Showing papers on "Similarity solution published in 2020"

Numerical modeling and analysis of bioconvection on MHD flow due to an upper paraboloid surface of revolution

Abstract: This article gives brief summary about the boundary layer flow characteristics of magnetic generalized Newtonian fluid due to a paraboloid revolution under bioconvection and chemical reactive species. The nanofluid model utilized in this work includes the behavior of Brownian motion and thermophoresis. The differential equations can be determined by a similarity solution. The determined ordinary differential equations have been solved numerically by fifth order Runge–Kutta Fehlberg method-based shooting technique. The behavior of different physical controlling dimensionless parameters on the base flow velocity, temperature, concentration, skin friction heat and mass transfer rates are analyzed numerically and graphically. We observed that the velocity, temperature and concentration profile reduce for increasing values of Hartmann number, Weissenberg number, wall thickness, stretching index, bioconvection, Prandtl number, Lewis number and Brownian motions whilst behavior is noticed for power law index. Moreover, for increases the values of Brownian and thermophoresis parameter the temperature profile shown increasing behavior. Comparison has been with represents date and found that the results have good agreement.

Thermal Radiation and MHD Effects in the Mixed Convection Flow of Fe3O4–Water Ferrofluid towards a Nonlinearly Moving Surface

Abstract: This paper investigated the magnetohydrodynamic (MHD) mixed convection flow of Fe3O4-water ferrofluid over a nonlinearly moving surface. The present work focused on how the state of suction on the surface of the moving sheet and the effects of thermal radiation influence the fluid flow and heat transfer characteristics within the stagnation region. As such, a similarity solution is engaged to transform the governing partial differential equations to the ordinary differential equations. A collocation method, namely the bvp4c function in the MATLAB software solves the reduced system, numerically. Two different numerical solutions were identified for the cases of assisting and opposing flows. The stability analysis was conducted to test the stability of the non-uniqueness solutions. The increment of the thermal radiation effect affects the rate of heat transfer to decrease. The stability analysis conveyed that the upper branch solution is stable and vice versa for the other solution.

Heat and mass transfer investigation of MHD Eyring–Powell flow in a stretching channel with chemical reactions

Abstract: In this paper, we studied the unsteady heat and mass transfer of magneto-hydrodynamics (MHD) Eyring–Powell squeezing flow in a channel by considering, radiation, chemical reaction and heat generation/absorption effects. Similarity solution was utilized to convert the 2-D governing partial differential equations to a set of non-linear ordinary differential equations and then a high accuracy spectral method based on the classical Galerkin approach developed to solve the equations. Comparison of the results with the fourth order Runge–Kutta method shows the accuracy and high agreement of the results for the velocity, temperature and concentration distribution in different locations of the channel. Effects of change in the values of several parameters on the velocity, temperature and concentration profiles were investigated. The results of the computation show that increasing the squeezing number will result in higher temperature and concentration values especially for the lower part of the channel.

Self-similar breakup of polymeric threads as described by the Oldroyd-B model

Abstract: When a drop of fluid containing long, flexible polymers breaks up, it forms threads of almost constant thickness, whose size decreases exponentially in time. Using an Oldroyd-B fluid as a model, we show that the thread profile, rescaled by the thread thickness, converges to a similarity solution. Using the correspondence between viscoelastic fluids and nonlinear elasticity, we derive similarity equations for the full three-dimensional axisymmetric flow field in the limit that the viscosity of the solvent fluid can be neglected. Deriving a conservation law along the thread, we can calculate the stress inside the thread from a measurement of the thread thickness. The explicit form of the velocity and stress fields can be deduced from a solution of the similarity equations. Results are validated by detailed comparison with numerical simulations.

