Flow Of Burgers Research Articles

Dynamical aspects of transient electro-osmotic flow of Burgers' fluid with zeta potential in cylindrical tube

Abstract In this article, we consider the flow of a Burgers’ fluid of transient electro-osmotic type in a small tube with a circular cross-section. Analytical results are found for the transient velocity and, electric potential profile by solving the Navier–Stokes and the linearized Poisson–Boltzmann equations. Moreover, these equations are solved with the help of the integral transform method. We consider cases in which the velocity of the fluid changes with time and those in which the velocity of the fluid does not change with time. Furthermore, special results for classical fluids such as Newtonian, second grade, Maxwell, and Oldroyd-B fluids are obtained as the particular cases of the outcomes of this work and that these results actually strengthen the results of the solution. This study of the nonlinear problem of Burgers’ fluid in a specified physical model will help us to understand the behavior of blood clotting and the block of any kind of problem in which this type of fluid is used. The solution of the complex velocity profile of Burgers’ fluid will help us in the future to solve the problems in which this transient electro-osmotic type of small tube is involved. At the end, numerical results are shown graphically that can help us to understand the complex behavior of the Burgers’ fluid, and also the analysis of the Burgers’ fluid shows dissimilarity with other fluids that are considered in this work.

Convected heat and mass transport in magnetic burgers’ nanoliquid subject to chemical responses

This paper investigates the effect of Burgers' nanofluid convinced as a stretching cylinder on heat source about magnetohydrodynamic stagnation point flow. Effect of the heat source/sink and chemical reaction are more appropriate to consider mass and heat transportation to the flow of Burgers’ fluid. Additionally, the effects of different convective actions i.e. convective condition by the exterior subordinate as two mass and heat transport arejoined in the analysis. The mathematical formulation was collected as the absorbing boundary layer theory and later coincidence transformations were imported in governing partial differential equations. The solutions of velocity, solutal, and thermal equations were declined to results, and graphs are interpreted from practical judgments. Fundamental physical announcement to the flow figure by Burgers' nanofluid improvement the lowering ideals magnetic force parameter. Also, The flow pattern of Burgers fluid parameters is contrary to the fluid detention time parameter. Furthermore, it was derived the thermal sketch and thermal density to the boundary layer of nanofluid enhance values of thermal Biot number and heat source parameter. The current examination was guaranteed to be recognised as study with previously presented scheduled.

Steady Flow of Burgers’ Nanofluids over a Permeable Stretching/Shrinking Surface with Heat Source/Sink

An engineered fluid, called nanofluid, is expected to have better thermal conductivity than conventional working fluids. The superior heat transfer performance and various possible applications promote the analysis of nanofluids in different flow geometries. This paper studies the flow of non-Newtonian Burgers’ nanofluids over a permeable stretching/shrinking surface with a heat source/sink. In the current study, we highlight the use of the single-phase nanofluid model in studying the boundary layer flow. The basic partial differential equations are transformed into ordinary (similarity) differential equations. Then, the resulting equations and boundary conditions are solved numerically in MATLAB using the bvp4c package. Triple solutions are presented, and stability analysis certifies that the first solution is physically realizable in practice. It is found that the increment of the heat source parameter raised the temperature profile of the nanofluids. Al2O3/H2O and Cu/H2O nanofluids produced the highest skin friction coefficient in the flow over stretching and shrinking surfaces, respectively. Meanwhile, Cu/H2O nanofluid showed a better heat transfer performance when compared to Al2O3/H2O and TiO2/H2O nanofluids. The present study is novel and could serve as a reference to other researchers for further analysis of heat transfer performance and the rheological behavior of nanofluids.

