACT FROM AUTHOR]

The utilization of solar energy is essential to all living things since the beginning of time. In addition to being a constant source of energy, solar energy (SE) can also be used to generate heat and electricity. Recent technology enables to convert the solar energy into electricity by using thermal solar heat. Solar energy is perhaps the most easily accessible and plentiful source of sustainable energy. Copper-based nanofluid has been considered as a method to improve solar collector performance by absorbing incoming solar energy directly. The goal of this research is to explore theoretically the Agrawal axisymmetric flow induced by Cu-water nanofluid over a moving permeable disk caused by solar energy. Moreover, the impacts of Maxwell velocity and Smoluchowski temperature slip are incorporated to discuss the fine points of nanofluid flow and characteristics of heat transfer. The primary partial differential equations are transformed to similarity equations by employing similarity variables and then utilizing bvp4c to resolve the set of equations numerically. The current numerical approach can produce double solutions by providing suitable initial guesses. In addition, the results revealed that the impact of solar collector efficiency enhances significantly due to nanoparticle volume fraction. The suction parameter delays the boundary layer separation. Moreover, stability analysis is performed and is found that the upper solution is stable and physically trustworthy while the lower one is unstable. [ABSTRACT FROM AUTHOR]

The present study looks at the heat transfer and the unsteady thin film flow of Al2O3 water nanofluid past an inclined stretching sheet having a buoyancy force effect. The boundary value problem solver (bvp4c) package in Matlab is utilized in solving the converted set of ordinary differential equations (ODEs). The multi-shape Al2O3 nanoparticles' impact with respect to the flow as well as heat transfer characteristics are studied and visually displayed for certain governing parameter values, which include the mixed convection, inclination angle, magnetic, slip, and Biot number. Thus, the skin friction coefficient and the local Nusselt number are also determined. Here, the platelet shape of Al2O3 nanoparticles possesses a high heat transfer and flow rate based on the outcomes. In addition, increasing the slip and magnetic parameters improves the temperature, whereas increasing the buoyancy and inclination angle parameters has reverse effects. The results also show that increasing the unsteadiness parameter and the magnetic parameter reduces the film thickness. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The utilization of hybrid nanofluids (HNs) to boost heat transfer is a promising area of study, and thus, numerous scientists, researchers, and academics have voiced their admiration and interest in this area. One of the main functions of nanofluids is their dynamic role in cooling small electrical devices such as microchips and associated gadgets. The major goal of this study is to perform an analysis of the buoyancy flow of a shrinking/stretching sheet, whilst considering the fascinating and practical uses of hybrid nanofluids. The influence of a nonlinear heat source/sink induced by a micropolar fluid is also inspected. Water-based alumina and copper nanoparticles are utilized to calculate the fine points of the fluid flow and the features of heat transfer. The governing equations are framed with acceptable assumptions and the required similarity transformations are used to turn the set of partial differential equations into ordinary differential equations. The bvp4c technique is used to solve the simplified equations. Dual solutions are presented for certain values of stretching/shrinking parameters as well as the mixed convective parameter. In addition, the shear stress coefficient in the first-branch solution (FBS) escalates and decelerates for the second-branch solution (SBS) with the superior impact of the magnetic parameter, the mass transpiration parameter, and the solid nanoparticles volume fraction, while the contrary behavior is seen in both (FB and SB) solutions for the larger values of the material parameter. [ABSTRACT FROM AUTHOR]

This paper aims to examine the MHD effects on Reiner–Philippoff fluid flow over a permeable shrinking wedge. The partial derivatives of multivariable differential equations are transformed into similarity equations by adopting appropriate similarity transformations. The resulting equations are solved in MATLAB using the bvp4c technique. The findings reveal that the existence of the magnetic field is proven to improve the friction factor and heat transfer performance. Similar effects are observed with the rise of the suction strength. However, increasing the Reiner–Philippoff fluid parameter lowers the heat transfer rate but increases the friction factor. Moreover, the Lorentz force created by the magnetic field essentially slows the fluid motion, thereby delaying the separation of the boundary layer. The dual solutions are established, leading to the stability analysis that supports the first solution's validity. [ABSTRACT FROM AUTHOR]

