The stagnation point flow of a ternary hybrid nanofluid (THNF) over a sheet that stretches or shrinks exponentially is investigated in this study. The primary goal is to assess the implication of Joule heating, magnetohydrodynamics (MHD), thermal radiation, and boundary slips on the physical quantities and flow profiles. Besides, attention is also given to the occurrences of multiple solutions in this fluid flow situation. The continuity, momentum and energy equations that described the fluid flow problem are converted into a simpler form of ordinary differential equations (ODEs). This is achieved by applying a similarity transformation, which make the equations easier to solve. Solving the resulting equations using the bvp4c solver in MATLAB software yields results that are analyzed and illustrated through a combination of tables and graphical representations. The analysis reveals that, for a shrinking sheet, an increase in Joule heating reduces the heat transfer. Similarly, a higher thermal slip factor leads to a decreased heat transfer rate in this case. In contrast, parameters such as magnetic field strength, radiation, velocity slip and suction contribute to enhancing the heat transfer rate of THNF. Furthermore, the results indicate that the THNF used in this study exhibits a better heat transfer rate compared to nanofluid (NF) and hybrid nanofluid (HNF). Notably, a shrinking sheet is observed to exhibit multiple solutions when the shrinking parameter falls within a defined range, specifically when lambda > lambda(c). By scrutinizing the analysis of stability, the first solution (upper solution) was determined to be consistently stable and applicable in real-world settings. These findings offer insightful information into the optimization of heat transfer processes in nanofluid-based systems under complex flow conditions. However, these findings apply only to a THNF mixture of alumina, copper, and titania. THNFs may have different flow dynamics and thermal properties depending on the mixtures of nanoparticles.

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.

PurposeIn recent times, ternary hybrid nanofluid has garnered attention from scientist and researchers due to its improved thermal efficiency. This study aims to delve into the examination of ternary hybrid nanofluid (Al2O3-Cu-TiO2/water), particularly concerning axisymmetric flow over a nonlinearly permeable stretching/shrinking disk. In addition, the investigation of convective boundary conditions and thermal radiation effects is also considered within the context of the described flow problem. Design/methodology/approachMathematical formulations representing this problem are reduced into a set of ordinary differential equations (ODEs) using similarity transformation. The MATLAB boundary value problem solver is then used to solve the obtained set of ODEs. The impact of considered physical parameters such as suction parameter, radiation parameter, nonlinear parameter, nanoparticle volumetric concentration and Biot number on the flow profiles as well as the physical quantities is illustrated in graphical form. FindingsThe findings revealed the thermal flux for the nonlinearly shrinking disk is approximately 1.33%, significantly higher when compared to the linearly shrinking disk. Moreover, the existence of dual solutions attributed to the nonlinear stretching/shrinking disk is unveiled, with the first solution being identified as the stable and reliable solution through temporal stability analysis. Practical implicationsUnderstanding ternary hybrid nanofluid behavior and flow has applications in engineering, energy systems and materials research. This study may help develop and optimize nanofluid systems like heat exchangers and cooling systems. Originality/valueThe study of flow dynamics across nonlinear stretching/shrinking disk gains less attention compared to linear stretching/shrinking geometries. Many natural and industrial processes involve nonlinear changes in boundary shapes or sizes. Understanding flow dynamics over nonlinear shrinking/stretching disks is therefore essential for applications in various fields such as materials processing, biomedical engineering and environmental sciences. Hence, this study highlights the axisymmetric flow over a nonlinear stretching/shrinking disk using ternary hybrid nanofluid composed of alumina (Al2O3), copper (Cu) and titania (TiO2). Besides, this study tackles a complex problem involving multiple factors such as suction, radiation and convective boundary conditions. Analyzing such complex systems can provide valuable insights into real-world phenomena where multiple factors interact.

Kesan nanozarah hibrid terhadap aliran bendalir Eyring-Powell pada permukaan mengecut dengan halaju hukum kuasa dikaji. Penjelmaan keserupaan yang sesuai digunakan untuk mengubah persamaan menakluk kepada persamaan keserupaan. Penyelesai masalah nilai sempadan bvp4c dalam perisian MATLAB digunakan untuk mendapatkan penyelesaian berangka. Hasil kajian mendapati bahawa nanozarah hibrid meningkatkan kedua-dua kecerunan halaju dan suhu, yang seterusnya meningkatkan geseran pada permukaan dan kadar pemindahan haba masing-masing pada 5.01% dan 0.59% berbanding bendalir asas. Namun, kuantiti fizikal tersebut menurun dan domain penyelesaiannya terjejas dengan kehadiran parameter bendalir Eyring-Powell. Daripada analisis kestabilan, hanya satu daripada dua penyelesaian tersebut stabil dalam jangka masa panjang.

The effect of hybrid nanoparticles on Eyring-Powell fluid flow over a shrinking sheet with power-law velocity is studied. The suitable similarity transformations are used to transform the governing equations into the similarity equations. The bvp4c solver in MATLAB software is employed to generate the numerical results. The outcomes show that the hybrid nanoparticles raise both the velocity and temperature gradients, which consequently increases the friction at the surface and the rate of heat transfer by 5.01% and 0.59%, respectively, compared with the base fluid. However, these physical quantities are reduced, and the domain of the solutions is affected in the presence of the Eyring-Powell fluid parameters. From the stability analysis, only one of the solutions is stable in the long run.