Magnetization for Burgers’ Fluid Subject to Convective Heating and Heterogeneous-Homogeneous Reactions

The flow of Burgers’ fluid in the magnetic field new mathematical modeling is introduced in this article which is heated convectively and maintained. The thermal energy transport aspects are examined by employing the space- and temperature-related heat source. In the present investigation, the homogeneous-heterogeneous reactions will present the features of scrutiny of the fluid concentration. For the purpose of dimensionless similarity transformations, ordinary differential equations (ODEs) are utilized practically. Developed ODEs are solved by introducing the concepts of Runge–Kutta–Fehlberg’s fourth-fifth method. The graphs show the pertinent outcome. The relaxation time parameter is exhibited by diminishing the thermal distribution of Burgers’ fluid property, and this will depend on the relaxation time factor. Biot number and retardation time factor behaviors are analyzed by opposing the behavior of the material factor of Burgers’ fluid. The response of homogeneous strength is deteriorated by the concentration rate of the fluid, and this will augment the data using the heterogeneous response with greater magnitude. By using already published studies, it is investigated that the present investigation is validated.

Modeling electro-osmotic flow and thermal transport of Caputo fractional Burgers fluid through a micro-channel

In this paper, we construct transient electro-osmotic flow of Burgers’ fluid with Caputo fractional derivative in a micro-channel, where the Poisson–Boltzmann equation described the potential electric field applied along the length of the microchannel. The analytical solution for the component of the velocity profile was obtained, first by applying the Laplace transform combined with the classical method of partial differential equations and, second by applying Laplace transform combined with the finite Fourier sine transform. The exact solution for the component of the temperature was obtained by applying Laplace transform and finite Fourier sine transform. Further, due to the complexity of the derived models of the governing equations for both velocity and temperature, the inverse Laplace transform was obtained with the aid of numerical inversion formula based on Stehfest's algorithms with the help of MATHCAD software. The graphical representations showing the effects of the time, retardation time, electro-kinetic width, and fractional parameters on the velocity of the fluid flow and the effects of time and fractional parameters on the temperature distribution in the micro-channel were presented and analyzed. The results show that the applied electric field, electro-osmotic force, electro-kinetic width, and relaxation time play a vital role on the velocity distribution in the micro-channel. The fractional parameters can be used to regulate both the velocity and temperature in the micro-channel. The study could be used in the design of various biomedical lab-on-chip devices, which could be useful for biomedical diagnosis and analysis.

Unsteady flow of fractional Burgers’ fluid in a rotating annulus region with power law kernel

Keeping in view of the complex fluid mechanics in bio-medicine and engineering, the Burgers’ fluid with a fractional derivatives model analyzed through a rotating annulus. The governing partial differential equation solved for velocity field and shear stress by using integral transformation method and using Bessel equations. The transformed equation inverted numerically by using Gaver-Stehfest’s algorithm. The approximate analytical solution for rotational velocity, and shear stress are presented. The influence of various parameters like fractional parameters, relaxation and retardation time parameters material constants, time and viscosity parameters are drawn numerically. It is found that the relaxation time and time helps the flow pattern, on the other hand other material constants resist the fluid rotation. Fractional parameters effect on fluid flow is opposite to each other. Finally, to check the validity of the solution there are comparisons for velocity field and shear stress for obtained results with an other numerical algorithm named Tzou’s algorithm.

Koopman operator for Burgers's equation

We consider the flow of Burgers' equation on an open set of (small) functions in $L^2([0,1])$. We derive explicitly the Koopman decomposition of the Burgers' flow. We identify the frequencies and the coefficients of this decomposition as eigenvalues and eigenfunctionals of the Koopman operator. We prove the convergence of the Koopman decomposition for $t>0$ for small Cauchy data, and up to $t=0$ for regular Cauchy data. The convergence up to $t=0$} leads to a `completeness' property for the basis of Koopman modes. We construct all modes and eigenfunctionals, including the eigenspaces involved in geometric multiplicity. This goes beyond the summation formulas provided by (Page & Kerswell, 2018), where only one term per eigenvalue was given. A numeric illustration of the Koopman decomposition is given and the Koopman eigenvalues compared to the eigenvalues of a Dynamic Mode Decomposition (DMD).

