Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium

Abbas, Zaheer; Shehzad, Sabir Ali; Rauf, A.

doi:10.1007/s10483-019-2488-9

Cited by 34 publications

(29 citation statements)

References 32 publications

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“…Investigations are made by considering cylindrical co‐ordinates.

\overset{V}{true} = [u (r, z; t), v (r, z; t), w (r, z; t)]

is the velocity vector at the disk and the velocity components

true(u, v, w true)

are taken in the directions of increasing

true(r, θ, z true)

. As the flow is considered to be axi‐symmetric, therefore, derivatives in the direction of the tangential co‐ordinate

θ

are omitted.…”

Section: Problem Formulationmentioning

confidence: 99%

“…The physical configuration of the flow model is described in Figure . By adopting the nanofluid Buongiorno model, the flow phenomenon governing equations are:

\frac{\partial u}{\partial r} + \frac{\partial w}{\partial z} + \frac{u}{r} = 0,

u \frac{\partial u}{\partial r} + w \frac{\partial u}{\partial z} - \frac{v^{2}}{r} + \frac{\partial u}{\partial t} = - \frac{1}{ρ} \frac{\partial p}{\partial r} + υ true(\frac{\partial^{2} u}{\partial r^{2}} + \frac{\partial^{2} u}{\partial z^{2}} + \frac{\partial}{\partial r} true(\frac{u}{r} true) true) - \frac{σ_{e} {β_{0}}^{2} u}{ρ_{f}} - \frac{μ_{f} ϕ_{1}}{ρ k_{1}} u,

u \frac{\partial v}{\partial r} + \frac{u v}{r} + w \frac{\partial v}{\partial z} + \frac{\partial v}{\partial t} = υ true(\frac{\partial^{2} v}{\partial r^{2}} + \frac{\partial}{\partial r} true(\frac{v}{r} true) + \frac{\partial^{2} v}{\partial z^{2}} true) - \frac{σ_{e} {β_{0}}^{2} v}{ρ_{f}} - μ_{f} <...>

…”

Section: Problem Formulationmentioning

confidence: 99%

“…Boundary conditions

(t > 0)

are formulated as:

{\begin{cases} left & u true(r, z; t true) = true(1 + ε \sin ω t true) a r + L_{1} \frac{\partial u}{\partial z}, v true(r, z; t true) = r γ + L_{1} \frac{\partial v}{\partial z}, w true(r, z; t true) = 0, \\ left & T true(z, t true) = T_{w} + L_{2} \frac{\partial T}{\partial z}, C true(z, t true) = C_{w} + L_{3} \frac{\partial C}{\partial z} normala normalt z = 0, \\ left & u true(r, z; t true) \to 0, v true(r, z; t true) \to 0, w true(r, z; t true) \to 0, \\ left & T true(r, z; t true) \to T_{\infty}, C true(r, z; t true) \to C_{\infty}, normalw normalh normale normaln z \to \infty, \end{cases}

with initial conditions:

u = v = w = 0 normalw normalh normale normaln t = 0 normalf ...

…”

Section: Problem Formulationmentioning

confidence: 99%

“…The following self‐similar transformations are established:

{\begin{cases} left & u = true(a r true) F false' true(η^{*}, t^{*} true), v = true(a r true) G true(η^{*}, t^{*} true), w = true(- 2 \sqrt{a υ} true) F true(η^{*}, t^{*} true), p = ρ a υ P_{0} true(η^{*}, t^{*} true), \\ left & θ true(η^{*}, t^{*} true) = \frac{T - T_{\infty}}{T_{w} - T_{\infty}}, ϕ true(η^{*}, t^{*} true) = \frac{C - C_{\infty}}{C_{w} - C_{\infty}}, η^{*} = \sqrt{\frac{a}{υ}} z, t^{*} = ω t, \end{cases}

…”

Section: Problem Formulationmentioning

confidence: 99%

See 3 more Smart Citations

Magnetohydrodynamics slip flow of a nanofluid through an oscillatory disk under porous medium supremacy

Rauf

Abbas

Shehzad

2019

Heat Trans. Asian Res.

