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This study explores the ternary nanofluid flow within the canonical gap between a cone and a disk with particle deposition and magnetic field effects. Reduced titanium dioxide, magnetite, and graphene oxide are used as nanoparticles in the base fluid ethylene glycol. The governing equations of the problem are in the form of partial differential equations, which are converted to nonlinear ordinary differential equations by using appropriate similarity transformations, and they are solved numerically by using Runge–Kutta–Fehlberg fourth fifth-order (RKF 45) technique. The main agenda of this work is to discuss the impacts of parameters on three cases. The effects of essential aspects on fluid flow, heat and mass transfer rates were studied and analyzed using a graphical representation. Additionally, the response surface methodology and sensitivity analysis are carried out to enhance the importance of the heat transfer rate. The results reveal that the flow field increases significantly with increased Reynolds numbers for both cone and disk rotations. It is observed that the sensitivity analysis of the Nusselt number toward the Eckert number is more for all the radiation parameter values and the Eckert number's middle level. [ABSTRACT FROM AUTHOR]

The need for efficient heating and cooling systems in the automotive, aerospace, and chemical industries is driving the growth of heat transfer technologies. The hybrid nanomaterials are preferred over traditional nanofluids due to their exceptional thermal effectiveness. Keeping in mind the need for efficient cooling and heating systems, the thermal flow model based on the hybrid nanoparticles (GO-MoS2) immersed in hybrid base liquid $ {\textrm{C}_\textrm{2}}{\textrm{H}_\textrm{6}}{\textrm{O}_2} - {\textrm{H}_\textrm{2}}\textrm{O} $ C 2 H 6 O 2 − H 2 O is presented in this novel attempt by considering the influence of homogeneous–heterogeneous (H–H) reactions and Hall current with a magnetohydrodynamic effect induced by a vertical stretching sheet. A simplified examination is examined in the existence of solar radiation, mixed convection, and viscous dissipation. Suitable transformations provide the system of ordinary differential equations. Later, the solution is tackled numerically for the flow problems using the Runge–Kutta–Fehlberg process with a shooting technique. The role of influential parameters on involved distributions is discussed graphically and is explained logically in view of physical significance. Results reveal that, the thermal profile declines near convectively heated surface and upsurges away from the surface for incline in mixed convection parameter. An upsurge in the Biot number inclines the rate of heat transfer, but a contrary trend can be seen for escalating values of volume fraction. [ABSTRACT FROM AUTHOR]

The features of ferromagnetic fluids make it supportive for an extensive range of usages in directing magnetic drugs and magnetic hyperthermia. Owing to all such potential applications, the current study is concerned with the ferromagnetic liquid flow past a stretching sheet with thermophoretic particle deposition and a magnetic dipole. The equations of described flow are transformed into ordinary differential equations (ODEs) by selecting suitable similarity variables. These ODEs are later solved numerically by the fourth and fifth-order Runge–Kutta–Fehlberg (RKF-45) technique by using a shooting scheme. The influence of sundry parameters on velocity, thermophoretic diffusive deposition velocity, skin-friction, Nusselt number, Sherwood number, thermal and concentration profiles are illustrated graphically. The results reveal that the increase in ferromagnetic interaction parameter improves the thermal profile but declines the velocity and concentration profiles. The imposition of thermophoretic particle deposition results in declination of the mass transfer. The escalating values of the ferromagnetic interaction parameter decline the rate of heat transfer. Finally, the rise in values of the thermophoretic parameter and thermophoretic coefficient decays thermophoretic diffusive deposition velocity. [ABSTRACT FROM AUTHOR]

This study examines the flow of the ternary nanofluid over a rotating stretchable cylinder with a torsional motion under the influence of a Cattaneo–Christov heat flux. In order to accomplish the goals of this simulation, a ternary hybrid nanofluid (THNF) that is based on water and incorporates nanoparticles with three distinct morphologies is considered. For assessing the colloidal mixture of spherical, cylindrical, and platelet shaped nanoparticles, the necessary models are used. By using appropriate similarity transformations, the modeled equations are reduced to a set of ordinary differential equations (ODEs). These ODEs are then solved using the finite element approach. The numerical integration's validity and reliability, as well as the newly obtained results, were thoroughly analyzed. Results reveal that the larger values of Reynolds number enhance the system's inertial force, which resists the liquid accelerating force and declines both velocities and heat transport. The rise in values of volume fractions and Reynolds number declines the skin friction coefficients along swirling and radial directions. The increase in values of both the thermal relaxation time parameter and Reynolds number improves the rate of heat transport. [ABSTRACT FROM AUTHOR]