Symmetric and Non-Symmetric Flows of Burgers’ Fluids through Porous Media between Parallel Plates

Unidirectional unsteady flows of the incompressible Burgers’ fluids between two infinite horizontal parallel plates are analytically studied when the magnetic and porous effects are taken into consideration. The fluid motion is induced by the two plates, which move in their planes with time-dependent velocities. Exact general expressions are established both for the dimensionless velocity and shear stress fields as well as the corresponding Darcy’s resistance in the channel using the Laplace transform. If both plates move with equal velocities in the same direction, the fluid motion becomes symmetric with respect to the mid-plane between them. Otherwise, its motion is non-symmetric. To bring to light the behavior of the fluid, the dimensionless velocity profiles versus the spatial variable as well as its time evolution are presented both for the symmetric and asymmetric case. Finally, for comparison, similar graphical representations are presented together for the velocities of the incompressible Oldroyd-B and Burgers’ fluids. For large values of the time t, as expected, the behavior of the two different fluids is almost identical. The Darcy’s resistance against y is also graphically represented for the symmetric flow at different values of the time t. The influence of the magnetic field on the fluid motion is graphically revealed and discussed.

On modified Fourier heat flux in stagnation point flow of magnetized Burgers' fluid subject to homogeneous–heterogeneous reactions

In the current article, an effort has been made to model the forced convection flow phenomenon of magnetized viscoelastic fluid near a stagnation point. Moreover, Cattaneo–Christov heat flux model and the impact of uniform heat rise/fall are employed to examine the aspects of thermal energy transport. Additionally, the scrutiny of the fluid concentration feature by utilizing homogeneous–heterogeneous reactions is also an important effort of the present investigation. Ordinary differential equations (ODEs) are achieved by adopting the method of similarity transformations. The characteristics of physical parameters are assessed by employing numerical technique BVP Midrich scheme. Pertained outcomes are depicted in the form of graphs. The thermal distribution of Burgers’ fluid exhibits a diminishing trend for escalation in the extent of thermal relaxation heat flux parameter. Moreover, the concentration rate of the fluid deteriorates for higher strength of homogenous response, whereas it augments for greater magnitude of heterogeneous response. The validation of the present investigation is ensured by comparing with already published studies. The numerical values for the coefficient of heat transfer rate of Burgers’ fluid are also computed and depicted in graph.

Stagnation point flow of magnetized Burgers’ nanofluid subject to thermal radiation

This article explores the impact of non linear thermal radiation on magnetohydrodynamics flow of Burgers’ nanofluid induced by stretching cylinder. The effects of thermal radiation and chemical reaction are also taken into account to investigate the heat and mass transportation in flow of Burgers’ fluid. Mathematical formulation is obtained by utilizing boundary layer theory and then similarity transformations are introduced to alter the governing partial differential equations into set of ordinary differential equations. The solutions of velocity, thermal and solutal equations are attained by adopting homotopy analysis method. Thermophysical properties of numerous physical parameters on flow, thermal and solutal profiles are depicted in graphs and outcomes are explained with realistic judgements. The essential physical declaration of obtained outcomes shows that the flow profile of Burgers’ nanoliquid boosts up for growing values of velocity ratio parameter A. Additionally, it is noticed that the thermal and solutal boundary layers of magneto Burgers’ nanofluid become more thicker for augmented values of Burgers’ material parameter $$\beta _{2}$$ while contrasting behavior is observed for retardation time parameter $$\beta _{3}$$ . Moreover, it is assessed that thermal profile and thermal thickness of boundary layer of nanoliquid enhance for growing values of temperature ratio parameter $$\theta _{w}$$ and radiation parameter $${ R}_{d}.$$ Also, it is explored that the solutal thickness of Burgers’ fluid weakens for positively increasing values of chemical reaction parameter.

The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique

The solutions for velocity and stress are derived by using the methods of Laplace transformation and Modified Bessel’s equation for the rotational flow of Burgers’ fluid flowing through an unbounded round channel. Initially, supposed that the fluid is not moving with t = 0 and afterward fluid flow is because of the circular motion of the around channel with velocity Ω R t p with time positively grater than zero. At the point of complicated expressions of results, the inverse Laplace transform is alternately calculated by “Stehfest’s algorithm” and “MATHCAD” numerically. The numerically obtained solutions in the terms of the Modified Bessel’s equations of first and second kind, are satisfying all the imposed conditions of given mathematical model. The impact of the various physical and fractional parameters are also indeed and so presented by graphical demonstrations.

