Analytic solution for axisymmetric flow over a nonlinearly stretching sheet

Sajid, Muhammad; Hayat, Tasawar; Asghar, S.; Vajravelu, K.

doi:10.1007/s00419-007-0146-9

Cited by 33 publications

(22 citation statements)

References 32 publications

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“…The equations for the conservation of mass, momentum, energy, and nanoparticle volume fraction, under the usual boundary layer assumptions can be obtained [23,24] as…”

Section: Formulation Of the Problemmentioning

confidence: 99%

On Unsteady Three-Dimensional Axisymmetric MHD Nanofluid Flow with Entropy Generation and Thermo-Diffusion Effects

Almakki¹,

Dey²,

Mondal³

et al. 2017

Preprint

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Abstract:We investigate entropy generation in unsteady three-dimensional axisymmetric MHD nanofluid flow over a non-linearly stretching sheet. The flow is subject to thermal radiation and a chemical reaction. The conservation equations were solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasilinearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account when the nanofluid particle volume fraction on the boundary in passively controlled. The results show that as the Hartman number increases, both the Nusselt number and the Sherwood number decrease whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with the physical parameters.

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“…The equations for the conservation of mass, momentum, energy, and nanoparticle volume fraction, under the usual boundary layer assumptions can be obtained [23,24] as…”

Section: Formulation Of the Problemmentioning

confidence: 99%

On Unsteady Three-Dimensional Axisymmetric MHD Nanofluid Flow with Entropy Generation and Thermo-Diffusion Effects

Almakki¹,

Dey²,

Mondal³

et al. 2017

Preprint

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“…Also these transformations can be reduced to the transformations corresponding to the linear stretching sheet. The governing non-linear problem is solved analytically using homotopy analysis method (HAM) [12][13][14][15][16][17][18][19][20] and numerically using the shooting method. Also a brief comparison with an excellent agreement with the existing literature is provided.…”

Section: Introductionmentioning

confidence: 99%

Analytic and numerical solutions for axisymmetric flow with partial slip

Ali

Shahzad

Khan

et al. 2015

Engineering with Computers

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importance in many engineering processes. Such flows are of much interest in aerodynamic extrusion of plastic sheet, wire drawing, glass-fibers and paper production, drawing of plastic films and many others. Particularly, radial stretching occurs during the expansion of balloons. Sakiadis [1] initiated the study of the boundary layer flow over a stretching surface and derived the boundary layer equations for two-dimensional axisymmetric flow. Erickson et al. [2] extended the work of Sakiadis and considered the effects of blowing or suction on the stretched surface. Chen and Strobel [3] investigated the effects of buoyancy-induced pressure gradient on the boundary layer of stretching sheet with constant surface velocity and temperature. The problems related to a stretching sheet under various physical conditions are studied, theoretically, numerically and experimentally, by many researchers [4][5][6][7].A literature survey reveals that a few works are available on axisymmetric flow over a radially stretching sheet. Ariel [8] considered slip effects on axisymmetric flow over a radially stretching sheet and obtained the exact and different numerical solutions, where homotopy perturbation method (HPM) provided the best results. Mirgolbabaei et al. [9] found the analytic solution using adapted variational iteration method. Ariel [10] investigated the axisymmetric flow of second grade fluid over a radially stretching sheet. Sahoo [11] investigated the numerical study describing the effects of partial slip on axisymmetric flow of an electrically conducting visco-elastic fluid over a surface stretched with linear velocity in the radial direction.The aim of this work is to analyze the slip effects on axisymmetric flow of an electrically conducting viscous fluid in the presence of a magnetic field over a non-linear stretching sheet. We introduce new similarity transformations to reduce the governing equations. These transformations possess the potential to deal with many different fluid Abstract This article deals with the slip effects on the axisymmetric flow of an electrically conducting viscous fluid in the presence of a magnetic field over a non-linear radially stretching sheet. By introducing new similarity transformations, the governing partial differential equations are reduced to an ordinary differential equation. The resulting ordinary differential equation is then solved analytically using the homotopy analysis method and numerically by shooting method to show the accuracy of the analytical solution. The significant effects of various parameters on velocity field are discussed in detail. The shear stress at the wall together with some other physical parameters is tabulated and compared with existing literature, which shows an excellent agreement.

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“…Due to this fact, rheological parameter involved in the constitutive equations of such fluids adds complexity in the arising systems. Regardless of all these complexities, several researchers [4][5][6][7][8] studied the flow of non-Newtonian fluids in different geometrical configurations. However, the microscopic properties like micro-rotation and rotation-inertia of micropolar fluids be different from the other non-Newtonian fluids.…”

Section: Introductionmentioning

confidence: 99%

Squeezing Flow of Micropolar Nanofluid between Parallel Disks

Khan¹,

Mohyud‐Din²,

Yang³

2016

Journal of Magnetics

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In the present study, squeezing flow of micropolar nanofluid between parallel infinite disks in the presence of magnetic field perpendicular to plane of the disks is taken into account. The constitutive equations that govern the flow configuration are converted into nonlinear ordinary differential with the help of suitable similarity transforms. HAM package BVPh2.0 has been employed to solve the nonlinear system of ordinary differential equations. Effects of different emerging parameters like micropolar parameter K, squeezed Reynolds number R, Hartmann number M, Brownian motion parameter Nb, thermophoresis parameter Nt, Lewis number Le for dimensionless velocities, temperature distribution and concentration profile are also discussed graphically. In the presence of strong and weak interaction (i.e. n = 0 and n = 0.5), numerical values of skin friction coefficient, wall stress coefficient, local Nusselt number and local Sherwood number are presented in tabulated form. To check the validity and reliability of the developed algorithm BVPh2.0 a numerical investigation is also a part of this study.

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Analytic solution for axisymmetric flow over a nonlinearly stretching sheet

Cited by 33 publications

References 32 publications

On Unsteady Three-Dimensional Axisymmetric MHD Nanofluid Flow with Entropy Generation and Thermo-Diffusion Effects

On Unsteady Three-Dimensional Axisymmetric MHD Nanofluid Flow with Entropy Generation and Thermo-Diffusion Effects

Analytic and numerical solutions for axisymmetric flow with partial slip

Squeezing Flow of Micropolar Nanofluid between Parallel Disks

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