Stagnation Point Flow Research Articles

Thermal instability of three-dimensional boundary layer stagnation point flow towards a rotating disc

In this paper, the thermal instability of a three-dimensional boundary layer axisymmetric stagnation point flow towards a heated horizontal rotating disk is considered. A large number of works have been done on stability analysis. However, they did not check the thermal stability of the non-parallel-flow in the face of small disturbances that occur in the vicinity of the heated rotating disk. The governing equations of the basic flow are reduced to three coupled nonlinear partial differ-ential equations, and solved numerically with the fourth-order Runge-Kutta method. Thermal stability is examined by making use of linear stability theory based on the decomposition of the normal mode of Görtler-Hammerlin. The resulting eigenvalue problem is solved numerically using a pseudo-spectral method based on the expansion of Laguerre’s polyno-mials. The obtained results are discussed in detail through multiple configurations. As the main result, for large Prandtl numbers (Pr), the rotation disk parameter (Ω) has a destabilizing effect while for small Pr (around the unity) it tends to stabilize the basic flow. It was found that as the disk radius r→0, the flow is linearly stable, and the disturbances grow rapidly away from the stagnation point. For low values of Pr, the flow becomes more stable, and strong thermal gradients are necessary to destabilize it. However, an increase in Pr leads to a significant expansion of the instability region.

Heat and mass transfer analysis in flow of Walter's B nanofluid: A numerical study of dual solutions

AbstractThis study investigates the behavior of Walter's liquid B fluid over a biaxially stretching/shrinking surface for Homann stagnation point flow, focusing on the rheological properties that are crucial for understanding physical phenomena in engineering and industrial processes. The problem is modeled using Buongiorno's model in the presence of a permeable surface subject to heat generation/absorption, Ohmic heating, and chemical reactions influenced by Arrhenius activation energy. The governing partial differential equations are solved numerically using an appropriate similarity transformation, and the results are graphically analyzed via MATLAB's bvp5c solver. The study highlights the importance of characterizing the intricate properties of viscoelastic fluids, with potential applications in biomedical engineering and materials science. The findings reveal the coexistence of two distinct flow regimes and dual solutions are obtained. It is noted that the activation energy parameter is shown to enhance mass distribution in both solutions, while chemical reactions accelerate reactant conversion but reduce mass distribution. Additionally, an increase in viscoelasticity shifts the fluid's behavior towards elasticity, creating greater resistance to shear deformation and reducing both velocity profiles.

Boundary Layer Flow of Dusty Ferrofluid: A Comparative Analysis of Stagnation Flow Influence

This research examines the characteristics of the boundary layer in the occurrence of dust particles within the ferrofluid boundary layer, aiming to understand the impact of stagnation flow or without stagnation flow in such systems. For this purpose, ferroparticles, namely magnetite (Fe3O4), are taken into consideration with kerosene and water as base fluids. The governing partial differential equations of the problem under consideration are converted into ordinary differential equations (ODEs) through the utilization of similarity transformations. Here, the equations obtained are then numerically solved utilizing MATLAB's built-in bvp4c solver. Moreover, the parameters’ effects, namely the dust particle loading, volume fraction of ferroparticles, and Eckert number to the flow with and without stagnation flow are computed and shown through tables and graphs. The findings indicate that the skin friction coefficient values for the stagnation-point flow are higher than those without stagnation-point flow. The Eckert number increases temperature profiles for both flows but more prominent in the flow without stagnation-point.

Numerical investigation of tangent hyperbolic stagnation point flow over a stretching cylinder subject to solutal and thermal stratified conditions

Numerical investigation of tangent hyperbolic stagnation point flow over a stretching cylinder subject to solutal and thermal stratified conditions

Improving turbulence modeling for gas turbine blades: A novel approach to address flow transition and stagnation point anomalies