Electro-magneto-hydrodynamics Flows of Burgers' Fluids in Cylindrical Domains with Time Exponential Memory

This paper investigates the axial unsteady flow of a generalized Burgers’ fluid with fractional constitutive equation in a circular micro-tube, in presence of a time-dependent pressure gradient and an electric field parallel to flow direction and a magnetic field perpendicular on the flow direction. The mathematical model used in this work is based on a time-nonlocal constitutive equation for shear stress with time-fractional Caputo-Fabrizio derivatives; therefore, the histories of the velocity gradient will influence the shear stress and fluid motion. Thermal transport is considered in the hypothesis that the temperature of the cylindrical surface is constant. Analytical solutions for the fractional differential momentum equation and energy equation are obtained by employing the Laplace transform with respect to the time variable t and the finite Hankel transform with respect to the radial coordinate r. It is important to note that the analytical solutions for many particular models such as, ordinary/fractional Burgers fluids, ordinary/fractional Oldryd-B fluids, ordinary/fractional Maxwell fluids and Newtonian fluids, can be obtained from the solutions for the generalized fractional Burgers' fluid by particularizing the material coefficients and fractional parameters. By using the obtained analytical solutions and the Mathcad software, we have carried out numerical calculations in order to analyze the influence of the memory parameters and magnetic parameter on the fluid velocity and temperature. Numerical results are presented in graphical illustrations. It is found that ordinary generalized Burgers’ fluids flow faster than the fractional generalized Burgers’ fluids.

Unsteady and steady non-linear state flow of Burgers’ fluid in the presence of magnetic field with heat generation/absorption

Unsteady and steady non-linear state flow of Burgers’ fluid in the presence of magnetic field with heat generation/absorption

Rheology of Burgers’ model with Cattaneo-Christov heat flux in the presence of heat source/sink and magnetic field

This investigation presents the characteristics of Cattaneo-Christov heat flux model for the boundary layer flow of Burgers’ fluid model. Instead of simple Fourier’s law of heat conduction, we presented the Cattaneo-Christov model to analyze the thermal relaxation properties when the heat source/sink is present in the system. Mathematical modeling the laws of momentum and energy are presented under the order analysis approach. It is revealed that the term “” is for the hydro-magnetic rheology of the Newtonian model whereas the generalized magnetic field term (as mentioned in Eq. 2) is for the Burgers’ model which is incorporated in the current analysis. Suitable transformations are utilized for the conversion of partial differential system into coupled nonlinear set of ordinary differential equations which are tackled analytically through homotopy analysis technique. The plots of various physical quantities are presented showing the dynamics of the considered analysis. Streamlines for Burgers’ and Newtonian model are presented which show a difference of rheology. Numerical values for skin friction and surface heat transfer rate are presented in the form of tables.

MHD Mixed Convection Flow of Burgers’ Fluid in a Thermally Stratified Medium

AbstractThis attempt addresses the effects of nonlinear thermal radiation and magnetohydrodynamics (MHD) in mixed convection flow of Burgers’ fluid over a stretching sheet embedded in a thermally stratified medium. A transformation method has been employed to reduce the nonlinear partial differential equation (PDE) into the nonlinear ordinary differential equation (ODE). The resulting nonlinear coupled ordinary differential equations are solved for the series solutions. Convergence of derived series solutions is explicitly explored. Physical interpretation of different parameters through graphs and numerical values of local Nusselt number is discussed.

