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The underlying intension of this study is to oversee the flow and thermal management of hybrid nanofluid (Magnesium oxide+ Zirconium oxide+ polyethylene glycol) within a conical gap among a cone and a disk. Forced convection is examined for two situations (a) rotating disk and the stationary cone; (b) stationary disk and the rotating cone. The dimensionless differential system for the proposed model is numerically simulated with a shooting procedure (RK 4th order). Outcomes are explained through graph and tables. The main outcomes of this study are found to be – Rotating disk and stationary cone show higher temperature field for increasing estimations of the radiation parameter ( $ Rd $ R d) and the magnetic parameter ( $ M $ M) near the boundary. Hence, for heat enhancement, one can use the disk – cone model. Furthermore, increases in $ M,Rd,{\phi _1},{\phi _2} $ M , R d , ϕ 1 , ϕ 2 and $ n $ n shows an increment in Nusselt number at the cone surface $ ({N{u_c}}) $ (N u c ) compared to that at the disk surface $ ({N{u_d}}) $ (N u d ). The desired cooling in the disk and cone device could be attained by keeping the cone fixed and the disk rotating and by maintaining the surface temperature constant. It is perceived that improvement in the volume fraction of $ MgO $ M g O and $ \,Zr{O_2} $ Z r O 2 nanoparticles significantly enhanced velocity of base fluid and heat transfer rate. [ABSTRACT FROM AUTHOR]

In this study, the effects of suction and buoyancy are used to analyze the Ternary hybrid nanofluid flow on a stretching sheet through a porous media. Ternary hybrid nanofluid is (Carbon nanotubes) CNT + Graphene + Al 2 O 3 with base fluid as Water. Case-1 Buoyancy Assisting flow and Case-2 Buoyancy Opposing flow. Hybrid nanofluids have been used to speed up the heat transfer process. Nonlinear partial differential equations (PDEs) have been converted to ordinary differential equations (ODEs) using Lie group transformations. The ODE45, an algorithmic approach, has been using the aid of this built-in solver, and the resulting Ordinary differential equations were resolved. The general relationship between temperature, velocity, heat transfer rate, and shear stress on a stretchy surface is shown for a range of values of the significant factors. The temperature profiles have been rising with the impact of Da , f w . Using streamlines to examine the flow pattern of a fluid and a method of machine learning, in terms of modern language, an artificial neural network (ANN) made up of artificial neurons or nodes is known as a neural network. A neural network is a network or circuit of genetic neurons. [ABSTRACT FROM AUTHOR]

The researchers explored the free convective flow of a hybrid nanofluid in a vertical microchannel with a rectangular cross‐section. Notably, both channel walls were heated alternately, and a transverse magnetic field was applied across the channel. The channel walls had unique properties, one of which was nonslip and the other was exceedingly hydrophobic. The major purpose was to investigate the effects of magnetism and superhydrophobicity on important flow parameters. The differential equations in the investigation were solved, producing accurate results. The study yielded some significant discoveries. First, when heated, the magnetic parameter reduced skin friction on both sides. Second, in both heating conditions, the magnetic field reduced flow rate and velocity. The flow rates in the two reported situations were similar at a crucial temperature jump coefficient. Furthermore, for low‐temperature jump coefficients, heating the superhydrophobic side reduced the Nusselt number whereas heating the nonslip side had no magnetic effect. The percentage change in the value of Nusselt number and velocity decreases continuously with increase in nonlinear density variation with temperature (NDT) parameter and magnetic parameter. The percentage increases in the value of skin friction with increase in temperature jump and slip length but decrease in the percentage of skin friction for the effect of magnetic term and NDT parameter. As the NDT parameter increases, the velocity percentage rises to 50.59% when the superhydrophobic surface is heated and to 84.30% when the nonslip surface is heated. The temperature jump is statistically significant for the value of the Nusselt number and skin friction for the no‐slip surface condition. These discoveries have practical consequences for the design and management of both tiny and large‐scale systems, with possible applications in microfluidics, microelectronics, nanoscience, and nanotechnology. [ABSTRACT FROM AUTHOR]

Numerous researchers have been interested in nanofluids because of their improved thermal characteristics and heat transmission capabilities. Recently, it has been possible to create a novel nanofluid with exceptional thermal properties by combining ternary nanoparticles of various shapes. In this respect, it is believed that the thickness of the fin will change with the length of the fin and that the impacts of thermal radiation, convection on a heat transfer mechanism, and internal heat production in a fin wetted with ternary hybrid nanofluid will depend on the length of the fin. As a result, several fin profiles, including triangular, convex, and rectangular, have been taken into consideration. This study also investigates the comparison of heat and thermal energy fluctuations in both wet and dry conditions. In order to examine the porous nature, Darcy's model is required. With the aid of the Maple computer program, the resultant nonlinear partial differential equation and boundary conditions are non-dimensionalized and numerically resolved using the implicit finite difference approach, the graphic explanation of fin efficiency, and transient thermal response for different values of the essential parameters. The investigation yielded the novel discovery that the effectiveness of the fins is enhanced by the presence of a ternary hybrid nanofluid. Three fins with varied shapes have been compared in both wet and dry circumstances. The study has discovered that triangular fins have a quicker rate of temperature decline, whereas rectangular fins have a greater efficiency. The investigation's results have a significant impact on improving heat transmission in industrial operations. [ABSTRACT FROM AUTHOR]