The use of hybrid nanoparticles to increase heat transfer is a favorable area of research, and therefore, numerous scientists, researchers, and scholars have expressed their appreciation for and interest in this field. Determining the dynamic role of nanofluids in the cooling of microscopic electronic gadgets, such as microchips and related devices, is also one of the fundamental tasks. With such interesting and useful applications of hybrid nanofluids in mind, the main objective is to deal with the analysis of the unsteady flow towards a shrinking sheet in a water-based hybrid ferrite nanoparticle in porous media, with heat sink/source effects. Moreover, the impact of these parameters on heat and mass transfers is also reported. Numerical results are obtained using MATLAB software. Non-unique solutions are determined for a certain shrinking strength, in addition to the unsteadiness parameter. The mass transfer and friction factor increase for the first solution due to the hybrid nanoparticles, but the heat transfer rate shows the opposite effect. [ABSTRACT FROM AUTHOR]

The mixed convection flow with thermal characteristics of a water-based Cu-Al2O3 hybrid nanofluid towards a vertical and permeable wedge was numerically and statistically analyzed in this study. The governing model was constructed using physical and theoretical assumptions, which were then reduced to a set of ordinary differential equations (ODEs) using similarity transformation. The steady flow solutions were computed using the Matlab software bvp4c. All possible solutions were presented in the graphs of skin friction coefficient and thermal rate. The numerical results show that the flow and thermal progresses are developed by enhancing the controlling parameters (wedge parameter, volumetric concentration of nanoparticles, and suction parameter). Moreover, the response surface methodology (RSM) with analysis of variance (ANOVA) was employed for the statistical evaluation and conducted using the fit general linear model in the Minitab software. From the standpoint of statistical analysis, the wedge parameter and volumetric nanoparticle concentration have a considerable impact on all responses; however, the suction parameter effect is only substantial for a single response. [ABSTRACT FROM AUTHOR]

The current exploration aims to inspect the features of thermal radiation on the buoyancy or mixed convective fluid flow induced by nanofluid through a stretching permeable bended sheet. The impact of activation energy and binary reaction along with slip migration is taken into account to discuss the fine points of water-based alumina nanoparticle flow. The structure of the curved sheet is assumed to be stretchable and the bended texture is coiled within a circular section with radius R b . The similarity technique is utilized to reduce the leading partial differential equations into ordinary differential equations. These reduced equations are then deciphered numerically by employing the bvp4c method. The outcomes of the model were constructed in the form of several figures and bar graphs for the case of opposing and assisting flows with varying distinct embedded control parameters. The results display that the velocity field curves escalate with a higher radius of curvature parameter while temperature and concentration profiles shrink. More precisely, the outcomes show that the temperature distribution profile increases with the increase in nanoparticle's volume fraction as well as thermal radiation parameter. Meanwhile, the concentration and velocity fields are decelerated with higher impacts of nanoparticle volume fraction. In addition, the heat and mass transfer rates were significantly improved for the higher value of the radiation and Schmidt number. On the other hand, the growing values of the velocity slip factor decrease the shear stress. Furthermore, the results are compared with the previous results in the limiting cases and observed a tremendous harmony. [ABSTRACT FROM AUTHOR]

In many industries, extremely high-performance cooling is a crucial requirement. However, the fundamental challenge to developing energy-efficient heat transfer fluids required for cooling is insufficient thermal conductivity. In this case, the utilization of nanofluid is effective to overcome these challenges. The current study aims to examine the two-dimensional (2D) stretching wall jet heat transfer fluid flow induced by a water-based alumina nanofluid embedded in a porous medium with buoyancy force. In addition, irregular heat sink/source and slip effects are assessed. The leading partial differential equations are changed into ordinary differential equations by incorporating similarity variables, then these equations are computationally or numerically worked out via the boundary-value problem of fourth-order (bvp4c) technique. The pertinent factors influencing the symmetry of the hydrothermal performance including friction factor, velocity, and temperature profiles, are illustrated using tables and graphs. The symmetrical outcomes reveal that the velocity declines in the presence of nanoparticles, whereas the temperature uplifts both assisting and opposing flows. Moreover, the friction factor augments due to porosity while the heat transfer rate declines. [ABSTRACT FROM AUTHOR]

