Axisymmetric 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.

Axisymmetric stagnation-point flow of a fractional Oldroyd-B hybrid nanofluid over a vertical cylinder by improved Buongiorno's model

This paper investigated the unsteady axisymmetric stagnation-point flow, heat and mass transfer of Oldroyd-B hybrid nanofluid over a vertical cylinder by using Caputo time fractional derivatives for the first time, with the consideration of second-order velocity slip conditions. Improved Buongiorno's model was adopted to build the governing equations and finite difference combined with L1-algorithm was employed to solve the numerical solutions. Effects of key physical parameters on velocity, heat and mass transfer were presented graphically and discussed in detail. Outcomes show that the fractional derivatives are capable to describe the memory effect and thermoelasticity of viscoelastic nanofluids. Both Brownian motion and thermophoresis, especially Brownian motion, improve the heat transfer on the cylinder wall. In addition, the sensitivity of average Nusselt (or Sherwood) number to velocity fractional derivates α and β rises with increasing α and β, while the sensitivity to temperature fractional derivate γ declines with increasing γ. When γ increases from 0.2 to 0.3, the relative growth rate of average Nusselt number is about 9.26 %. This study provides a reference for exploring the stationary-point flow of fractional order nanofluids on vertical cylinders.

Micro-PIV study on the influence of viscosity on the dynamics of droplet impact onto a thin film

This work presents a systematic experimental study of droplet impact onto a wet substrate. Four different silicone oils are used, covering a range of Reynolds number between 116<Re<1106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$116< \ ext{Re} <1106$$\\end{document} at two different initial wall film heights. The objective is to characterize the temporal and radial evolution of the velocity field within the crown crater by means of micro-PIV. Our findings show that the velocity field has the structure of an axisymmetric stagnation point flow with decaying strength a(t). The latter exhibits an exponential decay and can be explained in terms of the exponential decay of the pressure force exerted by the impacting droplet onto the wall film. In this context, the commonly accepted functional dependence a(t)∝t-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a(t) \\propto t^{-1}$$\\end{document} represents only the first-order Taylor approximation of the exponential decay and has therefore only a limited temporal validity. The analysis also corroborates the existence of an inertial regime concerning the velocity field for Re>270\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{Re}} > 270$$\\end{document}. This is not observed at lower Re numbers due to the increased pressure losses caused by the extensional (normal) strain during the radial spreading of the lamella. To validate these findings a holistic approach is chosen, which combines numerical results, analytical solutions and experimental data from literature. In particular, by using the continuity equation, it is shown that the experimental decay of the wall film height can be reconstructed from the velocity measurements. Consilience of results from different approaches provides a robust validation of the micro-PIV data obtained in this work.Graphical abstract

Numerical investigation of time-dependent axisymmetric stagnation point flow and heat transfer of $$A{l}_{2}{O}_{3}-{H}_{2}O$$ and $$Cu-{H}_{2}O$$ nanofluid over a stretching sheet with variable physical features

Numerical investigation of time-dependent axisymmetric stagnation point flow and heat transfer of $$A{l}_{2}{O}_{3}-{H}_{2}O$$ and $$Cu-{H}_{2}O$$ nanofluid over a stretching sheet with variable physical features

Radiation effect on stagnation point flow of Casson nanofluid past a stretching plate/cylinder

The exclusive behaviour of nanofluid has been actively emphasized due to the determination of improved thermal efficiency. Hence, the aim of this study is to highlight the laminar boundary layer axisymmetric stagnation point flow of Casson nanofluid past a stretching plate/cylinder under the influence of thermal radiation and suction/injection. Nanofluid comprises water and Fe3O4 as nanoparticles. In this article, a novel casson nanofluid model has been developed and studied on stretchable flat plate or circular cylinder. Adequate rational assumptions (velocity components) are employed for the transformation of the governing partial-differential equations into a group of non-dimensional ordinary-differential formulas, which are then solved analytically. The momentum and energy equations are solved through the complementary error function method and scaling quantities. Using various figures, the effects of essential factors on the nanofluid flow, heat transportation, and Nusselt number, are determined and explored. From obtained results, it is observed that the velocity field diminishes owing to magnification in stretching parameter B\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B$$\\end{document} and Casson fluid parameter Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda$$\\end{document}. The temperature field increases by amplifying radiation Nr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_{r}$$\\end{document}, and solid volume fraction parameter ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi$$\\end{document}. The research is applicable to developing procedures for electric-conductive nanomaterials, which have potential applications in aircraft, smart coating transport phenomena, industry, engineering, and other sectors.