Accurate prediction of temperature and Heat Transfer Coefficient (HTC) distributions over gas turbine blades is crucial for the design process and life assessment of these components. Numerical studies of flow over gas turbine blades face significant challenges in accurately simulating two complex phenomena: (1) the transition of flow from laminar to turbulent, and (2) stagnation point flow at the leading edge. Many turbulence models tend to overpredict the temperature on turbine blades, leading to incorrect identification of hot-spot regions and, consequently, erroneous estimations of blade life. This paper investigates the performance of various turbulence models in simulating flow and heat transfer over gas turbine vanes. The study includes three full turbulence models, i.e., Spalart-Allmaras (SA), Shear Stress Transport k−ω (SST-kw), and v2−f (V2F), as well as two transitional models, i.e., Transition SST (Trans-SST) and k−kL−ω (k-kl-w). Simulation results indicate that the v2−f, Trans-SST, and k−kL−ω models can detect flow transition. However, the transition length and onset location predicted by the Trans-SST and k−kL−ω models do not align with experimental data. Conversely, the v2−f model suffers from over-predictions at the leading edge due to stagnation point anomaly. To address these issues and due to capacities of the V2F model, this study proposes two modifications to enhance the performance of the V2F model. First, the production term of turbulent kinetic energy is redefined to mitigate the stagnation point anomaly. Second, the model is recalibrated to improve the prediction of flow transition. The new model, named the Production Modified V2F (PMV2F) model, shows promising results in predicting temperature and heat transfer coefficients.

Assisting and opposing mixed convective flow over a solid sphere at its bottom stagnation point with a constant surface heat, mass and motile microorganism flux

This study examined the laminar mixed convective flow around the lower point of stagnation for a solid sphere with a steady flux of gyrotactic microbial motility, mass and temperature. Biological convection phenomena have been considered in this study due to their intermixing traits and capacity in order to enhance mass transit in numerous biotechnology and biological systems. The first objective of this study is to examine and establish the mathematical formulation comprising partial differential equations for energy, momentum, mass conservation and mobile microorganism conservation balances. To do numerical calculations, the controlling partial differential equations are initially transformed by similarity transformations into a collection of interconnected non-linear ordinary differential equations. These equations are then solved by using the MATLAB Bvp4c scheme. The results indicate that several controlling parameters, particularly bioconvection parameters such as the Lewis number ( Le ), Bioconvection Lewis parameter ( Lb ) and Bioconvection Peclet number ( Pe ), have significant effects on flow transfer rates. A dual solution is observed in a certain region of mixed convection λ , where the mixed convection parameter is within the range of 0.41–0.65. The findings reveal significant results from dual solution analysis, highlighting the occurrence of unstable and stable phenomena for specific values of bioconvection parameters exclusively in the case of opposing flow. The assisting flow demonstrates only a single solution that is physically stable and unique. Observing lower stagnation point flow is essential for predicting and analysing complex fluid–microorganism interactions in various scientific and engineering applications such as designing spherical-shaped microbial fuel cell. Optimising flow conditions can enhance the efficiency of processes like wastewater treatment, where microorganisms play a crucial role in breaking down pollutants.

Magnetohydrodynamic Stagnation Point Flow and Heat Transfer of Casson Fluids Over a Stretching Sheet

This research investigates the effects of heat transfer on the stagnation-point flow of a non-Newtonian Casson fluid in a two-dimensional magnetohydrodynamic (MHD) boundary layer over a stretched sheet, considering thermal radiation impacts. By employing similarity transformations, the governing partial differential equations are transformed into nonlinear ordinary differential equations. The obtained self-similar equations are numerically solved using the Optimal Homotopy Analysis Method (OHAM). The numerical results are graphically represented, showcasing the influence of various parameters on fluid flow and heat transfer characteristics. The study uncovers important dynamics in transport phenomena. Examining and illustrating the effects of dimensionless parameters on velocity, temperature, and concentration profiles reveal significant insights. Moreover, skin friction and Nusselt number results for Casson fluids are analyzed and presented. The findings indicate that the Casson parameter and Hartman number act in opposition to fluid momentum, while the thermal conductivity parameter enhances fluid temperature. Thus, this research provides valuable insights into MHD boundary layer flows of non-Newtonian Casson fluids with thermal radiation effects, and the OHAM solution method proves effective in predicting flow transport properties.