In the recent decades, the increasing energy demands and its applications have seen the focus shifting to the hybrid nanofluid flows but so much is still left to be investigated. This analysis is executed to explore the hydro-magnetic flow to investigate the incompressible flow and heat transfer towards a stretching surface with velocity and thermal slips. The scaling similarity transformations are created using Lie group analysis and employing these to convert nonlinear partial differential equations to the nonlinear ordinary differential equations. Here, after converting equations from dimensional to non-dimensional, we will use the BVP4C solver (MATLAB) for plotting the graphs to analyze how distinct non-dimensional parameters affect the skin friction and Nusselt number transfer rate, case 1 graphene + CNT + aluminum oxide with base fluid as water and case 2 magnesium oxide + zirconium oxide + copper oxide with water as base fluid, here taking nanoparticles without different shapes. The hybrid nanofluid temperature profile has mixed behavior, and the velocity profile increases when M rises. The hybrid nanofluid temperature profile curvature has composite behavior when Pr rises. The link between several independent or predictor variables and one dependent or criterion variable has been examined using multilinear regression analysis (MLR). When coefficient values for many variables are subject to change, it can forecast a wide range of outcomes. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids combine two or more nano properties with a base fluid such as water ethylene. Usually, this helps enhance the heat transfer rate; in this article, using new similarity transformations created by Lie group analysis, the governing nonlinear partial differential equations are transformed into a system of connected nonlinear ordinary differential equations. The resulting design is numerically solved using a BVP4C solver with the shooting method (MATLAB). The magneto hydrodynamic flow of an incompressible fluid and the rate of heat and mass transfer were investigated for two cases, with various nanoparticle shapes including cylindrical, spherical, and platelet. Case 1 was CNT (1%), graphene (1%), and aluminum oxide (1%), and Case 2 was copper (1%), silver (1%), and cobalt ferrite (1%). When the Hartmann number rises, velocity and temperature exhibit inverse behavior: the velocity profile increases, and the temperature profile decreases. When the suction rises, the velocity and temperature profiles both increase. Optimization techniques were used from response surface methodology (RSM) to set factorial variables so that the response met the desired maximum or minimum value. Factorial methods like ANOVA were used to model the response, but they were expanded to simulate the effects in terms of extrapolation. [ABSTRACT FROM AUTHOR]

The wire coating method is an engineering development to cover a wire for wadding, motorized forte and ecological protection. In wire coating analysis, moreover, the polymer extruded on the wire is hauled into interior of a die occupied with melted polymer. By considering this significance, the magneto-hydrodynamic flow and heat transmission of Oldroyd-8 constant fluid with suspension of nanoparticles in the wire coating development had been investigated. The fluid with fixed viscosity is considered in porous medium. The flow is conducted with uniform magnetic field. The arising physical governing system is modelled mathematically. The mathematical model is executed by incorporation of thermal radiation and nanoparticles (Embedded in water + hematite nanoparticles). The wire coating is scrutinized mathematically with four cases ((Ω = 0. 5 , ∅ = 0) , Ω = 0. 5 , ∅ = 0. 0 5 , Ω = − 0. 5 , ∅ = 0 , Ω = − 0. 5 , ∅ = 0. 0 5) with constant viscosity and also included in the Reynolds model for constant viscosity. The subsequent flow and heat transmission system were elucidated via the Runge–Kutta technique and the possessions of appropriate governing factors are presented in graphically. The outcome of the current investigation was equated with the previous available outcomes as a specific situation. The results were executed with nanofluid and without nanofluid as well as with positive and negative pressure gradients (Ω = 0. 5 , ∅ = 0) , Ω = 0. 5 , ∅ = 0. 0 5 , Ω = − 0. 5 , ∅ = 0 , Ω = − 0. 5 , ∅ = 0. 0. It is seen that the temperature circulation is augmented due to the upsurge in magnetic parameter M. It is interesting to note that the positive pressure gradient with nanofluid has less momentum distribution compared to rest of the cases. It is also noted that the with negative pressure gradient, the distribution is more compared to positive pressure gradient case. [ABSTRACT FROM AUTHOR]

Adding variety of nanoparticles to the base fluid is current technique in order to boost the thermal performance of conventional fluids and mononanofluids. The forthright intention of the present investigation is to analyze numerically the up-to-date progress in flow and heat transport nature of magnetohydrodynamic, radiative Newtonian fluid, water-based Al2O3 nanofluid, water-based graphene nanofluid and water based Al2O3 + graphene hybrid nanofluid due to convectively heated stretching sheet. The flow equations are transformed by applying appropriate transformations into a pair of self-similarity equations. Further similarity equivalences are numerically solved through Runge–Kutta based shooting method. Graphs and tables are structured to analyze the behavior of sundry influential variables. From this study it is found that rate of heat transfer for Graphene + water is 2.921934, Al2O3 + H2O + Graphene is 2.250658 and Al2O3 + H2O is 3.260554. From this we conclude that water based Al2O3 + graphene hybrid nanofluid can be opted for cooling performance. Water based Al2O3 nanofluid significantly enhance convection heat transfer performance over a stretching sheet. Friction at the wall for Graphene + water is (− 1.719525), Al2O3 + H2O + Graphene is (− 2.256614) and Al2O3 + H2O is (− 1.959539). From this we conclude that water based Al2O3 + graphene hybrid nanofluid shows lower wall friction rate compared to other two mixture compositions. [ABSTRACT FROM AUTHOR]

