Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

Waini, Iskandar; Ishak, Anuar Mohd; Pop, Ioan

doi:10.1108/hff-01-2019-0057

Cited by 150 publications

(80 citation statements)

References 71 publications

(108 reference statements)

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“…The governing conservation equations (ie, mass, momentum, and energy) with hybrid nanofluid flow problem can be expressed as 18,41…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The governing conservation equations (ie, mass, momentum, and energy) with hybrid nanofluid flow problem can be expressed as 18,41

\frac{\partial u *}{\partial x *} + \frac{\partial v *}{\partial y *} = 0,

\frac{\partial u *}{\partial x *} u * + \frac{\partial u *}{\partial y *} v * = \frac{1}{ρ_{normalh normaln normalf}} true{μ_{h n f} \frac{\partial^{2} u *}{{\partial y *}^{2}} + \frac{\partial u *}{\partial y *} \frac{\partial}{\partial y *} (μ_{h n f}) true} + β_{h n f} g false(T * - T_{\infty} false) - \frac{σ B_{0}^{2}}{ρ_{normalh normaln normalf}} u * - \frac{ν_{f}}{ρ_{h n f} k} u *,

{(ρ C_{p})}_{h n f} true(\frac{\partial T *}{\partial x *} u * + \frac{\partial T *}{\partial y *} v * true) = k_{h n f} \frac{\partial^{2} T *}{{\partial y *}^{2}} - \frac{\partial q_{r}}{\partial y *} + Q * false(T * - T_{\infty} false)

…”

Section: Mathematical Formulationmentioning

confidence: 99%

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Cu‐Al₂O₃/H₂O hybrid nanofluid flow past a porous stretching sheet due to temperatue‐dependent viscosity and viscous dissipation

Venkateswarlu

Narayana

2020

Heat Trans

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The resent development of research in the field of nano technology introduced hybrid nanofluids which are advanced classes of fluids with augmented thermal properties and it gives better results comparing to regular nanofluid. The aim of the present work is to study the significant effects of variable viscosity and viscous dissipation on a porous stretching sheet in the presence of hybrid nanofluid and radiative heating. In this model, two types of nanoparticles, namely copper (Cu) and alumina oxide (Al 2 O 3), are suspended in the base fluid H 2 O to form a hybrid nanoliquid. The novelty of this study is to introduce variable viscosity along with natural convection in the momentum equation and viscous dissipation in the energy equation. Mathematical modeling is employed in this study, whereby partial differential equations for the fluid flow are constructed and transformed to a set of ordinary differential equations, and hence resolved computationally by Runge-Kutta-Fehlberg method along with shooting scheme. The most important results for relevant parameters concerning the flow heat measure, surface drag, and heat transfer coefficients are thoroughly examined and presented graphically for both Cu-Al 2 O 3 /water hybrid nanofluids. There is an increase in hybrid

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“…The governing conservation equations (ie, mass, momentum, and energy) with hybrid nanofluid flow problem can be expressed as 18,41…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The governing conservation equations (ie, mass, momentum, and energy) with hybrid nanofluid flow problem can be expressed as 18,41

\frac{\partial u *}{\partial x *} + \frac{\partial v *}{\partial y *} = 0,

\frac{\partial u *}{\partial x *} u * + \frac{\partial u *}{\partial y *} v * = \frac{1}{ρ_{normalh normaln normalf}} true{μ_{h n f} \frac{\partial^{2} u *}{{\partial y *}^{2}} + \frac{\partial u *}{\partial y *} \frac{\partial}{\partial y *} (μ_{h n f}) true} + β_{h n f} g false(T * - T_{\infty} false) - \frac{σ B_{0}^{2}}{ρ_{normalh normaln normalf}} u * - \frac{ν_{f}}{ρ_{h n f} k} u *,

{(ρ C_{p})}_{h n f} true(\frac{\partial T *}{\partial x *} u * + \frac{\partial T *}{\partial y *} v * true) = k_{h n f} \frac{\partial^{2} T *}{{\partial y *}^{2}} - \frac{\partial q_{r}}{\partial y *} + Q * false(T * - T_{\infty} false)

…”

Section: Mathematical Formulationmentioning

confidence: 99%

Cu‐Al₂O₃/H₂O hybrid nanofluid flow past a porous stretching sheet due to temperatue‐dependent viscosity and viscous dissipation