An MHD viscous liquid stagnation point flow and heat transfer with thermal radiation and transpiration

Abstract: The impact of kinematic parameters magnetohydrodynamic (MHD) and thermal radiation on the unsteady flow of a Newtonian liquid through stagnation point due to a linear sheet with mass transpiration is considered. The characteristics of heat and MHD impinging on the sheet are analyzed theoretically. The flow of an electrically conducting liquid through stagnation point has gained considerable interest due to its industrial relevance. In the chemical engineering applications involving cooling of the liquid namely glass blowing, food processing, metal thinning, polymer extrusion, silicon chip manufacturing and applications of similar kind. In all these chemical engineering applications, the interplay between the regulating kinematic parameters and the nature of the fluid is of at most priority. The flow problem is modelled into nonlinear unsteady Navier-Stokes’ partial differential equations. The similarity solution for the velocity distribution is obtained. Depending on the type of boundary heating, the analytical solutions for temperature distribution is derived by means of a power series (Gauss hypergeometric). Temperature distribution for two types of boundary heating processes viz., prescribed time-dependent constant surface temperature (PTDCST) and prescribed time-dependent wall heat flux (PTDWHF) is discussed. There found to exist branching of solutions for both velocity and temperature distribution for certain range of controlling parameters. In fact there exists dual solution for both cases of stretching/shrinking sheet and these are analyzed to see the impacts of various physical parameters on the solution domain. The impact of various regulating parameters on the velocity as well as temperature is analyzed by means of numerous plots.

Analysis of unsteady non-axisymmetric Homann stagnation point flow of nanofluid and possible existence of multiple solutions

Abstract: This study examines the unsteady 3D non-axisymmetric Homann flow of an electrically conducting nanofluid in the presence of buoyancy forces. We consider the uniform external magnetic field B 0 , by neglecting induced magnetic field and examine the three possible directions of magnetic field which coincides with the direction of axes. A similarity solution is derived which involves the important physical dimensionless parameters like the nanoparticles volume fraction φ , the unsteadiness parameter ω , the buoyancy parameter λ , Hartmann number M and shear to strain ratio γ . We have treated the case for forced convection when λ = 0 which arise from the singularity γ = ∓ 1 . We found that, for large γ and λ , the leading terms of the solutions are independent of M and ω , and the effects of φ in that solutions are negligible. Numerical results are found for illustrative values of all the flow parameters by using bvp4c scheme in MATLAB. The critical values λ c of λ are seen in opposing flow for small rate of deceleration parameter ω while it changes to assisting flow for large value of ω .

Dynamics of liquid nanothreads: Fluctuation-driven instability and rupture

Abstract: The instability and rupture of nanoscale liquid threads is shown to strongly depend on thermal fluctuations. These fluctuations are naturally occurring within molecular dynamics (MD) simulations and can be incorporated via fluctuating hydrodynamics into a stochastic lubrication equation (SLE). A simple and robust numerical scheme is developed for the SLE that is validated against MD for both the initial (linear) instability and the nonlinear rupture process. Particular attention is paid to the rupture process and its statistics, where the `double-cone’ profile reported by Moseler & Landmann [Science, 2000, 289(5482): 1165-1169] is observed, as well as other distinct profile forms depending on the flow conditions. Comparison to the Eggers’ similarity solution [Physical Review Letters, 2002, 89(8): 084502], a power law of the minimum thread radius against time to rupture, shows agreement only at low surface tension; indicating that surface tension cannot generally be neglected when considering rupture dynamics.

Symmetry reduction, conservation laws and acoustic wave solutions for the extended Zakharov-Kuznetsov dynamical model arising in a dust plasma

Abstract: In this article, we consider the extended Zakharov-Kuznetsov (EZK) equation, which describes the nonlinear plasma dust acoustic waves (DAWs) in a magnetized dusty plasma. Dusty plasmas consist of three components: electrons, highly negatively charged dust grains, and two-temperature ions (low-temperature ions and high-temperature ions). We study the Lie symmetries, reductions, conservation laws and new exact solutions of EZK equations. Conservation laws for EZK equation is derived by applying the new conservation theorem of Ibragimov. Similarity solution for EZK equation will be obtained using Lie symmetry method. We find the Lie symmetries group of EZK equation, using similarity variables, get reduction equation, solving the reduction equations and then get the similarity solution. solitary wave solutions of the EZK equation are derived from the reduction equation. Thus, some new exact explicit solutions of the EZK equation are obtained.