Passive systems that need exceptional apparent geometries, thermal packaging, or fluid additives. In passive procedures, a number of foremost efforts have been conducted. The passive methods are divided into two groups: geometry modification (e.g. nano/microchannels) and solid additives (e.g. micro/nano solid particles). In a recent development in microfabrication – the development of fabrication of minuscule buildings of micrometer measures – a variation of microstrategies including heat transfer have been industrialized. Viewing this, the heat and mass transfer characteristics of a free convective Casson fluid over an elastic stretching surface are numerically studied. Thermal radiation and non-Fourier flux are incorporated in the energy to balance the transformation. Similarity transformations are used to translate partial differential equations relating to momentum, diffusion, and energy into nonlinear ordinary differential equations. The shooting approach is used to achieve numerical solutions to these equations. The effect of various physical pertinent parameters including thermal radiation parameter, Brownian motion, thermophoresis, suction, curie parameter, thermal and diffusion buoyancy forces, thermal relaxation, stretching, or shrinking parameters on the concentration and temperature profiles is investigated. It is observed that the nonlinear case has highly mixed performance when compared to the linear case of temperature and concentration fields. [ABSTRACT FROM AUTHOR]

This research contemplates the flow and heat transport of MHD rheological Eyring-Powell fluid embedded with dust and graphene nanoparticles (GP) in an ethylene-glycol (EG) mixture in the presence of nonlinear convection, Cattaneo-Christov heat flux, and thermal radiation. Primarily existing PDEs (fluid and dust phase) are transferred to non-dimensional form by invoking similarity transformations then solved numerically through RKF-45 method. The graphene particles are significantly used in energy transmission in aerospace, power and propulsion generation etc. Through graphical illustrations, velocity and temperature profiles (fluid and dust phases) converse for various prominent parameters. The results of friction factor and heat transfer rate are presented and analyzed. Validation of the present result is made with the existing data. Results demonstrate that increasing nonlinear convection parameter has an inverse relationship with the Nusselt number and the velocity in the dust and fluid phases. This may happen due to the domination of unsteadiness in the flow. [ABSTRACT FROM AUTHOR]

AbstractThis study concentrates on heat transmission and momentum in the hydromagnetic flow of hybrid nano-dusty fluid over the thermal plate with radiation, Newtonian heating wall conditions, and heat sink/source. The outcome of this investigation finds application in wastewater management, groundwater treatment, soil remediation, magnetic separation, air pollution, biomedical diagnostics, continuous casting, and environmental engineering. MAPLE Software is used to solve flow-controlling equations numerically. The influence of physical parameters on the dust and fluid phases due to uniform lifting and sudden lifting of the thermal plate are compared by preparing graphs and tables. The obtained outcomes are validated. This study concludes that the fluid velocity and temperature are more significant in uniform lifting than the sudden lifting of the thermal plate. An increase in particle concentration, magnetic field, particle relaxation time, and porosity parameter results in growth in shearing stress with time. The fluid phase has a higher flow velocity and temperature than the dust phase. The temperature field is more in the fluid phase than the dust phase and is augmented with nanoparticle enhancement. [ABSTRACT FROM AUTHOR]

A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic (MHD) Casson fluid across a slendering sheet in the presence of microorganisms and Cattaneo-Christov heat flux. Multiple slips (diffusion, thermal, and momentum slips) are applied in the modeling of the heat and mass transport processes. The Runge-Kutta based shooting method is used to find the solutions. Numerical simulation is carried out for various values of the physical constraints when the Casson index parameter is positive, negative, or infinite with the aid of plots. The coefficients of the skin factors, the local Nusselt number, and the Sherwood number are estimated for different parameters, and discussed for engineering interest. It is found that the gyrotactic microorganisms are greatly encouraged when the dimensionless parameters increase, especially when the Casson fluid parameter is negative. It is worth mentioning that the velocity profiles when the Casson fluid parameter is positive are higher than those when the Casson fluid parameter is negative or infinite, whereas the temperature and concentration fields show exactly opposite phenomena. [ABSTRACT FROM AUTHOR]

A theoretical analysis is performed for investigating the flow and heat transfer characteristics of Maxwell fluid over a stretching cylinder with Cattaneo-Christov, heat source or sink, and suction/injection. The solution to the transformed similarity equations is derived using Runge-Kutta fourth-order method along shooting technique. The present result for both the surface shear stress and the local Nusselt number is validated with the previously published results, while a very sound agreement is attained. The impacts of the distinct parameters related to this study are presented in graph and tabular form, respectively. Moreover, the local Nusselt number and surface shear stress have been computed for both the suction and injection cases. It is found that strengthening the thermal relaxation parameter value increases the heat transfer rate. The dimensional heat transfer rate is observed being rising in the injection case when compared with the suction case. [ABSTRACT FROM AUTHOR]