Influence of solar thermal radiations and convective boundary on Al2O3/H2O transient model efficiency

Riga plate is a new, sophisticated magnetic field device that may be created by adjusting a group of permanent magnets and a different electrode over a plane surface. The heat transport and fluid movement in such physical setup are of paramount interest and have numerous engineering and industrial application particularly in submarines technologies. Due to the fixed magnetics the field produced which imperatively affect the model dynamics. Keeping in mind the influential applications of such physical setup, the purpose of this study is to introduce a new model based scrutinization of heat transport of stagnation point flow of Al2O3/water along vertically oriented convectively heated Riga surface. The conventional stagnation point flow model extended for nanofluid via radiative heat flux, dissipation effects and the first order thermal slip. The values of thermal conductivity values estimated via Corcione model and achieved the final nanoliquid model. For the results interpretation, the numerical scheme used and portrayed the results using different parametric ranges. The fluid motion is observed very slow due to stronger mixed convection and higher concentration of Al2O3 nanoparticles. The temperature is determined very high against the stronger convection effects and radiation number. However, the fluid layers in the vicinity of Riga surface have high heat transmission ability. Further, thermal slip and viscous dissipation effects also boost the temperature of Al2O3/water. Further, buoyancy number δ resists the fluid movement and thermal boundary region reduces in the presence of buoyancy factor.

Computational analysis of MHD hybrid nanofluid over an inclined cylinder: Variable thermal conductivity and viscosity with buoyancy and radiation effects

Due to their widespread use in engineering, hybrid nanofluids have been the primary focus of mathematical and physical research. Only the improvement of hybrid nanofluids’ variable heat conductivity and viscosity has been considered so far. Hybrid nanofluid flow across an inclined cylinder has many potential uses, including heat transfer and cooling in electrical devices, energy storage, refrigerants, and the automobile industry. Examining the effects of buoyant force, variable viscosity, variable thermal conductivity, mass suction, convective thermal conditions, and a magnetic field on the stagnation point flow of a Al2O3–Cu/H2O hybrid nanofluid in an inclined cylinder is our objective in this work. In order to find solutions to boundary-condition flow-describing partial differential equations, we turn them into ordinary differential equations using similarity transformations. We achieve this by employing a numerical strategy known as the fourth-order Runge–Kutta technique, which incorporates shooting techniques. A graphical representation of the findings emphasizes the influence of many physical parameters on flow dynamics. In addition, we address the influence of drag force and rate of heat transfer on various elements, such as the Biot parameter, magnetic variable, viscosity variable, and thermal conductivity variable. The mixed convection and magnetic parameters cause the velocity profile to rise while the temperature profile falls. The research’s results elucidate the cause behind the rise in thermal contour of hybrid nanofluids, which is seen when there is an increment in thermal conductivity, radiation parameter, and Biot number. The heat transfer rate exhibits a significant increase of 36.87% in the aiding flow scenario when a 2.0 mass suction is applied in conjunction with a 0.01 hybrid nanofluid, as compared to the conventional fluid. In the scenario of opposing flow, the heat transfer rate exhibits a significant increase of 36.96% when compared to that of ordinary fluid. Heat transfer increases 43.00% when Rd increases from 0.1 to 0.5 for both assisting and opposing flow.

Intelligent computing applications to study the tri-hybrid nanofluid past over the stretched surface

In this study, a recurrent neural network with the Levenberg-Marquardt backpropagation algorithm is used to examine the effects of various parameters on cooling mechanisms involving tri-hybrid nanofluid consisting of Al2O3, Cu, TiO2 and magnetohydrodynamic stagnation point flow. This research focus on nanofluid in the existence of an asymmetrically stretched disc in water, which plays an imprortant role for understanding heat transfer in addition to the dynamics of momentum and thermal boundary surface. Transform the complex partial differential system through suitable similarity transformations into the ordinary differential equations for numerical computing. These equations have been solved numerically by using the Adams method in Mathematica to generate datasets for various parameters.The current study demonstrates that the velocity profile rises with higher magnetic, velocity slip, and mass suction parameters. The fluid thermal level tends to decrease with an increase in mass suction parameters, whereas an increase in the magnetic parameter and Eckert number raises the fluid’s thermal level. Furthermore, it is noticed that the flow resistance and internal friction of the fluid are proportional to the viscosity parameter. The proposed scheme has shown its effectiveness in a wide range of scenarios and cases. This was achieved by comparing the mean square error metric for the squeezing flow tri-hybrid nanofluid problem with the obtained results. In addition, various statistical measures like state transitions, fitness assessments, error histograms, and regression analyses, provide further evidence of the solver’s robustness and reliability. The excellent agreement between the reference datasets and refined numerical solutions through the scheme showcases the method’s effectiveness, achieving remarkable accuracy levels ranging from 10-6 to 10-12.