This research examines the laminar magnetohydrodynamic (MHD) flow of a mixture of three different nanoparticles, known as a ternary hybrid nanofluid, over a permeable stretching sheet. In this analysis, we are considering a permeable stretching sheet that is decelerating, with unsteadiness parameter . The governing equations are turned into similarity equations by utilizing appropriate similarity transformations. The MATLAB software is then employed to program the code, utilizing the bvp4c function. The skin friction and heat transfer coefficients plots, along with velocity and temperature profiles, are delivered for various values of the suction, unsteadiness, magnet, and nanoparticle volume fraction parameters. According to the numerical findings, both unsteadiness and suction parameters play roles in boosting the heat transfer rate. Nevertheless, the heat transfer rate is reduced by the augmentation of magnetic parameter.

The thermal superiority of ternary hybrid nanofluids (THNFs) over conventional heat transfer fluid has led to growing interest in their applications. This new type of nanofluid can be customized for cooling systems, heat exchangers, and electronic cooling by carefully selecting nanoparticle types and their volume fraction. Hence, this study seeks to investigate the Heimenz flow in a Williamson THNF over a sheet that stretches or shrinks. The fundamental objective is to assess the effect of the stretching/shrinking parameter, the Weissenberg number, and the nanoparticle volume fraction on the physical quantities and flow profiles. Besides, attention is also given to the occurrences of multiple solutions in this fluid flow situation. By employing a similarity transformation, the governing equations are modified as a simpler form of ordinary differential equations (ODEs). Next, the numerical method is put to use to solve the resulting ODEs system, specifically the bvp4c solver in MATLAB. Significant changes in heat transmission occur due to variations in the Weissenberg number and volume fractions of nanoparticles, particularly when the sheet starts to shrink. The escalating Weissenberg number correlates with growing critical values of the stretching/shrinking parameter, suggesting that both parameters help to hold off the detachment of the boundary layer. These findings emphasize the capacity of THNFs to improve heat transfer performance in numerous applications. This study also reveals that while stretching sheets often have unique solutions, a shrinking sheet has multiple solutions when the shrinking parameter falls within a certain range. By scrutinizing the robustness of these solutions, it was concluded that only one of them maintains stability over an extended period. It is essential to highlight that these present discoveries apply exclusively to the mixture of copper, alumina, and titania. Various mixtures of nanoparticles can demonstrate distinct characteristics of THNFs concerning both flow dynamics and thermal transfer.

This paper undertakes a numerical exploration into the dynamics of fluid flow and heat transfer within the stagnation region of a mixed convection scenario involving thermally stratified ternary hybrid nanofluid. The study incorporates the impact of a magnetohydrodynamic and velocity slip, while also considering a permeable sheet that can stretch or shrink. The equations governed the flow problem are transformed into similarity equations using a similarity transformation. Then the similarity equations are solved utilizing the built in solver (bvp4c) in MATLAB. This flow problem has two solutions, as expected. Following that, the outcomes of the stability analysis show the viability and physical robustness of the first solution. Additionally, the study identifies magnetic, suction, and volume fraction as parameters capable of delaying turbulence onset in the boundary layer. Moreover, the heat transmission of the ternary hybrid nanofluid is enhanced by an increased volume fraction. It is important to note that the reported results specifically pertain to the combination of alumina, copper, and titania nanoparticles. Different combinations of nanoparticles may exhibits unique properties related to both flow behaviour and heat transmission.

The dynamics of unsteady flow of a ternary hybrid nanofluid on a stretching/shrinking sheet with wall mass suction is numerically analysed. In this study, a mixture of Al2O3, Cu, and TiO2 is employed as additives in water, which serves as the base fluid. The equations governed the problem are simplified into a collection of ODEs by adopting the similarity transformation. Maintaining the flow on a shrinking sheet is reliant on the essential aspect of suction. Furthermore, augmenting the strength of suction amplifies the thermal conductivity process of the flow. Additionally, this study unveils dual solutions existing within a defined range of parameters. It has been determined that one solution exhibits long-term stability, whereas the other solution is deemed unstable through the stability analysis conducted.

Purpose This study aims to investigate the dual solutions for axisymmetric flow and heat transfer due to a permeable radially shrinking disk in copper oxide (CuO) and silver (Ag) hybrid nanofluids with radiation effect. Design/methodology/approach The partial differential equations that governed the problem will undergo a transformation into a set of similarity equations. Following this transformation, a numerical solution will be obtained using the boundary value problem solver, bvp4c, built in the MATLAB software. Later, analysis and discussion are conducted to specifically examine how various physical parameters affect both the flow characteristics and the thermal properties of the hybrid nanofluid. Findings Dual solutions are discovered to occur for the case of shrinking disk ( λ < 0). Stronger suction triggers the critical values’ expansion and delays the boundary layer separation. Through stability analysis, it is determined that one of the solutions is stable, whereas the other solution exhibits instability, over time. Moreover, volume fraction upsurge enhances skin friction and heat transfer in hybrid nanofluid. The hybrid nanofluid’s heat transfer also heightened with the influence of radiation. Originality/value Flow over a shrinking disk has received limited research focus, in contrast to the extensively studied axisymmetric flow problem over a diverse set of geometries such as flat surfaces, curved surfaces and cylinder. Hence, this study highlights the axisymmetric flow due to a shrinking disk under radiation influence, using hybrid nanofluids containing CuO and Ag. Upon additional analysis, it is evidently shows that only one of the solutions exhibits stability, making it a physically dependable choice in practical applications. The authors are very confident that the findings of this study are novel, with several practical uses of hybrid nanofluids in modern industry.

The effects of homogeneous-heterogeneous reaction on the fluid flow over a shrinking sheet is examined. A hybrid nanofluid is considered, with alumina and copper as the nanoparticles and water as the base liquid. The governing equations are solved numerically using similarity approach with the help of MATLAB software. Two outcomes are attained for several ranges of the mass flux parameter . The friction factor as well as the concentration gradient enhances in the presence of nanoparticles, but the rate of heat transfer declines. Moreover, the concentration gradient is intensified for larger homogeneous and heterogeneous strength.