The need for effective heating and cooling systems in the automotive, chemical, and aerospace industries is driving a rapid proliferation of heat-transfer technology. In recent times, GO (Graphene Oxide) has been emerging as one of the most promising nanoparticles because of its uninterrupted behavior of electrical conductivity even at a minimum carrier concentration. Due to this incentive, the behavior of jet flow with heat and mass transfer features of electrically conducting based kerosene oil (KO) fluid dispensed by graphene nanoparticles was studied. In addition, the activation energy, irregular heat source/sink, thermophoretic particle deposition, and chemical reaction are also provoked. In order to provide numerical results, the boundary value problem of fourth-order (bvp4c) solver was used. The graphs were used to illustrate the effects of relevant parameters on the fluid flow, heat, and mass transfer rates. The incorporation of graphene nanoparticles significantly improves heat conductivity. Additionally, the nanoparticle volume fraction augments the temperature and concentration profile while the velocity profile declines. Moreover, the temperature enhances due to the heat source, whilst the contrary behavior is observed in the presence of the heat sink. Furthermore, the shear stress increases up to 12.3%, the Nusselt number increases up to 0.119%, and the Sherwood number increases up to 0.006% due to the presence of nanofluid. Finally, we can conclude that the latest work will be useful for thermal cooling systems, including cooling for engines and generators, nuclear systems, aviation refrigeration systems, and other systems. [ABSTRACT FROM AUTHOR]

The problem of 2D (two-dimensional) wall jet flow, along with heat transfer incorporated by nanofluid in a Darcy-Brinkman medium, while recognizing the requirement for efficient heating and cooling systems. Following the use of similarity variables, the resultant system of ODEs (ordinary differential equations) is solved using the well-known and efficient bvp4c (boundary-value problem of the 4th order) technique. The significance of physical quantities for the under-consideration parameters is illustrated and explained. The findings show that the nanoparticle volume fraction and porosity parameters decrease the velocity, but increase the temperature. In addition, the temperature uplifts in the presence of radiation effect. The suction parameter initially decreases and then increases the velocity near the surface, while the temperature declines. [ABSTRACT FROM AUTHOR]

Conventional liquids have poor thermal conductivity, thus limiting their use in engineering. Therefore, scientists and researchers have created nanofluids, which consist of nanoparticles dispersed in a base fluid, to improve heat transfer properties in various fields, such as electronics, medicine, and molten metals. In this study, we examine the micropolar nanofluid flow in a stagnation region of a stretching/shrinking sheet by employing the modified Buongiorno nanofluid model. The nanofluid consists of magnetite (Fe3O4) nanoparticles. The similarity equations are solved numerically using MATLAB software. The solution is unique for the shrinking strength λ ≥ − 1 . Two solutions are found for the limited range of λ when λ c < λ < − 1 . The solutions terminate at λ = λ c in the shrinking region. The rise in micropolar parameter K contributes to the increment in the skin friction coefficient Re x 1 / 2 C f and the couple stress Re x M w , but the Nusselt number Re x − 1 / 2 N u x and the Sherwood number Re x − 1 / 2 S h x decrease. These physical quantities intensify with the rise in the magnetic parameter M. Finally, we investigated the stability of the solutions over time. This work contributes to the dual solution and time stability analysis of the current problem. In addition, critical values of the main physical parameters are also presented. These critical values are usually known as the separation values from laminar to turbulent boundary layer flows. In this case, once the critical value is achieved, the process for the specific product can be planned according to the desired output to optimize the productivity. [ABSTRACT FROM AUTHOR]

In this work, the mixed convection flow of non-Newtonian Eyring–Powell fluid with the effects of temperature dependent viscosity (TDV) were studied together with the interaction of dust particles under the influence of Newtonian Heating (NH) boundary condition, which assume to move over a vertical stretching sheet. Alternatively, the dusty fluid model was categorized as a two-phase flow that consists of phases of fluid and dust. Through the use of similarity transformations, governing equations of fluid and dust phases are reduced into ordinary differential equations (ODE), then solved by efficient numerical Keller–box method. Numerical solution and asymptotic results for limiting cases will be presented to investigate how the flow develops at the leading edge and its end behaviour. Comparison with the published outputs in literature evidence verified the precision of the present results. Graphical diagrams presenting velocity and temperature profiles (fluid and dust) were conversed for different influential parameters. The effects of skin friction and heat transfer rate were also evaluated. The discovery indicates that the presence of the dust particles have an effect on the fluid motion, which led to a deceleration in the fluid transference. The present flow model can match to the single phase fluid cases if the fluid particle interaction parameter is ignored. The fluid velocity and temperature distributions are always higher than dust particles, besides, the opposite trend between both phases is noticed with β. Meanwhile, both phases share the similar trend in conjunction with the rest factors. Almost all of the temperature profiles are not showing a significant change, since the viscosity of fluid is high, which can be perceived in the figures. Furthermore, the present study extends some theoretical knowledge of two-phase flow. [ABSTRACT FROM AUTHOR]