Axisymmetric stagnation-point flow of non-Newtonian nanomaterial and heat transport over a lubricated surface: Hybrid homotopy analysis method simulations

Abstract The heat transfer phenomenon associated with the lubricated surfaces offers applications in the manufacturing processes, thermal systems, industrial systems, and engineering phenomenon. It is a well-established fact that improvement in heat transfer is recently successfully claimed with the interaction of nanoparticles. Following such motivation in mind, the prime objective of current continuation is to perform the prediction of heat transfer in second-grade material subject to the lubricated surface. The lubricants are filled with non-Newtonian power law material. The varying thickness of the thin lubricating layer permits an imperfect slip surface. The second-grade fluid interfaces with the boundary condition. The modified semi-analytical tool termed as hybrid homotopy scheme is used to perform the simulations. Shooting and homotopy methods are combined in this new approach. Relevant effects of parameters on physical phenomenon are explained. The importance of influencing parameters in relation to the velocity field, temperature, and concentration profiles is investigated graphically. It is claimed that analytical computations existed for shear thinning case. It is observed that there is a noticeable drop in concentration and thermal profiles due to the variation of viscoelastic parameter. The control of free stream velocity is claimed due to the interaction of slip parameters.

An unsteady instigated induced magnetic field’s influence on the axisymmetric stagnation point flow of various shaped copper and silver nanomaterials submerged in ethylene glycol over an unsteady radial stretching sheet

The axisymmetric stagnation point flow of brick and blade-shaped Silver and Copper nanoparticles immersed in an ethylene glycol base fluid under the influence of an induced magnetic field over an unsteady radial stretching surface is investigated in this study. The unsteady phenomenon is considered because most flow issues in practice are unsteady. The fundamental laws of mass, momentum, and energy conservation are used to present the physical model. Heat transmission is also examined under the effects of magnetohydrodynamics, Joule heating, viscous dissipation, and convective boundary conditions to give a realistic physical investigation. Scaling analysis transforms the flow-governing issue into a collection of higher-order nonlinear ODEs. These are, then, solved numerically using the fourth-order Runge–Kutta and shooting techniques. Moreover, the numerical technique is validated by calculating residual error. It is concluded that, compared to the Ag–EG nanofluid, the Cu–EG nanofluid had the highest IMF, lowest temperature, minimum surface drag, and maximum heat flux, making it the ideal choice for creating a radial module.

A note on the asymptotic behaviour of axisymmetric stagnation-point flow and heat transfer of a viscous fluid past a permeable stretching/shrinking cylinder

The forced convection flow near a stagnation point on a stretching/shrinking cylinder derived originally by Wang [1] and later extended by Lok and Pop [2] is further considered through obtaining the asymptotic behaviour for the relevant dimensionless parameters, namely the Prandtl number σ, the wall velocity λ, the wall transpiration rate S and the Reynolds number R. Additional numerical results are also obtained to confirm our asymptotic predictions. Critical values are seen in the numerical results for negative values of λ with an asymptotic solution valid for large negative λ gives an asymptotic expression for these critical values. It is found that multiple solutions are possible for the limiting range of shrinking and suction parameters. Besides, the asymptotic behaviour is similar for the case of large suction and large Reynolds number. Also, the asymptotic analysis shows that for the solution to continue to large shrinking parameter, the suction parameter should be positive and large.