Linear stability analysis of MHD flow of micropolar fluid with thermal radiation and convective boundary condition: Exact solution

Abstract: Magnetohydrodynamic (MHD) flow of micropolar fluid by including the thermal radiation and convective condition on a shrinking surface in the presence of mass suction effects has been investigated. The momentum, angular momentum and energy equations, and the solutions of these equations are valid for whole Navier stokes, and microrotational and energy equations have been solved exactly. We obtain the solution in the form of an incomplete γ function for the energy equation. The results reveal that dual solutions exist for certain domains of different physical parameters. Furthermore, high suction produces the high effect of drag force, and as a result, coefficient of skin friction increases in the first solution. Stability analysis has been performed and determined that the first solution is more stable.

A new similarity solution with stability analysis for the three-dimensional boundary layer of hybrid nanofluids

Abstract: Purpose The purpose of this study is to implement a new class of similarity transformation in analyzing the three-dimensional boundary layer flow of hybrid nanofluid. The Cu-Al2O3/water hybrid nanofluid is formulated using the single-phase nanofluid model with modified thermophysical properties. Design/methodology/approach The governing partial differential equations are reduced to the ordinary (similarity) differential equations using the proposed similarity transformation. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions. The features of the reduced skin frictions and the velocity profiles for different values of the physical parameters are analyzed and discussed. Findings The non-uniqueness of the solutions is observed for certain physical parameters. The dual solutions are perceived for both permeable and impermeable cases and being the main agenda of the work. The execution of stability analysis proves that the first solution is undoubtedly stable than the second solution. An increase in the mass transpiration parameter leads to the uniqueness of the solution. Oppositely, as the injection parameter increase, the two solutions remain. However, no separation point is detected in this problem within the considered parameter values. The present results are decisive to the pair of alumina and copper only. Originality/value The present findings are original and can benefit other researchers particularly in the field of fluid dynamics. This study can provide a different insight of the transformation that is applicable to reduce the complexity of the boundary layer equations.

Dense-gas effects on compressible boundary-layer stability

Abstract: A study of dense-gas effects on the stability of compressible boundary-layer flows is conducted. From the laminar similarity solution, the temperature variations are small due to the high specific heat of dense gases, leading to velocity profiles close to the incompressible ones. Concurrently, the complex thermodynamic properties of dense gases can lead to unconventional compressibility effects. In the subsonic regime, the Tollmien–Schlichting viscous mode is attenuated by compressibility effects and becomes preferentially skewed in line with the results based on the ideal-gas assumption. However, the absence of a generalized inflection point precludes the sustainability of the first mode by inviscid mechanisms. On the contrary, the viscous mode can be completely stable at supersonic speeds. At very high speeds, we have found instances of radiating supersonic instabilities with substantial amplification rates, i.e. waves that travel supersonically relative to the free-stream velocity. This acoustic mode has qualitatively similar features for various thermodynamic conditions and for different working fluids. This shows that the leading parameters governing the boundary-layer behaviour for the dense gas are the constant-pressure specific heat and, to a minor extent, the density-dependent viscosity. A satisfactory scaling of the mode characteristics is found to be proportional to the height of the layer near the wall that acts as a waveguide where acoustic waves may become trapped. This means that the supersonic mode has the same nature as Mack’s modes, even if its frequency for maximal amplification is greater. Direct numerical simulation accurately reproduces the development of the supersonic mode and emphasizes the radiation of the instability waves.