Understanding the film lifting and draining of fluid on a vertical belt with surface tension is crucial for improving predictive models in coating and lubrication processes. This paper presents a theoretical study on the film lifting and drainage of a third-grade fluid with surface tension. The driving mechanisms on a vertical belt are the belt's upward movement, the gradient of surface tension, and gravity. The formulated nonlinear ordinary differential equation (ODE) is solved for a series-form solution using the Adomian decomposition method. Numerical computations are used to determine the stationary point placements and the thickness of the uniform film. The study elucidated that lift velocity shows a decreasing trend, while drainage velocity exhibits an increasing trend with increasing values of inverse capillary number C and Stokes number S t . The lift velocity shows an increase, whereas the drainage velocity demonstrates a decrease with an increase in the Deborah number De. With increasing values of S t and C, the stationary points shift away from the fluid–air interface, while an increase in De causes them to move towards the interface. Surface tension plays a role in supporting drainage and leads to a shift in the stationary points towards the belt. Newtonian and third-grade fluids are also compared in terms of velocity, stationary points, uniform film, and surface tension, providing insight into their behavior. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the analysis of Oldroyd 8-constant fluid flow with nanoparticle suspension via a porous media during the coating of wire is carried out. A constant magnetic field and electrically conducting fluid are considered. The governing equations thus obtained for the present model are converted to nonlinear differential equations using variables in dimensionless form. These equations are analytically solved. The influence of some parameters, like magnetic field parameter, porosity parameter, dilatant constant, pseudo-plastic constant and Brinkman number on velocity and temperature distributions are discussed graphically. For fluctuating viscosity, two models, Reynold's and Vogel's are considered. It is observed that the magnetic parameter and the Brinkman number increase, both temperature and velocity profiles show a retarding effect in both Reynold's and Vogel's models. [ABSTRACT FROM AUTHOR]

This attempt demonstrates the nature of mass and heat transportation in non-Newtonian Reiner–Philippoff liquid flow over moving surface by considering zero and nonzero normal mass flux conditions and transverse magnetic field. Thermophoresis and Brownian movement is accounted due to the Buongiorno model of nanofluid. The expressions of flow are reframed through appropriate variables into pairs of self-similar expressions. Further, these self-similar expressions are executed numerically through the Shooting procedure (Runge–Kutta 4th order). Numerical benchmarks and graphical illustrations are prepared to visualize the role of influential constraints on interesting quantities. It is observed that Lorentz force is beneficial in obtaining effective velocity and heat transfer. Improvement in thermophoresis factor enriches temperature field in case of active control while reverse nature is observed in passive control situation. [ABSTRACT FROM AUTHOR]

The utilization of a ternary hybrid nanofluid, a recent development in the realm of nanofluids, can result in improved heat transfer. In the ongoing study, a ternary hybrid nanofluid flow is utilized, and it is carried out atop a porous spinning disc, which is exposed to a magnetic field, heat generation, thermal radiation, and Casson fluid. In this study, Blood/Water are taken as base fluids and (Ag–Au–Al2O3) are considered as a ternary hybrid nanoparticle. Nanoparticles made of gold and silver are put to use in a vast number of industries and fields, including nanotechnology and medicine. As a result of surface effects and quantum effects, these precious metals exhibit unique features in nanoform that play a vital role in with optical, magnetic, chemical, and mechanical behavior. Al2O3 unique optical, physical and biochemical qualities make it worthwhile for numerous uses, including nanophotonic, catalysis and the fabrication of high-energy composites. A set of relevant similarity transformations is used to generate non-dimensional forms of controlling paired nonlinear Partial Differential Equations (PDEs). MATLAB is used to perform a numerical solution with ODE45. In addition, the velocity outline decreases, and the temperature profile increases slightly before decreasing over a revolving disk when the values of magnetic parameters are increased. The distribution and radiant heat components heat up as the level gets higher. Aim and objectives of the study: The aim of this study is to analyze the Comprehensive Scrutinization of Ternary hybrid and Casson flow in a conducting porous rotating disk with internal heating. The primary objective of this analysis is to increase awareness of the impending energy crisis among those working in the industrial and technological sectors. Ternary nanoparticles (NPs) have a wide range of applications, which lends credence to the developed model. For example, Al2O3 can be used in a variety of ways that benefit society, it is used in water purification to remove water from the gas streams and extend people's lives. [ABSTRACT FROM AUTHOR]

In this paper, we have analysed a binary chemical nanofluid dissipative flow (in two cases i.e., 50% EG + 50% water/silica and 50% EG + 50% water/graphene oxide) due to a curved stretching sheet with activation energy. Appropriate transformations yield the nonlinear ordinary differential system. Shooting procedure (R-K 4th order based) is executed to solve the resultant equations. Graphical illustrations thoroughly demonstrate the features of the involved pertinent parameters. We have deliberated the behaviour of the alike parameters on the rate of transfers (heat and mass) and surface drag force (skin friction coefficient) by means of tables. This investigation reveals that (a) reaction rate parameter and temperature difference parameter are helpful to ameliorate the mass transfer rate (b) concentration enhances for higher estimation of activation energy variable (c) increasing the volume fraction of nanoparticles reflects an escalation in temperature (d) heat transfer rate enhancement is recognized for the influence of heat transfer Biot number. At the end this study, we came to know that the EG-Water + Graphene Oxide mixture has more heat transfer rate compared to EG-Water + Silica mixture. This outcome helps to conclude that, whenever the more heat transport required in manufacturing and industries, we can take the EG-Water + Graphene Oxide mixture. [ABSTRACT FROM AUTHOR]