Dual solutions of unsteady two-dimensional electro-magneto-hydrodynamics (EMHD) axisymmetric stagnation-point flow of a hybrid nanofluid past a radially stretching/shrinking Riga surface with radiation effect

PurposeThis paper aims to analyse numerically the unsteady stagnation-point flow of Cu-Al2O3/H2O hybrid nanofluid towards a radially shrinking Riga surface with thermal radiation.Design/methodology/approachThe governing partial differential equations are transformed into a set of ordinary (similar) differential equations by applying appropriate transformations. The numerical computation of these equations including the stability analysis is conducted using the bvp4c solver.FindingsTwo solutions are possible within the allocated interval: shrinking parameter, unsteadiness decelerating parameter, electro-magneto-hydrodynamics (EMHD) parameter, nanoparticles volumetric concentration, radiation parameter and width parameter, whereas the stability analysis certifies that the first (upper branch) solution, which fulfills the boundary conditions is the physical/real solution. The EMHD parameter generated from the application of Riga plate enhances the skin friction coefficient as well as the heat transfer process. The width parameter d is also one of the factors in the deterioration of the skin friction coefficient and heat transfer rate. It is crucial to control the width parameter of the magnets and electrodes to obtain the desired outcome. The radiation parameter is not affecting the boundary layer separation because the critical values are unchanged. However, the addition of radiation and unsteadiness decelerating parameters boosts the thermal rate.Originality/valueThe results are novel and contribute to the discovery of the flow and thermal performance of the hybrid nanofluid subjected to a radially shrinking Riga plate. Besides, this work is beneficial to the other researchers and general audience from industries regarding the factors which contribute to the thermal enhancement of the working fluid.

Dissipative induced magnetic field on axisymmetric stagnation point flow of Propylene Glycol (PG) infused with multiple shape Tin (Sn), and Tungsten W (nanometer) particles

The present study focuses on investigating the influence of Induced Magnetic Field (IMF) and stagnation point flow over a radial stretching surface. For detailed comparative analysis multiple shape nanoparticles of Tin and Tungsten are submerged in Propylene glycol base fluid. The physical model is presented using the basic laws of mass, momentum, and energy conservation. To provide a realistic physically analysis, magnetohydrodynamics, viscous dissipation, and convective boundary conditions effects are incorporated. Using scaling analysis, the flow governing problem is converted into a set of higher-order nonlinear ODEs, which are then numerically solved. Quantities of practical importance, such as skin friction and Nusselt numbers, are depicted using bar graphs and physically examined in depth. The blade-shaped Tungsten-Propylene Glycol nanofluid had the lowest velocity, greatest IMF, and maximum heat flux compared to the Tin-Propylene Glycol nanofluid, making it the best option for producing radial modules.

Thermal aspect of boron nitride nanotubes (BNNT) and multiwall carbon nanotubes (MWCNT) with distinct physical features: Keller Box simulations

AbstractThe research on hybrid nanofluid has been focused by researchers widely in the current decade. Being the combination of two distinct nanoparticles, the researchers have predicted the thermal efficiencies of hybrid nanofluid model in view of distinct nanoparticles. However, the no attention is devoted by researchers towards the thermal mechanism of hybrid nanofluid with boron nitride nanotubes (BNNTs) and multiwall carbon nanotubes (MWCNTs) with distinct impressive characteristics. This communication aims explore the thermal flow of BNNTs and MWCNTs confining the axisymmetric rotational stagnation point flow executing by a bi‐axial stretching surface. The numerical computations are performed the implementation of Keller Box numerical technique. The results verification is done via making the comparative analysis. The thermal aspect of hybrid nanofluid model is entertained. The physical inspection of the formulated problem with flow parameters is done in terms of distinct graphs. It is observed that increase in the solid volume fraction of BNNTs enhanced the velocity profile. The temperature profile declined with stretching parameter for MWCNTs and hybrid nanofluid. The Nusselt number increases for thermal Biot number and increasing change is more progressive for hybrid nanomaterials as compared to MWCNTs.