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Unsteady, three-dimensional, hydromagnetic, nanofluid flow via a circular disk in porous medium is considered. The fluid motion is subject to disk rotation and time-based sinusoidal oscillations. The flow problem is normalized via similarity variables. Partial slip boundary conditions on velocity, concentration, and temperature are considered. A well-established numerical technique (successive over relaxation method) is used for the time-based flow problem. Results are discussed for both the time-based and linearly rotating disk case. Graphical representations for one, two, and three dimensions are sketched. The results are also discussed through tabular forms. K E Y W O R D S magnetohydrodynamics, nanofluid, oscillatory rotating disk, partial slip, porous medium, time-dependent flow 1 | INTRODUCTIONThe fluid flow concept through rotating disk systems has attracted significant attention from research scientists world-wide as a key area for future modernization and development in industrial processes. The major applications of such systems include the modeling of conditions that are found inside the wheel spacing of gas turbines, rotation of disks in an infinite rotating disk or resting fluid, contra-rotating disks for wheel space modeling in contra-rotating disks of existing engines, rotating cavity to model the conditions between compressor disks or corotating turbines, thin film fluid flow through a rotating surface, conical diffuser circulative flow, impinging jet disk cooling, shrouded rotation of disks and so forth. Moreover these systems are widely applicable in electrochemistry, power engineering, chemical engineering, aerodynamical

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“…Investigations are made by considering cylindrical co‐ordinates.

\overset{V}{true} = [u (r, z; t), v (r, z; t), w (r, z; t)]

is the velocity vector at the disk and the velocity components

true(u, v, w true)

are taken in the directions of increasing

true(r, θ, z true)

. As the flow is considered to be axi‐symmetric, therefore, derivatives in the direction of the tangential co‐ordinate

θ

are omitted.…”

Section: Problem Formulationmentioning

confidence: 99%

“…The physical configuration of the flow model is described in Figure . By adopting the nanofluid Buongiorno model, the flow phenomenon governing equations are:

\frac{\partial u}{\partial r} + \frac{\partial w}{\partial z} + \frac{u}{r} = 0,

u \frac{\partial u}{\partial r} + w \frac{\partial u}{\partial z} - \frac{v^{2}}{r} + \frac{\partial u}{\partial t} = - \frac{1}{ρ} \frac{\partial p}{\partial r} + υ true(\frac{\partial^{2} u}{\partial r^{2}} + \frac{\partial^{2} u}{\partial z^{2}} + \frac{\partial}{\partial r} true(\frac{u}{r} true) true) - \frac{σ_{e} {β_{0}}^{2} u}{ρ_{f}} - \frac{μ_{f} ϕ_{1}}{ρ k_{1}} u,

u \frac{\partial v}{\partial r} + \frac{u v}{r} + w \frac{\partial v}{\partial z} + \frac{\partial v}{\partial t} = υ true(\frac{\partial^{2} v}{\partial r^{2}} + \frac{\partial}{\partial r} true(\frac{v}{r} true) + \frac{\partial^{2} v}{\partial z^{2}} true) - \frac{σ_{e} {β_{0}}^{2} v}{ρ_{f}} - μ_{f} <...>

…”

Section: Problem Formulationmentioning

confidence: 99%

“…Boundary conditions

(t > 0)

are formulated as:

{\begin{cases} left & u true(r, z; t true) = true(1 + ε \sin ω t true) a r + L_{1} \frac{\partial u}{\partial z}, v true(r, z; t true) = r γ + L_{1} \frac{\partial v}{\partial z}, w true(r, z; t true) = 0, \\ left & T true(z, t true) = T_{w} + L_{2} \frac{\partial T}{\partial z}, C true(z, t true) = C_{w} + L_{3} \frac{\partial C}{\partial z} normala normalt z = 0, \\ left & u true(r, z; t true) \to 0, v true(r, z; t true) \to 0, w true(r, z; t true) \to 0, \\ left & T true(r, z; t true) \to T_{\infty}, C true(r, z; t true) \to C_{\infty}, normalw normalh normale normaln z \to \infty, \end{cases}

with initial conditions:

u = v = w = 0 normalw normalh normale normaln t = 0 normalf ...