Flow of Burgers’ fluid over an inclined stretching sheet with heat and mass transfer

Effects of heat and mass transfer in the flow of Burgers fluid over an inclined sheet are discussed. Problems formulation and relevant analysis are given in the presence of thermal radiation and non-uniform heat source/sink. Thermal conductivity is taken temperature dependent. The nonlinear partial differential equations are simplified using boundary layer approximations. The resultant nonlinear ordinary differential equations are solved for the series solutions. The convergence of series solutions is obtained by plotting the ħ -curves for the velocity, temperature and concentration fields. Results of this work describe the role of different physical parameters involved in the problem. The Deborah numbers corresponding to relaxation time (β1 and β2) and angle of inclination (α) decrease the fluid velocity and concentration field. Concentration field decays as Deborah numbers corresponding to retardation time (β3) and mixed convection parameter (G) increase. Large values of heat generation/absorption parameters A/B, and the temperature distribution across the boundary layer increase. Numerical values of local Nusselt number, −θ′(0), and local Sherwood number, −ϕ′(0), are computed and analyzed. It is found that θ′(0) increases with an increase in β3.

Analysis of MHD flow of Burgers’ fluid with heat transfer in helical screw rheometer

This paper aims to study the influence of Hall current and heat transfer on the magnetohydrodynamics (MHD) flow of an electrically conducting, incompressible Burgers’ fluid in a helical screw rheometer. The screw and barrel are electrically insulated and kept at two different constant temperatures. A uniform magnetic field is applied perpendicular to the flow. Exact solutions are obtained for the velocity profile, volume flow rate, temperature distribution and rate of heat transfer. Expressions for the shear and normal stress components are also calculated. It is observed that the Burgers’ fluid parameters contribute in normal and tangential stresses, only. The effects of Hall parameter, Hartmann number, pressure distribution, and Brinkman number are investigated on flow profile, temperature distribution, and heat flux.

Influence of MHD on Some Oscillating Motions of a Fractional Burgers' Fluid

This paper presents a study for the influence of magnetohydrodynamic (MHD) on the oscillating flows of fractional Burgers’ fluid. The fractional calculus approach in the constitutive relationship model is introduced and a fractional Burgers’ model is built. The exact solution of the oscillating motions of a fractional Burgers’ fluid due to cosine and sine oscillations of an infinite flat plate are established with the help of integral transforms (Fourier sine and Laplace transforms). The expressions for the velocity field and the resulting shear stress that have been obtained, presented under integral and series form in terms of the generalized Mittag-Leffler function, satisfy all imposed initial and boundary conditions. Finally, the obtained solutions are graphically analyzed for variations of interesting flow parameters. While the MATHEMATICA package is used to draw the figures velocity components in the plane.

Influence of MHD on Some Oscillating Motions of a Fractional Burgers' Fluid

This paper presents a study for the influence of magnetohydrodynamic (MHD) on the oscillating flows of fractional Burgers’ fluid. The fractional calculus approach in the constitutive relationship model is introduced and a fractional Burgers’ model is built. The exact solution of the oscillating motions of a fractional Burgers’ fluid due to cosine and sine oscillations of an infinite flat plate are established with the help of integral transforms (Fourier sine and Laplace transforms). The expressions for the velocity field and the resulting shear stress that have been obtained, presented under integral and series form in terms of the generalized Mittag-Leffler function, satisfy all imposed initial and boundary conditions. Finally, the obtained solutions are graphically analyzed for variations of interesting flow parameters. While the MATHEMATICA package is used to draw the figures velocity components in the plane.

Steady flow of Burgers’ nanofluid over a stretching surface with heat generation/absorption

Analysis has been conducted to analyze the steady free convection boundary layer flow of a Burgers’ nanofluid near a linear stretched sheet. The effects of the heat generation/absorption and nanoparticles on the flow are considered. Similarity transformations are presented to convert the coupled nonlinear partial differential equations into coupled nonlinear ordinary differential equations. The reduced coupled transformed boundary layer equations of Burgers’ nanofluid model are then solved analytically using the homotopy analysis method. The variations of the dimensionless velocity, temperature, and nanoparticle with various physical parameters, namely the Deborah numbers \( \beta_{1} \), \( \beta_{2}, \) and \( \beta_{3} \), the Prandtl number \( \Pr \), the Brownian motion parameter \( N_{\text{b}} \), the thermophoresis parameter \( N_{\text{t}}, \) and the Lewis number \( {\text{Le}} \) are graphed and discussed.