Thermal analysis for axisymmetric stagnation point flow of viscoelastic magnetised nanofluid over a lubricated disk

This numerical study elaborates on the impacts of non-linear thermal radiation, Ohmic heating quadratic chemical reaction, an applied magnetic field on thermal characteristics of an axisymmetric flow of viscoelastic fluid in the vicinity of the axisymmetric stagnation point of a lubricated disk. The phenomena of the Brownian motion and thermophoresis with zero mass flux condition are also taken into account. The similarity transformation is used to reduce the number of independent variables in governing boundary layer equations and the transformed system of boundary value problem is solved using the box method. Variation in axial velocity, temperature and concentration profiles for various involved parameters of interest are graphically presented and categorically discussed. The local Nusselt number is documented for linear and non-linear radiations, whereas the Sherwood number is presented for linear and quadratic chemical reactions. It is observed that lubrication enhance both heat and mass transfer rates.

Nonlinear thermal radiation and activation energy features in axisymmetric rotational stagnation point flow of hybrid nanofluid

The present study particularizes the effects of nonlinear thermal radiation and the novel accepts of activation energy in the axisymmetric rotational stagnation point flow of hybrid fluid. Thermophysical properties of water and CWCNT/MWCNT are used for base fluid and nanoparticles respectively. The modeled partial differential equations are reduces to system of ordinary differential equations. The resulting equations are integrated numerically and the impact of involved parameters on velocity, temperature and nanoparticle concentration presented graphically. The tabular values for local Nusselt numbers in case of linear and nonlinear thermal radiation and the Sherwood number with and without activation energy are documented. It is observed that concentration of nanoparticles reduces with activation energy and increasing the solid volume fraction of SWCNT as well as MWCNT nanoparticles. Moreover the axial velocity increases while secondary velocity decreases by increasing the rotation parameter.

Near-wall forces on a neutrally buoyant spherical particle in an axisymmetric stagnation-point flow

Abstract

Numerical Study of Nanofluid Transport Subjected to the Collective Approach of Generalized Slip Condition and Radiative Phenomenon

This study investigates theoretically, the effects of axisymmetric magnetohydrodynamic stagnation point flow of nanofluid over a surface lubricated by taking the general slip condition: The application perspective in biological farming and irrigation system. The impacts of radiation, chemical reaction, thermophoresis, and Brownian motions are further taken into account. In this model, PDEs are appropriately transformed into dimensionless ODEs. A numeric techniques BVP4C is implemented for the solutions of all the involved transport variables. Influences by the physical significance parameters on the velocity, temperature, and concentration profiles are studied. Physically, the effects of the skin friction coefficient on the heat transfer and concentration rate at the surface are analyzed. The Lorentz force has visible diversity on the flow properties. A transition of slip to no-slip condition is evident in the present study.

Axisymmetric stagnation point flow on linearly stretching surfaces and heat transfer: Nanofluid with variable physical properties

Stagnation point flow on a linearly stretching surface is considered and heat transfer analysis incorporating nanofluid with variable properties is presented. In the analysis, the stretching surface is considered to be extending radially while the extended surface is heated convectively. The nanofluid physical properties are taken to be a function of volume fraction of the constituting nanoparticles and their distribution within the flow boundary layer is also incorporated. The governing equations of momentum, energy, and species (nanoparticle concentration) are formulated in line with the Buongiorno model. The resulting equations are reduced to three coupled nonlinear ordinary differential equations via using the similarity transformations. The transformed equations are solved numerically adopting the appropriate boundary conditions. The findings reveal that incorporating the variable properties of the nanofluid in the governing equations results in larger heat transfer rates as compared to those corresponding to the homogenous property fluid. This is more pronounced for large volume fractions of nanoparticles within the region of the boundary layer. In addition, Prandtl number, stretching rate of the surface, and nanoparticles volume fraction significantly influence the Nusselt number.