In this paper, the importance of mass and heat transfer characteristics of mixed convective conditions on nonlinear free convection flow embedded with non-Fourier flux and thermal radiation is numerically investigated. A partial Casson slip and mixed impact of thermophoresis and Brownian motion is considered at the elastic surface. To change the highly nonlinear partial differential equations into ordinary differential system, we used the similarity transformations and then the shooting method is employed to solve resulting equations. The significance of various physical parameters on the velocity, concentration and temperature profiles are investigated for both negative value of ferromagnetic interaction ( β 1 = − 0. 2) and positive value of ferromagnetic interaction ( β 1 = 0. 2). The governing physical aspects of coefficient of skin friction, the Sherwood and Nusselt numbers are obtained for various embedded parameters. Our findings concluded that the ferromagnetic interaction is positive and then more mass transfer rate is identified compared to the negative value of ferromagnetic interaction, but whereas in friction and heat transfer rate, it was completely mixed sense (i.e., different effects have different results). Brownian motion has less Nusselt number values in positive ferromagnetism compared to negative ferromagnetism and quite opposite behavior is observed in the presence of thermophoresis, this happened due to nonlinear flux and buoyancy. [ABSTRACT FROM AUTHOR]

Nonlinear convective flow and heat transfer characteristics are analyzed between stationary nonporous and porous rotating disks utilizing graphene nanoparticles in a water and ethylene glycol base fluid. Heat transfer characteristics are analyzed via incorporating thermal radiation and heat absorption/generation. The governing fluid equations are computed numerically using Runge–Kutta based shooting technique after employing appropriate transformations. Characteristics of sundry variables are elaborated graphically as well as through the construction of Table for water base and ethylene glycol based graphene nanoparticles. It is observed that improvements in nonlinear convection variable owing to temperature and heat generation variable improve wall friction in radial direction. Improvement in Hartman number decreased wall friction in radial and tangential directions along with Nusselt number in graphene/ethylene glycol and graphene/water nanofluid. Ethylene glycol based graphene nanofluid takes less time for execution as compared to water based nanofluid. [ABSTRACT FROM AUTHOR]

The forthright intention of the present investigation is to analyze the up-to-date progress in Jeffrey nanofluid flow past an electromagnetic sheet by utilizing the properties of nonlinear convection, radiation, convective boundary condition, zero mass flux condition and Arrhenius activation energy. The flow equations are transformed by applying appropriate transformations into a pair of self-similarity equations. Further similarity equivalences are numerically solved through Runge–Kutta-based shooting method. Graphs and tables are structured to analyze the behavior of sundry influential variables. The results acquired showed good agreement with the previous notable works. Through this study we observed that improvement in Lorentz force in the positive x-direction strengthens the momentum, which intensifies the transfer of heat energy from the boundary, resulting in reduced fluid temperature. [ABSTRACT FROM AUTHOR]

Analyzed in this paper is an investigation of the impacts of the varying source of heat or thermal sink and viscous dissipation on Casson fluid flow from a moving wedge by considering thermal and momentum slips in a mathematical model. Regarding the regulation of concentration fields, we incorporated the Soret and Dufour phenomena. The outcomes are analyzed numerically by using the shooting technique. The governing parametric effects of the flow characteristics are revealed graphically. We also presented the local Sherwood and Nusselt number values for non-Newtonian fluid (Casson fluid) and Newtonian. It is discovered that the thermal and concentration boundary layer is more extensive in Casson fluid while equated with the Newtonian fluid. The thermal and mass transmission in Newtonian fluid is significantly larger than in non-Newtonian fluid. The heat source/sink, Eckert number and Dufour number boost the rate of thermal transport and depreciate the rate of mass transport for both the Newtonian and non-Newtonian fluid cases. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This study explores the magneto hydrodynamic Carreau fluid in the interruption of titanium alloy nanoparticles with heat generation and porosity. The simulation is performed by combination of titanium alloy nanoparticles into base water. Titanium is strong and light in weight and sit is used in military and aerospace, in bio science it is used as anti-microbial, anti-biotic, and anti-fungal agents. The arising set of partial differential equations (P.D.E) are converted into set of ordinary differential equation (O.D.E) using suitable similarity transformation and then solved by the help of Runge-Kutta with shooting method technique. The computational results for non-dimensional temperature and velocity are presented with graphs. We analyzed the numerical values of physical quantities (friction factor and local Nusselt number) for various values physical parameters and they are presented in tables. We also compared the current result with existing result under some limited cases. At end of our analysis we notified that the temperature profiles are enriched with increasing values of heat generation and porosity parameter. [ABSTRACT FROM AUTHOR]

This is a theoretical exploration of the magnetohydrodynamic Carreau fluid in a suspension of dust and graphene nanoparticles. Graphene is a two-dimensional single-atom thick carbon nanosheet. Due to its high thermal conductivity, electron mobility, large surface area, and stability, it has remarkable material, electrical, optical, physical, and chemical properties. In this study, a simulation is performed by mixing of graphene+water and graphene+ethylene glycol into dusty non-Newtonian fluid. Dispersion of graphene nanoparticles in dusty fluids finds applications in biocompatibility, bio-imaging, biosensors, detection and cancer treatment, in monitoring stem cells differentiation, etc. Graphene+ water and graphene+ethylene glycol mixtures are significant in optimizing the heat transport phenomena. Initially arising set of physical governing partial differential equations are transformed to ordinary differential equations (ODEs) with the assistance of similarity transformations. Consequential highly nonlinear ODEs are solved numerically through Runge-Kutta Fehlberg scheme. The computational results for nondimensional temperature and velocity profiles are presented through graphs. Additionally, the numerical values of friction factor and heat transfer rate are tabulated numerically for various physical parameter obtained. We also validated the present results with previous published study and found to be highly satisfactory. The formulated model in this study reveals that heat transfer rate and wall friction is higher in mixture of graphene+ethylene glycol when compared to graphene+water. [ABSTRACT FROM AUTHOR]