Water has drawn a lot of interest as a manufacturing lubricant since it is affordable, eco-friendly, and effective. Due to their exceptional mechanical qualities, water solubility, and variety of application scenarios, graphene oxide (GO)-based materials have the potential to increase the lubricant performance of water. The idea of this research was to quantify the linear 3D radiative stagnation-point flow induced by nanofluid through a vertical plate with a buoyancy or a mixed convection effect. The opposing, as well as the assisting, flows were considered in the model. The leading partial differential equations (PDEs) were transformed into dimensionless similarity equations, which were then solved numerically via a bvp4c solver. The influences of various physical constraints on the fluid flow and thermal properties of the nanofluid were investigated and are discussed. Water-based graphene oxide nanoparticles were considered in this study. The numerical outcomes indicated that multiple solutions were obtained in the case of the opposing flow (λ < 0). The critical values increased as the nanoparticle volume fraction became stronger. Furthermore, as the nanoparticles increased in strength, the friction factor increased and the heat transfer quickened. The radiation factor escalated the heat transfer in both solutions. In addition, a temporal stability analysis was also undertaken to verify the results, and it was observed that the branch of the first outcome became physically reliable (stable) whilst the branch of the second outcome became unstable, as time passed. [ABSTRACT FROM AUTHOR]

Heat transfer technologies are experiencing rapid expansion as a result of the demand for efficient heating and cooling systems in the automotive, chemical, and aerospace industries. Therefore, the current study peruses an inspection of mixed convective radiative Williamson flow close to a stagnation point aggravated by a single nanoparticle (alumina) from a vertical flat plate with the impact of Hall. The convective heating of water conveying alumina (Al2O3) nanoparticles, as appropriate in engineering or industry, is investigated. Using pertinent similarity variables, the dominating equations are non-dimensionalized, and after that, via the bvp4c solver, they are numerically solved. We extensively explore the effects of many relevant parameters on axial velocity, transverse velocity, temperature profile, heat transfer, and drag force. In the opposing flow, there are two solutions seen; in the aiding flow, just one solution is found. In addition, the results designate that, due to nanofluid, the thickness of the velocity boundary layer decreases, and the thermal boundary layer width upsurges. The gradients for the branch of stable outcome escalate due to a higher Weissenberg parameter, while they decline for the branch of lower outcomes. Moreover, a magnetic field can be used to influence the flow and the properties of heat transfer. [ABSTRACT FROM AUTHOR]

Riga surface can be utilized to reduce the pressure drag and the friction of the submarine by stopping the separation of the boundary layer as well as by moderating turbulence production. Therefore, the current symmetry of the work investigates the slip impacts on mixed convection flow containing water-based hybrid Ag-MgO nanoparticles over a vertical expanding/contracting Riga wedge. In this analysis, a flat surface, wedge, and stagnation point are also discussed. A Riga surface is an actuator that contains electromagnetic where a span-wise array associated with the permanent magnets and irregular electrodes accumulated on a smooth surface. A Lorentz force is incorporated parallel to the surface produced by this array which eases exponentially normal to the surface. Based on the considered flow symmetry, the physical scenario is initially modeled in the appearance of partial differential equations which are then rehabilitated into a system of ordinary differential equations by utilizing the pertinent similarity variables. A bvp4c solver is engaged to acquire the numerical solution. The flow symmetry and the influences of pertaining parameters involved in the problem are investigated and are enclosed in graphical form. The findings confirm that the velocity reduces, and temperature enhances due to nanoparticle volume fraction. A modified Hartmann number increases the velocity and diminishes the temperature. Moreover, the suction parameter enhances the velocity profiles and reduces the dimensionless temperature profiles. The heat transfer gradually increases by diminishing the contracting parameter and increasing the expanding parameter. [ABSTRACT FROM AUTHOR]