Entropy generated nonlinear mixed convective beyond constant characteristics nanomaterial wedge flow

Background and objectiveNanomaterial flows at present have received much attention of the researchers. Such motivation stems for their utilization in pharmaceutical, industrial, petroleum, manufacturing and engineering applications including regenerative medicine, treatment of cancer, electronic device cooling, solar collector, mineral oil, antimicrobial agents, thermal storage system, transformer cooling and X-imaging etc. Higher thermal energy requirement in several electrical and mechanical systems is desired in recent time due to high advancement of science and technology. For important application here the stagnation point flow due to wedge with nonlinear convection is explored. For porous media, the Darcy-Forchheimer relation is considered. Characteristics of nanofluid is added by utilizing Buongiorno's model. Variable fluid characteristics are under consideration. Applied magnetic field is accounted. Energy expression comprises thermal radiation, Brownian motion, Ohmic heating, thermophoresis and heat generation. First order reaction and entropy rate are considered. MethodologyNonlinear differential expressions are changed into dimensionless ordinary systems through adequate transformations. The resultant nonlinear ordinary systems are solved through optimal homotopy analysis technique (OHAM). ResultsOutcomes for influential variables about temperature, velocity, concentration and entropy rate have been arranged. Here results show that for magnetic field the liquid flow and entropy rate have opposite scenarios. Thermal distribution and concentration have reverse effects for random motion variable while similar effect holds for thermophoresis parameter. Magnetic field and diffusion parameters contribute to augment entropy generation. Higher values of temperature dependent electrical conductivity variable lead to increase entropy rate. Thermal distribution for radiation and Eckert number is similar.

Chebyshev spectral Newton iterative analysis on unsteady oblique stagnation flow of Maxwell fluids over an oscillating-rotating disk with Cattaneo–Christov double diffusion

Oblique stagnation flow on a rotating disk is commonly observed in processes such as spinning coating and thin film deposition techniques. The investigation of the unsteady oblique stagnation point flow for Maxwell fluid over an oscillating-rotating disk embedded in a porous medium is meticulously conducted by employing the Darcy–Maxwell framework in conjunction with Cattaneo–Christov double diffusion model. A transformation of similarity is applied to reframe the governing equations into a system of non-dimensional coupled partial differential equations, whose numerical solutions are secured by the Chebyshev Spectral Newton Iterative Scheme. The outcomes underscore that an escalation in the Darcy parameter escalates the resistance within the porous medium, consequently leading to a reduction in velocity. Both the first-order slip and the second-order slip mitigate the fluid's interaction with the disk wall, leading to a retardation in flow velocity. Additionally, the presence of augmented thermal radiation parameters is observed to enhance heat transfer efficiency, resulting in a more homogenized temperature distribution. The two-dimensional and three-dimensional streamlines provide a precise depiction of the flow characteristics at the oblique stagnation point on the oscillating-rotating disk. These findings offer a theoretical foundation that can be instrumental for forthcoming research in analogous fields.

Significances of melting heat transfer and bioconvection phenomena in nanofluid flow over a three different geometries

This study addresses the numerical investigation of the steady and two-dimensional flow of magnetohydrodynamic nanofluid containing motile microorganisms over three distinct configurations: a wedge, a plate, and the stagnation point of a flat plate. The impacts of activation energy, melting phenomena, thermophoresis, and Brownian motion are taken into account. The dimensionless form of the governing coupled nonlinear partial differential equations is obtained by using similarity transformations. The system of ordinary differential equations is numerically solved using the “bvp4c” solver in MATLAB, and obtained results are also validated with an analytical approach Optimal Auxiliary Function Method (OAFM). Skin friction, heat, mass and motile microorganisms transfer rates are discussed through graphs and tables. Findings indicate that profile for Nusselt number enhances for higher inputs of melting parameter while Sherwood number lowers with increasing inputs of activation energy parameter. An improving pattern of velocity profiles is magnificent for stagnation point flow [f(η = 1) = 0.943711] compared to wedge [f(η = 1) = 0.915698]and horizontal plate [f(η = 1) = 0.868617]with respect to wedge angle parameter keeping velocity ratio parameter A < 1. For the wedge surface, the temperature profiles decrease [θ(η = 1.5) = 0.933075, 0.895245, 0.858931] for increasing inputs of radiation parameter (2.5 ≤ Nr ≤ 4.5) while motile microorganism profiles enhance [χ(η = 1.3) = 0.532505, 0.621569, 0.690635] with bioconvection Schmidtt number (0.3 ≤ Sb ≤ 0.7) respectively. Furthermore, it was found that, as velocity slip parameter increases then velocity of fluid also improves over a plate, wedge, and stagnation point of a flat plate considering velocity ratio parameter A < 1 .