This paper investigates the mixed convection of MHD Maxwell, Jeffery, and Oldroyd-B nanofluid models with heat source/sink over a cone geometry. The nonlinear ordinary differential equations are solved numerically by using Runge-Kutta-based shooting technique for transformed systems. Moreover, the non-homogenous Buongiorno’s model is employed, which accounts for both the impact of thermophoresis and Brownian motion of the nanofluids. The accuracy of the numerical data is obtained by comparison against the existed results in the literature. Furthermore, the effects of important physical parameters such as thermophoresis, Biot number, Brownian motion, and magnetic field parameters on the concentration, temperature, and velocity profiles are evaluated in this research. As the vital outcome of this research, it is revealed that the heat and mass transfer rates are more significant in Jeffery model than other two models Maxwell and Oldroyd-B nanofluid models. [ABSTRACT FROM AUTHOR]

We study the velocity, thermal, and mass slips on chemically reacting magnetohydrodynamic boundary layer flow over a radiated stretching surface in the presence of suction. The governing momentum boundary layer and thermal boundary layer equations with boundary conditions are transformed into a system of nonlinear ordinary differential equations that are solved numerically using the Runge-Kutta-Fehlberg method. The involved differential systems are solved for velocity, temperature, and mass fraction. Graphical and numerical results are described for the analysis of various parameters of attention entering the modeled problems. Various tables are constructed to show rheological effects of different physical parameters. Combined effects of thermal and concentration jump are analyzed. We found that the slips have the propensity to control boundary layer flow. Velocity, temperature, and concentration show the increasing nature before and after a point, as the velocity slip increases and the momentum, thermal, and concentration boundary layer thickness become thinner for velocity slip. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Over the last 10 years, heat transfer performance in immediate cooling and heating applications has grown into the foremost concern for heat transfer practitioners in Engineering and manufacturing practices. Henceforward, the study in new heat transfer fluids is extremely intense and challenging. This study examines flow and thermal management in axisymmetric hydrodynamic pure water-based hybrid solid nanoparticles in a flow induced by a swirling cylinder with Fourier Heat source. Flow and heat transfer are analyzed and compared for CNT+Graphene+Al 2 O 3 and Paraffin wax+Sand+AA7072 hybrid nanofluid flow. Shooting technique (R-K 4th order) is applied to work out the flow equations numerically. Simulated results are exhibited through graphs and tables. The computational results are statistically validated with the published research work and a modest concurrence is found. The main outcome of this study is found to be in Multi-regression analysis, where the Λ w.r.t Pr has higher domination compared to Φ w.r.t Pr. Also, it is interesting to know that Φ w.r.t Re has more rate of heat transfer compared to Φ w.r.t M. As the volume fraction rises, the size of the particle is less and Reynolds number dominated the flow, due to this, a decrement is seen in the friction values. Overall, it is observed that heat transfer rate is higher in CNT+Graphene+Al2O3 compared with Paraffin wax+Sand+AA7072. [ABSTRACT FROM AUTHOR]

Nowadays, the heat thrust liquid electric heater is generally used in profitable applications since it protects upto 2–3 times the energy of ordinary liquid electric heater. The heat pump makes use of a refrigerant for its process. The small-temperature refrigerant engrosses permitted heat from full of atmosphere midair in the evaporator which is crushed by an extremely well-organized electrical compressor to an extraordinary-temperature and high-pressure vapor refrigerant. For entire heat transfer connoisseurs, heat transfer performance in cooling and heating applications has become a top priority. Hence, research towards new heat transfer fluids is extremely intense and challenging. This investigation examines flow and heat transfer analysis in axisymmetric magnetohydrodynamic flow polyethylene glycol (PEG)-based nanofluid, hybrid nanofluid and ternary hybrid nanofluid flow induced by a swirling cylinder. Flow and heat transfer are analyzed and compared for three cases PEG-based copper oxide, magnesium oxide and zirconium oxide ternary nanofluid (PEG + ZrO2 + CuO + MgO), PEG-based copper oxide (PEG + CuO) nanoparticles and PEG-based zirconium and magnesium oxide hybrid nanofluid (PEG + ZrO2 + MgO). Shooting technique (R–K fourth-order) is employed to work out the flow equations numerically. Simulated results are displayed through graphs. The computational results are validated with the published research work and a modest concurrence is found. The main outcome of this study is found to be as follows: It is interesting to note that C f x Re (x R) is lesser in nanofluid case compared with ternary and hybrid nanofluid cases. It is found that C f ϕ Re (G H R) is more in ternary hybrid nanofluid compared with hybrid and nanofluid cases. Overall, it is observed that heat transfer rate is higher in nanofluid compared with ternary and hybrid nanofluid cases whereas lesser rate of heat transfers in ternary nanofluid case. [ABSTRACT FROM AUTHOR]

The heat and mass transfer of two immiscible fluids in an inclined channel with thermal diffusion, vicious, and Darcy dissipation is studied. The first region consists of a clear fluid, and the second one is filled with a nanofluid saturated with a porous medium. The behaviors of Cu-H2O, In-H2O, and Au-H2O nanofluids are analyzed. The transport properties are assumed to be constant. The coupled non-linear equations of the flow model are transformed into the dimensionless form, and the solutions for the velocity, temperature, and concentration are obtained by the regular perturbation technique. Investigations are carried out on the flow characteristics for various values of the material parameters. The results show that the velocity and temperature of the fluids enhance with the thermal Grashof number, solutal Grashof number, and Brinkman number while decrease with the porosity parameter and solid volume fraction. [ABSTRACT FROM AUTHOR]