Oblique stagnation flow towards a rotating disc

This work endeavours to study the problem of axisymmetric oblique stagnation point flow above a rotating disc. An external flow impinges obliquely on a disc when the disc is rotating with constant angular velocity. Suitable similarity variables are introduced, for the first time, to transform the governing Navier–Stokes equations into a highly nonlinear system of ordinary differential equations, governed by a rotation ratio parameter α and an obliquity parameter γ. These resulting equations are then solved numerically via the routine bvp4c function from MATLAB software. Impact of different parameters on the flow and velocity profiles are discussed through tables and graphs. Further, three-dimensional streamlines are drawn to reveal the detailed effects of the parameters on the flow domain. It is noticed that streamlines are to shift the location of the stagnation point towards the incoming flow. There is also a rotational motion around the stagnation point for the rotating disc case.

Theoretical Investigation of Entropy Generation in Axisymmetric Stagnation Point Flow of Nanofluid Impinging on the Cylinder Axes with Constant Wall Heat Flux and Uniform Transpiration

Dimensionless temperature, Nusselt number and entropy generation in stagnation flow of incompressible nanofluid impinging on the infinite cylinder with uniform suction and blowing have been presented in this study. Initial stream rate of steady free stream is . Similarity solution of Navier-stokes and energy equations has been presented. These equations are simplified implementing appropriate transformations introduced in this research. The governing equations are solved where the heat flux at the cylinder’s wall is constant. All these solutions are acceptable for Reynolds numbers of 0.1-1000, various dimensionless surface diffusion and specific volume fractions of nanoparticles where a is the cylinder radius and is the kinematic viscosity of the base-fluid. The results show that for all Reynolds numbers, diffusion depth of radial and axial components of velocity field and wall shear stress increases as a result of decline in nano particles volume fraction and growth in surface diffusion. Moreover, increase in nanoparticles volume fraction and surface suction raises heat transfer coefficient and Nusselt number. Also the most entropy generated is calculated.

Activation Energy and Thermal Radiation Aspects in Bioconvection Flow of Rate-Type Nanoparticles Configured by a Stretching/Shrinking Disk

Abstract Recent trends in advanced nanotechnology developed thermal consequences of nanoparticles due to increasing significance in various engineering and thermal extrusion systems. The current continuation analyzes the axisymmetric stagnation point flow of magnetized rate-type nanoparticles configured by a porous stretching/shrinking rotating disk in the presence of motile microorganisms. A famous rate-type polymeric liquid namely Maxwell fluid has been used to examine the rheological consequences. Constitutive expressions based on the Buongiorno nanofluid model are used to examine the thermophoresis and Brownian motion features. With imposing similarity variables proposed by von Karman, the formulated problem is composed into dimensionless form. With the implementation of famous numerical technique bvp4c, the solution of governing flow equations is simulated. Graphical significance for each physical parameter is interpolated with relevant physical aspects. The variation in local Nusselt number, local Sherwood number, and motile density number corresponding to engineering parameters is numerically iterated and expressed in a tabular form. The study revealed that radial direction velocity component decreases by increasing the Deborah number and buoyancy ratio parameter. An enhanced temperature distribution for both stretching and shrinking cases has been noted by increasing the Biot number and thermophoresis parameter. A lower motile microorganisms distributed is noted due to the involvement of motile diffusivity.

Lubrication aspects in an axisymmetric magneto nanofluid flow with radiated chemical reaction

AbstractThis paper addresses the effects of axisymmetric magnetohydrodynamic stagnation point flow of nanofluid through the lubrication of power‐law fluid by taking the general slip at the interfacial condition. The impacts of radiated chemical reaction, thermophoresis, and Brownian motions are further accounted. The fluid is impinging orthogonally on the surface via power‐law slim coating liquid lubrication. The partial differential system is governed for both the lubricant and the base fluid. Using dimensional analysis, the arisen partial differential system is modified to ordinary differential systems subject to nonlinear boundary conditions. An implicit numerical technique namely the Keller‐Box method is executed to formulate the solution of developed nonlinear expressions. The influence of different involved constraints on quantities of interest are sketched and discussed. The effects of the skin friction coefficient, heat transfer, and concentration rate at the surface are given and analyzed. The condition from full slip to the no‐slip can be achieved from the present solution. The obtained solutions are matched through the existing data and observed good agreement.