Stagnation point flow of hybrid nanofluid driven towards a sinusoidal-radius permeable circular cylinder

ABSTRACT Recent advancements in nanofluid technology have emphasized the potential of ternary hybrid nanofluids (THNFs) to significantly enhance thermal and hydrodynamic properties. The implementation of a wavy sinusoidal cylinder is proposed as a novel approach to optimize heat transfer in a variety of engineering applications. This study focuses on analysing the flow and thermal behaviour of TiO2-Al2O3-MoS2/Kerosene oil a THNF around a circular cylinder with a sinusoidal radius, demonstrating enhanced heat conduction capabilities compared to conventional hybrid nanofluids. The governing equations, formulated as partial differential equations, are solved using the bvp4c solver. The study reveals that the shape of nanoparticles plays a crucial role in heat transfer efficiency. Specifically, when the solid volume fraction increases from 1% to 3%, brick-shaped particles exhibit the lowest heat transfer enhancement of 25.80%, while blade-shaped particles achieve the highest enhancement of 68.24%. Additionally, the heat transfer coefficient improves from 1.5% to 1.8% across different nanoparticle shapes under varying dissipation parameters. Similar trends are observed in the reduction of drag force with changes in the velocity slip parameter. These findings underscore the significant impact of nanoparticle shape and volume fraction on the thermal performance of THNFs, offering valuable insights for optimizing heat transfer systems in engineering applications.

Featuring the stagnation point flow of Casson nanofluid with thermal radiation and swimming microorganisms over a stretching sheet: A computational modeling via analytical method

Here, the investigation examines the flow of a nanomaterial toward stagnation point past stretching sheet having microorganism. The thermal radiative and heat generation have been accounted as well as convective boundary conditions. The influence of thermophoretic and Brownian movment has been considered. It has been proposed that the suitable transformation be utilized in order to convert the system of PDEs into ODEs. The analytical solutions are created through the Homotopy Analysis Method (HAM). The physical parameters with modelled equations have been graphically explained with related physical results. The numeric magnitude of drag friction, heat, mass transport and motile microorganism dendity were also computed and described for numerous emerging parameters. The result shows that the flow decreases with the rinsing value of Casson parameter. The impact of enhancing fluid parameters is too depressed the momentum and thermal boundary layer. The augment in the radiation boost the thermal layer whereas an enlargement in the input of the Lb tends to depreciation the motile density. Validation of the work is existed by validating the current outcomes with previous publishing results. The existing and potential applications of bioconvection have generated a new fascination in the theoretical investigation of the synthesis and process control in biofuel cells and bioreactors.

Characteristics of unsteady thermo-bioconvection chemical reactive stagnation point flow of trihybrid nanofluid around rotating sphere with Oxytactic Microorganisms

The present study is to highlight the significance of viscous dissipation, Joule heating and magnetic field on the stagnation point Darcy-Forchheimer flow of THNF (trihybrid nanofluid) around a spinning sphere containing Oxytactic and gyrotactic microorganisms. The analysis also includes the effects of heat generation and higher-order chemical reaction. A trihybrid nanofluid consisting of water (H2O) as the base fluid and TiO2,Cu and Fe3O4 nanoparticles is used. The Hamilton–Crosser model of trihybrid nanofluid is used in this work to compare their respective performance. This model is applicable to the optimization and design of sophisticated cooling systems where effective heat transfer is necessary, like electronic cooling, nuclear reactors, and high-performance heat exchangers. This model is used in biomedical engineering to comprehend drug delivery systems where exact control over reactions and fluid dynamics is required. Oxytactic microorganisms are important because they help break down contaminants in environmental engineering and wastewater treatment procedures. The fundamental system of the PDEs (partial differential equations) and the pertinent BCs (boundary conditions) have been transformed for computation using a few appropriate transformations. The numerical estimations for the appropriate system of differential equations are derived by employing the shooting approach (Bvp4c). Extensive studies are conducted to examine the effects of pertinent limitations on the rates of heat transfer, mass transfer, density of Oxytactic and gyrotactic microorganisms for both hybrid and trihybrid nanofluid. Among the various findings of this investigation is the observation that a higher Oxytactic and gyrotactic microorganisms Schmidt numbers result in a slower trihybrid nanofluid and hybrid nanofluid Oxytactic and gyrotactic microorganism's distributions. By increasing the value of Peclet number up to 7% the values of local density gyrotactic microorganisms enhance up to 9% .