Venkateswarlu

Narayana

2020

Heat Trans

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“…There are few of literatures that discussed the bvp4c procedure in solving steady flow problem (Waini et al 2019;Yahaya et al 2018). Generally, the basic syntax in the bvp4c solver is sol = bvp4c (@OdeBVP, @OdeBC, solinit, options).…”

Section: Numerical Proceduresmentioning

confidence: 99%

Thermal Marangoni Flow Past a Permeable Stretching/Shrinking Sheet in a Hybrid Cu-Al2O3/Water Nanofluid

Khashi’ie¹,

Arifin²,

Pop³

et al. 2020

JSM

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The present study accentuates the Marangoni convection flow and heat transfer characteristics of a hybrid Cu-Al 2 O 3 / water nanofluid past a stretching/shrinking sheet. The presence of surface tension due to an imposed temperature gradient at the wall surface induces the thermal Marangoni convection. A suitable transformation is employed to convert the boundary layer flow and energy equations into a nonlinear set of ordinary (similarity) differential equations. The bvp4c solver in MATLAB software is utilized to solve the transformed system. The change in velocity and temperature, as well as the Nusselt number with the accretion of the dimensionless Marangoni, nanoparticles volume fraction and suction parameters, are discussed and manifested in the graph forms. The presence of two solutions for both stretching and shrinking flow cases are noticeable with the imposition of wall mass suction parameter. The adoption of stability analysis proves that the first solution is the real solution. Meanwhile, the heat transfer rate significantly augments with an upsurge of the Cu volume fraction (shrinking flow case) and Marangoni parameter (stretching flow case). Both Marangoni and Cu volume fraction parameters also can decelerate the boundary layer separation process.

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“…They discovered that only one of the solutions is stable and thus physically reliable as time evolves. Besides, Waini et al [32][33][34][35][36][37] in a series of papers have extended the problem to different surfaces. Moreover, the effects of MHD and viscous dissipation have been studied by Lund et al 38 , considering Cu-Fe 3 O 4 /H 2 O hybrid nanofluid in a porous medium.…”

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confidence: 99%

Hybrid nanofluid flow towards a stagnation point on a stretching/shrinking cylinder

Waini

Ishak

Pop

2020

Sci Rep

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This paper examines the stagnation point flow towards a stretching/shrinking cylinder in a hybrid nanofluid. Here, copper (Cu) and alumina (Al 2 o 3) are considered as the hybrid nanoparticles while water as the base fluid. The governing equations are reduced to the similarity equations using a similarity transformation. The resulting equations are solved numerically using the boundary value problem solver, bvp4c, available in the Matlab software. It is found that the heat transfer rate is greater for the hybrid nanofluid compared to the regular nanofluid as well as the regular fluid. Besides, the nonuniqueness of the solutions is observed for certain physical parameters. It is also noticed that the bifurcation of the solutions occurs in the shrinking regions. In addition, the heat transfer rate and the skin friction coefficients increase in the presence of nanoparticles and for larger Reynolds number. It is found that between the two solutions, only one of them is stable as time evolves.

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Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

Cited by 150 publications

References 71 publications

Cu‐Al₂O₃/H₂O hybrid nanofluid flow past a porous stretching sheet due to temperatue‐dependent viscosity and viscous dissipation

Cu‐Al₂O₃/H₂O hybrid nanofluid flow past a porous stretching sheet due to temperatue‐dependent viscosity and viscous dissipation

Thermal Marangoni Flow Past a Permeable Stretching/Shrinking Sheet in a Hybrid Cu-Al2O3/Water Nanofluid

Hybrid nanofluid flow towards a stagnation point on a stretching/shrinking cylinder

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Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

Cited by 150 publications

References 71 publications

Cu‐Al2O3/H2O hybrid nanofluid flow past a porous stretching sheet due to temperatue‐dependent viscosity and viscous dissipation

Cu‐Al2O3/H2O hybrid nanofluid flow past a porous stretching sheet due to temperatue‐dependent viscosity and viscous dissipation

Thermal Marangoni Flow Past a Permeable Stretching/Shrinking Sheet in a Hybrid Cu-Al2O3/Water Nanofluid

Hybrid nanofluid flow towards a stagnation point on a stretching/shrinking cylinder

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Cu‐Al₂O₃/H₂O hybrid nanofluid flow past a porous stretching sheet due to temperatue‐dependent viscosity and viscous dissipation

Cu‐Al₂O₃/H₂O hybrid nanofluid flow past a porous stretching sheet due to temperatue‐dependent viscosity and viscous dissipation