An analysis is carried out to study the two-dimensional stagnant point flow of titanium dioxide (T i O 2) -titanium alloy (T i 6 A l 4 V) /carboxymethyl cellulose (CMC) water-based hybrid nanoliquid over an expanding surface characterized by the induced magnetic field (IMF). Further, the consideration of thermal buoyancy and the additional nonuniform heat source is involved in the modeling. The intent of this work has significant novelty due to the elastic deformation behavior over a stretching surface. The governing mathematical equations of the problem are reduced to a set of simultaneous ordinary differential equations and are elucidated numerically by employing the Runge-Kutta-Fehlbergs fourth-and-fifth (RKF-45) order process combined with a shooting approach. This article examines the properties of change in parameters on the functions including temperature profiles, induced magnetic field, and velocity profiles of hybrid nanoliquid, shown through graphs. The impact of the Elastic deformation coefficient reduces the temperature where as magnetic field enhance the velocity profile. Magnetic parameter boosts skin friction coefficient with an increase in the buoyancy effect. Momentum profile and induced magnetic field are affected most by the Magnetic Prandtl number [ABSTRACT FROM AUTHOR]

The current study explores a three-dimensional swirling flow of titania–ethylene glycol-based nanofluid over a stretchable cylinder with torsional motion. The heat transfer process is explored subject to heat source/sink. Here, titania–ethylene glycol–water-based nanofluid is used. The Maxwell–Bruggeman models for thermal conductivity and modified Krieger–Dougherty models for viscosity are employed to scrutinize the impact of nanoparticle aggregation. A mathematical model based on partial differential equations (PDEs) is developed to solve the flow problem. Following that, a similarity transformation is performed to reduce the equations to ordinary differential equations (ODEs), which are then solved using the finite element method. It has been proven that nanoparticle aggregation significantly increases the temperature field. The results reveal that the rise in Reynolds number improves the heat transport rate, whereas an increase in the heat source/sink parameter value declines the heat transport rate. Swirling flows are commonly found in many industrial processes such as combustion, mixing, and fluidized bed reactors. Studying the behavior of nanofluids in these flows can lead to the development of more efficient and effective industrial processes. [ABSTRACT FROM AUTHOR]

The accurate forecasting of thermal processes is one of the primary concerns of those working in the area of heat transfer as well as those in the energy research community. The present investigation makes use of a simplified mathematical model as an illustration in order to investigate the properties of heat transport under the lack of local thermal equilibrium conditions. The LTNE model results in two distinct primary thermal gradients, one for the fluid phase and another for the solid phase. The non‐Newtonian fluid flow containing Ti6Al4V and AA7075 nanoparticles with a base fluid sodium alginate over a stretching sheet in a porous media with magnetic effect is studied here. The shooting approach is used to transform the resultant equations of boundary value problems into initial value problems, which are subsequently solved using Runge–Kutta–Fehlberg 45 process. The impact of pertinent parameters on the involved fields have been discussed graphically. Results reveal that the increase in porosity and magnetic parameters value decreases velocity and increases thermal performance. An upsurge in inter‐phase heat transfer parameter increases the heat transport rate of solid phase but, decreases the liquid phase heat transport rate. [ABSTRACT FROM AUTHOR]

The current paper explores the flow of dusty nanoliquid over a rotating and stretchable disk with non-uniform heat sink/source. Further, we have done a comparative study on Single wall carbon nanotubes (SWCNT)-water and multi wall carbon nanotubes (MWCNT)-water based dusty fluid flows. By means of apt similarity variables, the governing equations are converted to set of nonlinear ordinary differential equations and then they are numerically tackled using Runge–Kutta–Fehlberg's fourth fifth order (RKF45) method by adopting shooting technique. The influence of non-dimensional parameters on the heat transfer fields are incorporated and extensively discussed by means of appropriate graphs. Further, the reduced shear stresses at the disk in the tangential direction, in the radial direction and the heat transference rates of the fluid and particles are deliberated graphically. Results reveal that, the escalating values of space and temperature dependent heat source/sink parameters improves the heat transference of both liquids. The SWCNT-water based fluid shows improved shear stress in tangential and radial direction when compared to MWCNT-water based fluid for both the phases. The SWCNT-water based fluid shows enhanced heat transfer rate than MWCNT-water based fluid for both fluid and dust phases. [ABSTRACT FROM AUTHOR]