The aluminum nanoparticle is adequate for power grid wiring, such as the distribution of local power and the transmission of aerial power lines, because of its higher conductivity. This nanoparticle is also one of the most commonly used materials in applications in the electrical field. Thus, in this study, a radiative axisymmetric flow of Casson fluid, induced by water-based Al2O3 nanofluid by using the Koo–Kleinstreuer–Li (KKL) correlation, is investigated. The impact of the magnetic field is also taken into account. KKL correlation is utilized to compute the thermal conductivity and effective viscosity. Analytical double solutions are presented for the considered axisymmetric flow model after implementing the similarity technique to transmute the leading equations into ordinary differential equations. The obtained analytic forms were used to examine and discuss the velocity profile, the temperature distribution, reduced heat transfer, and coefficient of reduced skin friction. The analytic solutions indicate that the velocity profile decreases in the branch of the first solution and uplifts in the branch of the second solution due to the presence of an aluminum particle, whereas the dimensionless temperature enhances in both solutions. In addition, the Casson parameter increases the friction factor, as well as the heat transport rate. [ABSTRACT FROM AUTHOR]

The flow of fluids over the boundaries of a rotating disc has many practical uses, including boundary-layer control and separation. Therefore, the aim of this study is to discuss the impact of unsteady magnetohydrodynamics (MHD) hybrid ferrofluid flow over a stretching/shrinking rotating disk. The time-dependent mathematical model is transformed into a set of ordinary differential equations (ODE's) by using similarity variables. The bvp4c method in the MATLAB platform is utilised in order to solve the present model. Since the occurrence of more than one solution is presentable, an analysis of solution stabilities is conducted. Both solutions were surprisingly found to be stable. Meanwhile, the skin friction coefficient, heat transfer rate—in cooperation with velocity—and temperature profile distributions are examined for the progressing parameters. The findings reveal that the unsteadiness parameter causes the boundary layer thickness of the velocity and temperature distribution profile to decrease. A higher value of magnetic and mass flux parameter lowers the skin friction coefficient. In contrast, the addition of the unsteadiness parameter yields a supportive effect on the heat transfer rate. An increment of the magnetic parameter up to 30% reduces the skin friction coefficient by 15.98% and enhances the heat transfer rate approximately up to 1.88%, significantly. In contrast, the heat transfer is rapidly enhanced by improving the mass flux parameter by almost 20%. [ABSTRACT FROM AUTHOR]

The hybrid nanofluid has sparked new significance in the industrial and engineering sectors because of their applications like water heating in solar and analysis of heat exchanger surfaces. As a result, the current study emphasizes the analysis of heat transfer and Agrawal axisymmetric flow towards a rotational stagnation point incorporated via hybrid nanofluids imposing on a radially permeable shrinking/stretching rotating disk. The leading partial differential equations are refined into ordinary differential equations by using appropriate similarity variables. The bvp4c solver in MATLAB is then employed to solve the simplified system numerically. The current numerical procedure is adequate of generating double solutions when excellent initial guesses are implemented. The results show that the features of fluid flow along with heat transfer rate induced by hybrid nanofluid are significantly influenced. The Nusselt number and the tendency of the wall drag force can be improved as the concentration of nanoparticles and the suction factor are increased. Moreover, the results of the model have been discussed in detail for both solution branches due to the cases of rotating disk parameter as well as non-rotating disk parameter. Therefore, an extraordinary behavior is observed for the branch of lower solutions in the case of rotating disk parameter. In addition, the shear stress in the radial direction upsurges for the first solution but declines for the second solution with higher values of suction. Moreover, the rotating parameter slows down the separation of the boundary layer. [ABSTRACT FROM AUTHOR]