Exploration of dilatant nanofluid effects conveying microorganism utilizing scaling group analysis: FDM Blottner

Abstract: Biological transport in nanofluid is an essential new focus in fluid dynamics since the suspensions of microorganisms and nanoparticles proved to enhance the thermal conductivity of the fluid, which benefits many industrial applications for instances, biofuel cells and bio-microfluidics devices. In this regard, the present work is dedicated to investigating the effects of magnetohydrodynamics (MHD) and chemical reaction in the boundary layer flow, heat, mass and living microorganism transfer past a permeable stretching surface in a dilatant nanofluid. At the surface of the stretching sheet, there are multiple kinds of slips which affect the mechanisms within the vicinity of the boundary layer. The scaling group analysis has been performed to produce the appropriate similarity solution specifically for the present model. The governing boundary layer model in the form of the partial differential equations are reduced to a system of ordinary differential equations via similarity solutions to ease the computational process. The transformed mathematical model is then solved numerically via the Blottner’s finite difference method (FDM). The presences of the velocity slip at the surface of the stretching sheet decelerated the fluid flow.

Revisiting the Taylor-Culick approximation. II. Retraction of a viscous sheet

Abstract: The retraction of a viscous liquid sheet is studied using direct numerical simulations and long-wave asymptotic models. In the viscous regime, there exists a self-similar solution for the interface and the velocity profiles of a retracting sheet. This similarity solution reveals that the tip speed decreases as a function of time for a finite liquid sheet in contrast to the steady speed reached in the inertia dominated regime. Direct numerical simulations corroborate these theoretical predictions.

An approximate similarity solution for spatial fractional boundary-layer flow over an infinite vertical plate

Abstract: In this paper, an approximate similarity solution of a fractional laminar boundary layer of viscous fluid flow over an infinite vertical plate has been presented. We introduce new fractional similarity transformations to convert the partial differential equation into a similarity ordinary differential equation with a fractional context. The viscous term of the flow momentum equation is written based on the Caputo fractional derivative. The proposed analytical solution has been developed using fractional power-series technique, and the convergence of the solution has been examined. The velocity distributions with the similarity variable are plotted against different values of the fractional order to illustrate the effects of fractional argument on the velocity behavior.

Local similarity solution for steady laminar planar jet flow of viscoelastic FENE-P fluids

Abstract: Three local self-similar solutions are obtained for the laminar planar jet flow of viscoelastic fluids, described by the FENE-P constitutive equation, through an order of magnitude simplification of the governing equations. The more general solution is shown to be more accurate than two further simplified solutions, here called the delta and the Olagunju-type solutions, at least for the profiles of conformation tensor components. In the limit of vanishing viscoelasticity, all conformation tensor components reduce to the same low elasticity asymptotic behavior, and the polymer stresses become Newtonian-like. The general solution is then used to obtain the laws of the decay of the centerline velocity and of the growth of the jet half-width and to ascertain the effects of the Weissenberg number, maximum polymer extensibility parameter and the ratio of polymer to total viscosities upon the flow characteristics. The general local self-similar solution compares well with results of numerical simulations obtained by the RheoFoam module of the freeware OpenFoam code.

Triple Solutions and Stability Analysis of Micropolar Fluid Flow on an Exponentially Shrinking Surface

Abstract: In this article, we reconsidered the problem of Aurangzaib et al., and reproduced the results for triple solutions. The system of governing equations has been transformed into the system of non-linear ordinary differential equations (ODEs) by using exponential similarity transformation. The system of ODEs is reduced to initial value problems (IVPs) by employing the shooting method before solving IVPs by the Runge Kutta method. The results reveal that there are ranges of multiple solutions, triple solutions, and a single solution. However, Aurangzaib et al., only found dual solutions. The effect of the micropolar parameter, suction parameter, and Prandtl number on velocity, angular velocity, and temperature profiles have been taken into account. Stability analysis of triple solutions is performed and found that a physically possible stable solution is the first one, while all leftover solutions are not stable and cannot be experimentally seen.