This work analyzes the two-dimensional flow of an incompressible magneto-hydrodynamic fluid over linear stretching sheet in the presence of suction or injection and convective boundary conditions. A scaling group transformation method is applied to the flow governing equations. The system remains invariant due to the relation between the transformation parameters. Upon finding three absolute invariants, third-order ordinary differential equations (ODEs) corresponding to momentum equation and second-order ODEs corresponding to energy and diffusion equations are derived. Shooting technique (R-K fourth-order) is applied to work out the flow equations numerically. MATLAB is used for the simulation and the results are exhibited through graphs. The computational results are validated with the published research work and a modest concurrence was found. The main outcome of this study is found to be that raising values of f si and Γ 1 decline the friction, whereas Γ 1 and Γ 2 show the opposite (increasing). The rising values of f si and M in addition to M and Γ 2 show a decline in friction factor. The Nusselt number values are improved as raising values of Pr versus f si and Pr versus M. It is very clear the monotonically increasing M versus f si and strictly increasing f si versus M cases. It is very clear the mass-transfer rate is smoothly improved L e 1 versus L e 2 and strictly increased L e 1 versus  Γ 1 . [ABSTRACT FROM AUTHOR]

Compared with methanol (pure) and blood, methanol‐ and blood‐based nanofluids are significant with numerous characteristics, including thermophysical effects and immersion rate of CO2 in tray column absorber. Blood‐based liquids show importance in biological treatments like digestion as well as breathing systems. Mixed convective conditions and suction or injection are helpful in controlling the heating or the cooling in industrial applications. Keeping this in view, we examined the physical perception of entropy generation (EG) in a mixed convective hybrid nanofluid (HBN) flow with chemical reaction, cross‐diffusion, and transpiration in a curved surface with activation energy and thermal radiation. Transformed principal equations are determined with the assistance of a fourth‐order Runge–Kutta method with a shooting technique. We obtained solutions for two different cases, that is, for hybrid (mixture of cases) (magnetite + hematite + blood) and (magnetite + hematite + methanol). Obtained results are discussed via graphs and tables. Also, we discussed the effects of the Bejan number and the EG. We found that the EG appears more conspicuously in the case of magnetite + hematite + methanol compare to magnetite + hematite + blood case. We also found that in the magnetite + hematite + methanol case the flow and heat transfer characteristics are more pronounced compared with that in the case of magnetite + hematite + blood. This helps us to choose magnetite + hematite + blood or magnetite + hematite + methanol compositions in the manufacturing industry. Furthermore, the rate of heat transfer can be enhanced up to 16.42% in the case of methanol‐based HBN while the rate of heat transfer can be enhanced up to 19.16% in the case of blood‐based HBN. [ABSTRACT FROM AUTHOR]

The study of convective heat transfer in differently shaped fins with radiation, internal heat generation and variable thermal conductivity was considered. The energy equation of the model was converted into the dimensionless form by adopting the proper variables, which was later solved using the differential transformation method. The impact of the parameters on the thermal performance, efficiency and heat transfer of the fins was analyzed graphically and also by performing thermal analysis on the fins. It was noticed that there was a significant effect on the thermal performance of the fins with different shapes, and also the heat transfer rate of the fin increased for improved values of the internal heat generation and radiation parameters. The exponential profile showed better results than other profiles, and the results obtained were supported by thermal analysis using ANSYS software. [ABSTRACT FROM AUTHOR]

In this study we analyze the boundary layer flow of a thermophoretic magnetohydrodynamic dissipative nanofluid over an unsteady stretching sheet in a porous medium with space and time dependent internal heat source/sink. The governing equations are transformed to ordinary differential equations by using similarity transformation. Numerical solutions of these equations are obtained by using the Shooting Technique. The effects of non-dimensional governing parameters on the velocity, temperature, concentration profiles, friction factor, Nusselt and Sherwood numbers are discussed and presented through graphs and tables. Accuracy of the results compared with the existing ones. Excellent agreement is found with earlier studies. [ABSTRACT FROM AUTHOR]

With the fast improvement of the industry and the utilization of inventive strategies, scientists want to think over the steady blending convection of water-based nanofluids past static wedges. The Buongiorno model with convection is applied. Also, incorporated the Brownian motion and thermophoresis. The attention is on the nature of mixed wedge-formed convective heat and mass transfer of the nanofluid flow. Utilizing comparable change, the governing partial differential equations (PDEs) are reduced to ordinary differential equations (ODEs) solved by the R-K Gill method. The physical quantities of velocity, temperature and concentration fields, as well as diffusion and thermal transfer rates with friction factor coefficients, is discussed. The investigation demonstrated that the temperature convergence of the liquid was higher within the sight of the thermophoresis parameter and Biot numbers. It has been seen that divider pressure increments with expanding wedge and mixed convection parameters. [ABSTRACT FROM AUTHOR]

The performance of copper selenide and effectiveness of chemical catalytic reactors are dependent on an inclined magnetic field, the nature of the chemical reaction, introduction of space heat source, changes in both distributions of temperature and concentration of nanofluids. This report presents the significance of increasing radius of nanoparticles, energy flux due to the concentration gradient, and mass flux due to the temperature gradient in the dynamics of the fluid subject to inclined magnetic strength is presented. The non-dimensionalization and parameterization of the dimensional governing equation were obtained by introducing suitable similarity variables. Thereafter, the numerical solutions were obtained through shooting techniques together with 4th order Runge–Kutta Scheme and MATLAB in-built bvp4c package. It was concluded that at all the levels of energy flux due to concentration gradient, reduction in the viscosity of water-based nanofluid due to a higher radius of copper nanoparticles causes an enhancement of the velocity. The emergence of both energy flux and mass flux due to gradients in concentration and temperature affect the distribution of temperature and concentration at the free stream. [ABSTRACT FROM AUTHOR]