This study examines the Blasius flow with Cu-Al2O3 hybrid nanoparticles over a moving plate. Additionally, the effects of viscous dissipation and radiation are considered. Similarity transformation is employed to convert the respective model into similarity equations. The results are generated by using bvp4c in MATLAB. Findings reveal that two solutions are attained when both the free stream and the plate move in opposite directions. Moreover, the domains of the velocity ratio parameter are extended when suction is available. Besides, the upsurge of radiation and hybrid nanoparticles lead to the heat transfer enhancement. The rise in radiation heat energy incorporated in radiation parameter leads to the development of fluid temperature as well as the thermal boundary layer. Meanwhile, hybrid nanoparticles offer good thermal characteristics because of synergistic effects. However, the effects reduce with the rise in Eckert number. The first solution is stable and acceptable based on the temporal stability analysis. Furthermore, the critical/separation values of the physical parameters are also reported. With these findings, the optimized productivity will be achieved as well as the processes on certain products can be planned according to the desire output. This significant preliminary study provides future insight to the engineers and scientist on the real applications. [ABSTRACT FROM AUTHOR]

The field of magnetohydrodynamics (MHD) encompasses a wide range of physical objects due to their stabilising effects. Thus, this study concerns the numerical investigation of the radiative non-Newtonian fluid flow past a shrinking sheet in the presence of an aligned magnetic field. By adopting proper similarity transformations, the governing partial derivatives of multivariable differential equations are converted to similarity equations of a particular form. The numerical results are obtained by using the bvp4c technique. According to the findings, increases in the suction parameter resulted in higher values of the skin friction and heat transfer rate. The same pattern emerges as the aligned angle and magnetic parameter are considered. On the other hand, the inclusion of the Bingham number, the Reiner--Philippoff fluid, and the thermal radiation parameters deteriorate the heat transfer performance, evidently. The dual solutions are established, which results in a stability analysis that upholds the validity of the first solution. [ABSTRACT FROM AUTHOR]

Recent nanotech advancements have created a tremendous platform for the development of a superior ultrahigh performance coolant referred to as nanofluid for several industrial and engineering technologies. In this research, the impact of thermophoretic and viscous dissipation on the radiative mixed convective flow comprising hybrid nanofluid through an inclined permeable moving flat plate with a magnetic field is examined numerically. A model of non-linear differential equations is derived based on some realistic assumptions and tackled numerically using the bvp4c technique. The impact of the specific set of distinguished parameters on the velocity profiles, shear stress, temperature distribution profiles, heat transfer, concentration distribution profile, and mass transfer for the two dissimilar branch solutions are discussed in detail. In addition, it has been discovered that double solutions exist in the case of an opposing flow, while a single solution is observed in the case of an assisting flow. The temperature distribution profile escalates with the radiation parameter, while decelerating the velocity and concentration profiles. [ABSTRACT FROM AUTHOR]

This study examines the radiative and magnetohydrodynamic micropolar fluid flow over a stretching/shrinking sheet consisting of Al2O3 and Cu nanoparticles. Besides, the effects of the Joule heating and viscous dissipation are taken into consideration. The similarity variables are employed to convert the governing equations into similarity equations. Then, the bvp4c in MATLAB is utilized to obtain the numerical results. The accuracy of the current formulation and method has been done by comparing the present results with those previously published data. Findings discovered that two solutions are obtained for the limited range of S and K , and these solutions are terminated at S = S c and K = K c . The influence of Ec and R is to reduce the local Nusselt number of Re x - 1 / 2 Nu x . Meanwhile, the values of Re x - 1 / 2 Nu x increase with the increase in φ hnf when larger values of R are considered. The rise of M contributes to the increment in the values of Re x 1 / 2 C f , Re x M w , and Re x - 1 / 2 Nu x , but the effect of K lowers the values of these physical quantities. Lastly, it was discovered that the first solution is physically reliable and in a stable mode. [ABSTRACT FROM AUTHOR]