…”

Section: Problem Formulationmentioning

confidence: 99%

“…The following self‐similar transformations are established:

{\begin{cases} left & u = true(a r true) F false' true(η^{*}, t^{*} true), v = true(a r true) G true(η^{*}, t^{*} true), w = true(- 2 \sqrt{a υ} true) F true(η^{*}, t^{*} true), p = ρ a υ P_{0} true(η^{*}, t^{*} true), \\ left & θ true(η^{*}, t^{*} true) = \frac{T - T_{\infty}}{T_{w} - T_{\infty}}, ϕ true(η^{*}, t^{*} true) = \frac{C - C_{\infty}}{C_{w} - C_{\infty}}, η^{*} = \sqrt{\frac{a}{υ}} z, t^{*} = ω t, \end{cases}

…”

Section: Problem Formulationmentioning

confidence: 99%

See 2 more Smart Citations

Magnetohydrodynamics slip flow of a nanofluid through an oscillatory disk under porous medium supremacy

Rauf

Abbas

Shehzad

2019

Heat Trans. Asian Res.

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“…The numerical simulation of the convective boundary of hydromagnetic stagnation point flow with non-Newtonian Williamson liquid with impacts of the Cattaneo–Christov model over an extended surface is executed by Ramzan et al 21 . Some recent investigations featuring the Cattaneo–Christov heat effect may be found in 22 – 27 .…”

Section: Introductionmentioning

confidence: 99%

Irreversibility minimization analysis of ferromagnetic Oldroyd-B nanofluid flow under the influence of a magnetic dipole

Ramzan

Howari

Chung

et al. 2021

Sci Rep

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Studies highlighting nanoparticles suspensions and flow attributes in the context of their application are the subject of current research. In particular, the utilization of these materials in biomedical rheological models has gained great attention. Magneto nanoparticles have a decisive role in the ferrofluid flows to regulate their viscoelastic physiognomies. Having such substantial interest in the flow of ferrofluids our objective is to elaborate the melting heat transfer impact in a stretched Oldroyd-B flow owing to a magnetic dipole in the presence of entropy generation optimization. Buongiorno nanofluid model expounding thermophoretic and Brownian features are considered. Moreover, activation energy with chemical reaction is also considered. The Cattaneo–Christov heat flux model is affianced instead of conventional Fourier law. The renowned bvp4c function of MATLAB is utilized to handle the nonlinearity of the system. Impacts of miscellaneous parameters are portrayed through graphical fallouts and numeric statistics. Results divulge that the velocity and temperature profiles show the opposite trend for growing estimates of the ferromagnetic parameter. It is also noticed that the temperature ratio parameter diminishes the entropy profile. Moreover, it is seen that the concentration profile displays a dwindling trend for the Brownian motion parameter and the opposite trend is witnessed for the thermophoretic parameter.

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Time‐dependent double phase dusty fluid flow over an oscillatory rotating disk

Alahmadi,

Rauf,

Mushtaq

et al. 2024

Heat Trans

Self Cite

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The dispersion of solid particles in a viscous fluid leads to a two‐phase flow nature. The present study incorporates the time‐dependent three‐dimensional dusty fluid flow generated by a periodically oscillatory rotating disk. The disk is stretchable along the radial axis with time‐based sinusoidal fluctuations. The governing incompressible flow equations for two‐phase equilibrium are normalized in the form of similarity systems consisting of the fluid stage and dust phase. The whole normalized system reduces to the familiar Von Kármán similarity system for the flow configuration of rotating disk by removing the dust phase and periodic oscillations of the disk. The two‐phase flow model is then numerically solved by a built‐in method namely “pdsolve” in Maple built program. The graphical aspects of the obtained physical parameters on velocity and thermal fields of the dust particle stage are investigated to show how the oscillatory disk contributes to the dusty flow features. The wall shears and thermal rates of the fluid and dust particles are also calculated in limiting case of disk rotation. It is observed that in time‐based flow, the oscillatory profiles preserve a phase shifting phenomenon. For centrifugal forces, the particle cloud moves away from the surface along a tangential direction. The thermal field is reduced by the dust particle stages.

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Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium

Cited by 34 publications

References 32 publications

Magnetohydrodynamics slip flow of a nanofluid through an oscillatory disk under porous medium supremacy

Magnetohydrodynamics slip flow of a nanofluid through an oscillatory disk under porous medium supremacy

Irreversibility minimization analysis of ferromagnetic Oldroyd-B nanofluid flow under the influence of a magnetic dipole

Time‐dependent double phase dusty fluid flow over an oscillatory rotating disk

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