On unsteady two-dimensional and axisymmetric squeezing flow between parallel plates

Khan, Umar; Ahmed, Naveed; Khan, Sheikh Irfanullah; Zaidi, Syed Zulfiqar Ali; Yang, Xiao‐Jun; Mohyud‐Din, Syed Tauseef

doi:10.1016/j.aej.2014.02.002

Cited by 52 publications

(29 citation statements)

References 24 publications

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“…(9) and (10) with the associated boundary conditions (11) using VPM [40][41][42][43][44][45] the velocity and temperature can be written as,…”

Section: Solution Using Vpmmentioning

confidence: 99%

“…To cope up with this problem, many analytical techniques have been developed and have been extensively used to study different non-linear problems governing physical phenomena [30][31][32][33][34][35][36][37][38]. Variation of parameters method (VPM) is one of these analytical techniques [39][40][41]. This techniqueneither requires any discretization nor does it dependonthe existence of small or large parameter to be implemented.…”

Section: Introductionmentioning

confidence: 99%

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A Study of Velocity and Temperature Slip Effects on Flow of Water Based Nanofluids in Converging and Diverging Channels

Mohyud‐Din

Khan

Ahmed

et al. 2015

Int. J. Appl. Comput. Math

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Copper (Cu) and silver (Ag) nanoparticle are added to water as a base fluid to study the effects of velocity and temperature slip on the flow between converging and diverging channels. A similarity transform has been employed to reduce the nonlinear partial differential equations to a system of nonlinear ordinary differential equations which is then solved by using two analytical schemes variational iteration and variation of parameters methods. For the sake of comparison, a numerical solution using fourth order Runge-Kutta method (RK-4) is also presented. Effects of velocity slip, temperature jump and the other parameters on the flow are discussed and demonstrated graphically. Comparison with already existing results in literature shows the efficiency of the method used.

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“…(9) and (10) with the associated boundary conditions (11) using VPM [40][41][42][43][44][45] the velocity and temperature can be written as,…”

Section: Solution Using Vpmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Study of Velocity and Temperature Slip Effects on Flow of Water Based Nanofluids in Converging and Diverging Channels

Mohyud‐Din

Khan

Ahmed

et al. 2015

Int. J. Appl. Comput. Math

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“…(10) subject to boundary conditions (11), the following standard procedure is proposed for VPM [33][34][35][36][37][38], the recurrence relation is given by…”

Section: Variation Of Parameters Methods (Vpm)mentioning

confidence: 99%

“…The main advantage of using this method is that, it is free from round off errors, calculation of the so-called Adomian's polynomials, perturbation, linearization or discretization and uses only the initial conditions which are easier to be implemented. Different studies are available that prove the accuracy and effectiveness of this technique [33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Effects of Velocity Slip on MHD Flow of a Non-Newtonian Fluid in Converging and Diverging Channels

Khan

Sikandar

Ahmed

et al. 2015

Int. J. Appl. Comput. Math

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Velocity slip effects on MHD flow of a non-Newtonian fluid in non-parallel walls are presented. Casson fluid model is taken into account. A suitable similarity transform has been applied to reduce the governing nonlinear partial differential equations to a relatively simpler ordinary differential equation. Adomian's decomposition method (ADM) and variation of parameters method (VPM) are then employed to solve resulting equation. Same problem is also solved numerical by using Runge-Kutta order 4 method. A convergence analysis is also carried out to check the efficiency of VPM solutions. Also, comparison between ADM, VPM and numerical solutions shows the accuracy of the obtained results. Graphical simulation explains effects of emerging parameters are demonstrated both for diverging and converging channels coupled with comprehensive discussions.Keywords Casson fluid · Adomian's decomposition method (ADM) · Variation of parameters method (VPM) · Converging and diverging channels · Runge-Kutta order 4 method

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“…They used HAM to solve the resulting nonlinear system of ordinary differential equations. Since then squeezing flow has been of great interests for various researchers [17][18][19]. Investigations with heat transport phenomenon are important in many industrial applications such as wire coating, hot rolling, metal spinning, glass blowing, paper manufacturing, glass fiber, glass sheet productions, the drawing of plastic films, continuous casting and the aerodynamic extrusion of plastic sheets.…”

mentioning

confidence: 99%

Thermal Radiation Effects on Squeezing Flow Casson Fluid between Parallel Disks

Khan¹,

Khan²,

Ahmed³

et al. 2016

Communications in Numerical Analysis

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In this paper, we investigate the thermal radiation effects in a time-dependent two-dimensional flow of a Casson fluid between two parallel disks when upper disk is taken to be impermeable and lower one is porous. Suitable similarity transforms are employed to convert governing partial differential equations into system of ordinary differential equations. Well known Homotopy Analysis Method (HAM) is employed to obtain the expressions for velocity and temperature profiles. Effects of different physical parameters such as squeeze number S, Prandtl number Pr, Eckert number Ec and the dimensionless length on the flow are also discussed with the help of graphs for velocity and temperature coupled with a comprehensive discussions. The skin friction coefficient and local Nusselt number along with convergence of the series solutions obtained by HAM are presented in tabulated form, while numerical solution is obtained by RK-4 method and comparison shows an excellent agreement between both the solutions.

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On unsteady two-dimensional and axisymmetric squeezing flow between parallel plates

Cited by 52 publications

References 24 publications

A Study of Velocity and Temperature Slip Effects on Flow of Water Based Nanofluids in Converging and Diverging Channels

A Study of Velocity and Temperature Slip Effects on Flow of Water Based Nanofluids in Converging and Diverging Channels

Effects of Velocity Slip on MHD Flow of a Non-Newtonian Fluid in Converging and Diverging Channels

Thermal Radiation Effects on Squeezing Flow Casson Fluid between Parallel Disks

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