In this investigation, the flow of an unsteady mixed convection boundary layer viscous nanofluid on a stretchable sheet is considered. The flow examination is affected by a magnetic field. The reason for the examination exhibited is to create models for nanomaterials that incorporate the Brownian movement and thermophoresis phenomena. The created nonlinear standard differential condition is illuminated numerically utilizing the Runge"Kutta"Gill technique and the start program. The different factors of speed, temperature, and concentration are reported and discussed. The examination shows that the speed, temperature, and concentration are lower in contrast with the consistent stream on account of an assisting flow, whereas the opposite situation is noticed in the opposing flow case. The effects of Brownian movement and thermophoresis in the concentration case are totally different. [ABSTRACT FROM AUTHOR]

The aim of present work is to investigate the mass transfer of steady incompressible hydromagnetic fluid near the stagnation point with deferment of dust particles over a stretching surface. Most researchers tried to improve the mass transfer by inclusion of cross-diffusion or dust particles due to their vast applications in industrial processes, extrusion process, chemical processing, manufacturing of various types of liquid drinks and in various engineering treatments. To encourage the mass transport phenomena in this study we incorporated dust with microorganisms. Conservation of mass, momentum, concentration and density of microorganisms are used in relevant flow equations. The arising system of nonlinear partial differential equations is transformed into nonlinear ordinary differential equations. The numerical solutions are obtained by the Runge-Kutta based shooting technique and the local Sherwood number is computed for various values of the physical governing parameters (Lewis number, Peclet number, Eckert number). An important finding of present work is that larger values of these parameters encourage the mass transfer rate, and the motile organisms density profiles are augmented with the larger values of fluid particle interaction parameter with reference to bioconvection, bioconvection Lewis number, and dust particle concentration parameter. [ABSTRACT FROM AUTHOR]

The Editor-in-Chief is retracting this article because there are several major errors in the basic equations that seriously undermine the reliability of the results. The authors do not agree with this retraction. [ABSTRACT FROM AUTHOR]

A theoretical study on the effect of magnetohydrodynamic field on the classical Blasius and Sakiadis flows of heat transfer characteristics with variable conditions and variable properties are studied in this paper. Hydromagnetic flows and heat transfer in porous media have been considered extensively in recent years due to their occurrence in several engineering processes such as compact heat exchangers, metallurgy, casting, filtration of liquid metals, cooling of nuclear reactors and fusion control. The governing partial differential equations are converted into ordinary differential equations using the suitable similarity transformations. The transformed boundary layer equations like momentum and energy equations are solved numerically by using Runge–Kutta method. The effect of governing physical parameters over the velocity and temperature distributions is demonstrated graphically. Moreover, the local friction factor coefficient and rate of heat transfer in terms of Nusselt number are computed and discussed through tables. We validated the present solutions with already existing studies under limited cases. It is found that the thermal buoyancy parameter enhances the velocity depreciates the temperature field for both the Sakiadis and Blasius flow cases. The influence of Biot number increases skin friction coefficient and local Nusselt number for both Sakiadis and Blasius flow cases.The rate of heat transfer for temperature ratio parameter is high in Blasius flow case when compared with Sakiadis flow case. [ABSTRACT FROM AUTHOR]

The present study emphases on the three-dimensional (3D) Casson nanofluid flow across a slendering sheet in porous layers by considering the thermophoresis and Brownian motion effect. The proposed mathematical model has a tendency to characterise the effect of the non-uniform heat source/sink. In the present simulation, the graphene–water-based nanoparticles have been used at two different temperatures namely 10 and 50 °C. The nonlinear ordinary differential equations are solved using the Runge–Kutta Feldberg integration method. The characteristics of velocity, temperature and concentration boundary layers in the presence of graphene–water nanoparticles are presented for different physical parameters such as heat source/sink parameter, thermophoresis parameter, Brownian motion parameter, Casson fluid parameter, porosity parameter, volume fraction and velocity power index parameter. Moreover, the friction factor coefficients, Nusselt number and Sherwood number are also estimated and discussed for aforesaid physical parameters. It is found that there is a significant increase in the thermal and concentration boundary layer thickness when the strength of the thermophoresis parameter is increased. In contrast, thermal boundary layer increases with the rise in the Brownian motion parameter, while the reverse trend holds true for concentration field. In addition, the rate of heat and mass transfer rate are higher in case of graphene–water nanoparticle at 50 °C compared to 10 °C temperature. [ABSTRACT FROM AUTHOR]

The present work explores the analytical study of nanofluid flow above a stretching medium with the heat source and viscous dissipation. Additional radiative effects are also incorporated. The main physical problem is offered and changed into an arrangement of combined nonlinear differential equations with appropriate transformations. Optimal homotopy analysis method is used to attain the analytical solutions of the set of nonlinear differential equations. Important predictions of the flow phenomena are explored and deliberated by means of graphs and numerical tables. Moreover, the accurateness of the existing findings is verified by equating them with the previously available work. [ABSTRACT FROM AUTHOR]