This study examines the stagnation point flow over a stretching/shrinking sheet in a hybrid nanofluid with homogeneous-heterogeneous reactions. The hybrid nanofluid consists of copper (Cu) and alumina (Al2O3) nanoparticles which are added into water to form Cu-Al2O3/water hybrid nanofluid. The similarity equations are obtained using a similarity transformation. Then, the function bvp4c in MATLAB is utilised to obtain the numerical results. The dual solutions are found for limited values of the stretching/shrinking parameter. Also, the turning point arises in the shrinking region (λ < 0). Besides, the presence of hybrid nanoparticles enhances the heat transfer rate, skin friction coefficient, and the concentration gradient. In addition, the concentration gradient is intensified with the heterogeneous reaction but the effect is opposite for the homogeneous reaction. Furthermore, the velocity and the concentration increase, whereas the temperature decreases for higher compositions of hybrid nanoparticles. Moreover, the concentration decreases for larger values of homogeneous and heterogeneous reactions. It is consistent with the fact that higher reaction rate cause a reduction in the rate of diffusion. However, the velocity and the temperature are not affected by these parameters. Fromthese observations, it can be concluded that the effect of the homogeneous and heterogeneous reactions is dominant on the concentration profiles. Two solutions are obtained for a single value of parameter. The temporal stability analysis shows that only one of these solutions is stable and thus physically reliable over time. [ABSTRACT FROM AUTHOR]

The proficiency of hybrid nanofluid from Cu-Al2O3/water formation as the heat transfer coolant is numerically analyzed using the powerful and user-friendly interface bvp4c in the Matlab software. For that purpose, the Cu-Al2O3/water nanofluid flow between two parallel plates is examined where the lower plate can be deformed while the upper plate moves towards/away from the lower plate. Other considerable factors are the wall mass suction/injection and the magnetic field that applied on the lower plate. The reduced ordinary (similarity) differential equations are solved using the bvp4c application. The validation of this novel model is conducted by comparing a few of numerical values for the reduced case of viscous fluid. The results imply the potency of this heat transfer fluid which can enhance the heat transfer performance for both upper and lower plates approximately by 7.10% and 4.11%, respectively. An increase of squeezing parameter deteriorates the heat transfer coefficient by 4.28% (upper) and 5.35% (lower), accordingly. The rise of suction strength inflates the heat transfer at the lower plate while the presence of the magnetic field shows a reverse result. [ABSTRACT FROM AUTHOR]

This study investigates the unsteady flow of Al2O3‐Cu/water hybrid nanofluid on a stagnation point of a permeable rigid surface. The similarity equations are obtained using similarity variables and then solved using the bvp4c solver. The outcomes show that dual solutions exist for the negative unsteadiness and some mass flux parameters. Besides, the heat transfer rate is intensified with the hybrid nanoparticles. Moreover, the increasing of the mass flux parameter tends to increase the heat transfer rate and the skin friction on the surface. Also, the reduction of the skin friction coefficient is observed, and a higher heat transfer rate is achieved for smaller values of the unsteadiness parameter. Finally, by a temporal stability analysis, it is found that the first solution is stable and reliable as time evolves. [ABSTRACT FROM AUTHOR]

This paper examines the behaviour of a hybrid nanofluid flow towards a stagnation point on a stretching or shrinking surface with second-order slip and melting heat transfer effects. Copper (Cu) and alumina (Al2O3) are considered as the hybrid nanoparticles while water as the base fluid. The governing equations are reduced to the similarity equations using similarity transformations. The resulting equations are programmed in MATLAB software through the bvp4c solver to obtain the numerical solutions. The results reveal that two solutions are possible for the shrinking case (λ < 0) , where the bifurcation of the solutions occurs in this region. Moreover, the heat transfer rate and the skin friction coefficient enhance with the rise of the melting parameter. Meanwhile, these quantities decrease for a smaller second-order slip parameter. The temporal stability analysis shows that only one of the two solutions is stable as time evolves. [ABSTRACT FROM AUTHOR]

This paper examines the stagnation point flow towards a stretching/shrinking cylinder in a hybrid nanofluid. Here, copper (Cu) and alumina (Al2O3) are considered as the hybrid nanoparticles while water as the base fluid. The governing equations are reduced to the similarity equations using a similarity transformation. The resulting equations are solved numerically using the boundary value problem solver, bvp4c, available in the Matlab software. It is found that the heat transfer rate is greater for the hybrid nanofluid compared to the regular nanofluid as well as the regular fluid. Besides, the non-uniqueness of the solutions is observed for certain physical parameters. It is also noticed that the bifurcation of the solutions occurs in the shrinking regions. In addition, the heat transfer rate and the skin friction coefficients increase in the presence of nanoparticles and for larger Reynolds number. It is found that between the two solutions, only one of them is stable as time evolves. [ABSTRACT FROM AUTHOR]