Exact Similarity Solution for the Propagation of Spherical Shock Wave in a van der Waals Gas with Azimuthal Magnetic Field, Radiation Heat Flux, Radiation Pressure and Radiation Energy Under Gravitational Field

Abstract: We investigated the exact similarity solutions for shock wave propagation in non-ideal gas with radiation heat flux under gravitational field by taking radiation pressure and radiation energy into account in the presence of azimuthal magnetic field for spherical geometry. The solutions are in terms of analytical expressions. Similarity method is used to transform the basic equation from a system of partial differential equation into a system of ordinary differential equations. The system of ODE yields exact solutions for initial magnetic field distributions as power law. Consideration of isothermal approximations, radiation pressure, radiation energy and adiabatic compressibility in gravitating medium into accounts leads to new insights into explosion problem in contrast to earlier model. Finally, the product solution of progressive wave given by Mc. Vittie is used to obtain the exact similarity solution under the consideration that the radiation pressure is not equal to zero and the energy loss due to radiation escape is significant. The Alfven–Mach number effect, the parameter of gravitational effect, the parameter of non-idealness of the gas, the radiation pressure number and the adiabatic exponent gamma of the gas are discussed in detail.

A Similarity Solution for Natural Convection Flow near a Vertical Plate with Thermal Radiation

Abstract: This paper examined the fluid transport on boundary layer near a vertical wall with thermal radiation effect. The coupled nonlinear partial differential equations are reduced to a system of ordinary differential equations through similarity transformation. The resultant system of ordinary differential equations is integrated with maple software using RKF45 method. The effect of the active parameters such as Grashof number, thermal radiation parameter, temperature difference, Prandtl number, and local convective heat transfer parameter on the velocity profile, skin friction, temperature profile and Nusselt number are presented using graphs and tables. The outcome of the study revealed that the Prandtl number has a decreasing effect on thermal boundary layer thickness. It also revealed that the thermal radiation has an increasing effect on the Nusselt number, temperature distribution, temperature gradient and skin friction. The temperature distribution increases with increasing values of the temperature difference and local convective heat transfer parameter whereas decreases with Grashof number.

A body in nonlinear near-wall shear flow: impacts, analysis and comparisons

Abstract: Interaction between body motion and fluid motion is considered inside a nonlinear viscous wall layer, with this unsteady two-way coupling leading to impact of the body on the wall. The present paper involves a reduced system analysis which is shown to be consistent with computational solutions from direct numerical simulations for a basic flat-plate shape presented in an allied paper (Palmer & Smith, J. Fluid Mech., 2020). The occurrence of impact depends mainly on fluid parameters and initial conditions. The body considered is translating upstream or downstream relative to the wall. Subsequent analysis focusses on the unusual nature of the impact at the leading edge. The impacting flow structure is found to have two nonlinear viscous–inviscid regions lying on either side of a small viscous region. The flow properties in the regions dictate the lift and torque which drive the body towards the wall. Pronounced flow separations are common as the impact then cuts off the mass flux in the gap between the body and the wall; here, a nonlinear similarity solution sheds extra light on the separations. Comparisons are made between results from direct simulations and asymptotics at increased flow rate.

Analytic similarity solutions of the Navier–Stokes equations for a jet in a half space with the no-slip boundary condition

Abstract: We consider steady axisymmetric no-swirl viscous flows in a half space driven by a concentrated force. A method of finding physically meaningful similarity solutions of the Navier–Stokes equations with finite values of mass and momentum fluxes satisfying the no-slip boundary condition is developed. A new one-parameter set of analytic similarity solutions that describes impinging or emerging jets depending on the value of the parameter is found. A unique emerging-jet solution can be found for an arbitrary value of the Reynolds number. The accomplished analysis of momentum balance has resulted in an algorithm to estimate the best parameter of the similarity solution corresponding to the given physical characteristics of the jet source.

Performance of heat transfer in MHD mixed convection flow using nanofluids in the presence of viscous dissipation: Local non-similarity solution

Abstract: In this study, an investigation has been carried out to examine the effects of thermal radiation, heat generation/absorption, viscous dissipation and suction parameter on MHD flow of water-base nan...