The aim of this paper is to examine the influence of heat source/sink on boundary layer flow of a fourth-grade liquid over a stretchable Riga plate on taking account of induced magnetic field and mixed convection. Analysis of mass and heat transport is studied through modified Fourier heat flux model. The governing flow issue is demonstrated with the help of momentum, energy, temperature and concentration equation. The modeled equations are reduced into nondimensional ODEs by opting suitable similarity transformations. The analytic solutions are discussed by means of the optimal technique of homotopy analysis. The influence of several nondimensional parameters on velocity, thermal and concentration gradients are deliberated by using suitable graphs. Also, the skin friction is discussed with the help of graphs. The result outcomes reveal that, velocity of fluid diminishes for advanced values of viscoelastic parameter and fourth-grade liquid parameter but contrary movement is seen for third grade fluid parameters. Fluid temperature boosts up for thermal relaxation parameter and concentration is abridged for rising values of solutal concentration parameter and Schmidt number. [ABSTRACT FROM AUTHOR]

The investigation focuses on the consequences of various thermal distributions examined in the context of Magneto–Darcy–Rayleigh–Bénard (MDRB) convection onset under local thermal non-equilibrium (LTNE). The system under consideration consists of a two-layer configuration, with an incompressible fluid and horizontally positioned adiabatic peripheries. An analytical solution to the resultant problem is accomplished using the regular perturbation method. Concerning the six thermal distributions, we examine variables such as the ratio of heat expansion in the solid phase, the ratio of heat diffusivities in the solid phase, and the inter-phase heat diffusivity ratio, which exhibits a propensity towards LTNE. Furthermore, we investigate the consequences of modifying the values of constraints, namely, the ratio of heat expansion in the fluid phase, the ratio of heat diffusivities in the fluid phase, the porous parameter, the heat ratio, and the Chandrasekhar number. The empirical observations indicate that the model (iii) exhibits a significantly higher degree of instability when compared to other distributions. Conversely, model (v) demonstrates a notable level of stability. Moreover, it is intriguing that the system governed by the model (vi) exhibits higher stability than the model (iv) thermal distribution within the context of a composite system. [ABSTRACT FROM AUTHOR]

AbstractThe fascinating thermal behavior of nanofluids and their many applications in heat transfer systems have gained the curiosity of many researchers from different fields. A cellulose derivative called carboxymethyl cellulose (CMC) is frequently utilized due to its high viscosity. The thermophoresis and Brownian motion impact is utilized to study the three-dimensional flow of a water-based hybrid nanofluid-containing CMC as base fluid over a gap between the cone and disk. The titanium dioxide and titanium alloy are the two nanoparticles employed in this study. Additionally, the modeling takes thermal radiation into account. It is presumed that the cone–disk equipment consists of a rotating disk and a stationary cone. Using similarity transformations, the modeling equations are converted into ordinary differential equations (ODEs). The Runge–Kutta Fehlberg fourth- fifth-order (RKF-45) technique is used to solve the reduced ODEs. The graphs are used to explore the behavior of flow profiles. The results demonstrate that at higher levels of the radiation parameter exhibits better-quality heat transmission. The velocity profile is inclined by the upsurge in the value of the Reynolds number based on the velocity of the disk. The rise in the thermophoresis parameter upsurges the thermal and concentration profile. The thermal profile rises and concentration profile declines for the growth of the Brownian motion parameter values. [ABSTRACT FROM AUTHOR]

AbstractIn the field of nanotechnology research, fluid–nanoparticle interaction is attracting a lot of attention. A wide variety of technological and industrial areas that include convection flows, low-velocity heat exchangers, emergency shut nuclear reactors, exposed solar receivers to wind currents, and fans cooling electronic equipment. The flow of ternary-hybrid nanofluid (NF) due to forced, mixed, and free convection comprising platelet, cylindrical, and spherical shaped nanoparticles is explored in this study. Nonlinear governing equations are changed into ordinary differential equations (ODEs) by employing the proper similarity variables. The numerical outcomes of the reduced equations are attained using a shooting method and the Runge–Kutta–Fehlberg 45 (RKF-45) order. Graphical displays are used to convey the numerical results. It is investigated how the various parameters affect each profile. Results reveal that the velocity for the forced convection case near the surface declines faster than the free and mixed convection case for distinct values of the porosity parameter. The heat transport for the free convection case shows less heat transport than the forced and mixed convection case. The mass transport for the forced convection case shows improved mass transport than the free and mixed convection case for distinct values of chemical reaction rate parameter. [ABSTRACT FROM AUTHOR]