Stagnation point radiative flow with Cattaneo-Christov theory and heat generation

Heat generation and magnetohydrodynamics for flow of Burgers liquid. Stagnation point flow towards stretched wall is considered. Radiation aspect is nonlinear. Cattaneo-Christov theory and boundary layer approximations are utilized. Related differential systems are formulated. Computations by Optimal homotopy analysis method (OHAM) are implemented. Total residual error is arranged. Graphical illustrations lead to the impacts of sundry parameters. Important points have been concluded. Higher Deborah number lead to velocity enhancement. Decrease in velocity occurs for magnetic field whereas reverse trend witnessed regarding thermal field. Temperature upsurges for higher radiation and heat generation variables. Higher radiation results in Nusselt number enhancement. Mass transport rate enhancement versus Schmidt number is observed. Reduction of thermal distribution occurs for thermal relaxation time.

Nanofluids' thermal assessment: Active and passive control approach

The nanofluids are decomposition of nano-sized metallic particles with base materials maintaining peak thermal properties. Owing to enhanced thermal features, various applications of nanofluids are observed in enhancing energy resources and cooling processes. The objective of current work is exploring the thermal impact of nanofluid associated to the oblique stagnation point flow. The thermal interpretation of nanofluid is subject to active and passive control approach. The heat trnasfer analysis is identified by using convective thermal flow constraints. The Buongiorno nanofluid model is adopted, endorsing the Brownian and thermophoresis consequences. The flow problem is first simplfied intodimensionless form. The numerical computations are performed by using famous shooting scheme with justifiable accuracy. A comparative change in the thermal phenomenon given the passive and active frameworks is presented. It is exmained that heat transfer reduces for stretching ratio parameter. The concentration profile reduces for angle of incidence for both active and passive control approach.

Exact solutions of a hybrid nanofluid model for the flow across a heated stretching cylinder at a stagnation point

We examined the two-dimensional, Stagnation flow across a thermally extending cylinder and identify the precise analytical solutions. As hybrid nanoparticles, Copper (Cu) and Alumina Oxide solid [Formula: see text] particles are employed with base fluid [Formula: see text]. We added nanoparticles of Copper (Cu) and Alumina Oxide solid [Formula: see text] to the water being that its heat permeability is low. The fundamental fluid’s ([Formula: see text]) thermal efficiency has risen as a result. A computational model of stationary point flow through a heated stretching cylinder is constructed using the theory behind the mechanism of the flow strategy. Carefully considered is the interaction between the impinging stagnation flow and the flow produced by stretching the cylinder’s surface. For this fascinating subject, precise analytical solutions are obtained, and the results are also graphically evaluated. The flow picture is evaluated using streams for any indications of evolved flow stretching or impinging stagnation flow dominating under pressure. A thorough investigation of heat transport is also offered, along with a graphical description of the Nusselt number (Nu). When the stretching cylinder has a lower stretching velocity A, an impinging stagnation flow that is more forceful or completely developed is seen for larger values of the approaching flow pressure parameter. When greater approaching pressure P flow values are applied, stagnation flow dominates over stretching flow. A significant portion of stagnation point flow research takes a numerical approach to the subject; nevertheless, in this work, we seek to present a precise solution to the challenge at hand. Behavior of fluid as stream lines and graphs of velocity profile, temperature profiles are plotted by using Mathematica software.

Numerical Solution for Plane Stagnation Point Flow

Numerical Solution for Plane Stagnation Point Flow