Dual nature solution of water functionalized copper nanoparticles along a permeable shrinking cylinder: FDM approach

Soomro, Feroz Ahmed; Zaib, Aurang; Haq, Rizwan Ul; Sheikholeslami, M.

doi:10.1016/j.ijheatmasstransfer.2018.10.051

Cited by 68 publications

(21 citation statements)

References 27 publications

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“…Table 3. Numerical values of −θ (0) and −φ (0) for the case of dual stratified nanofluid over shrinking sheet (ε = −1) and stretching sheet (ε = 1) when The existence of dual solutions for S > 2 in the present study is in accordance to the result by Miklavčič and Wang [2], Fang et al [4], Jusoh et al [5] and Soomro et al [6]. It is apparent from these previous studies that the flow will produce two solutions by employing S > 2 for a suitable combination of the control parameters.…”

Section: Resultssupporting

confidence: 90%

“…Jusoh et al [5] also concluded that the application of suction at certain values of the involving parameters contributed to the appearance of the second solution. Very recently, Soomro et al [6] obtained dual solutions for mixed convective flow of a viscous fluid with copper nanoparticles over a permeable shrinking cylinder. The findings showed that the mixed effects of opposing flow and wall mass suction might generate two solutions.…”

Section: Introductionmentioning

confidence: 99%

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Dual Stratified Nanofluid Flow Past a Permeable Shrinking/Stretching Sheet Using a Non-Fourier Energy Model

et al. 2019

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The present study emphasizes the combined effects of double stratification and buoyancy forces on nanofluid flow past a shrinking/stretching surface. A permeable sheet is used to give way for possible wall fluid suction while the magnetic field is imposed normal to the sheet. The governing boundary layer with non-Fourier energy equations (partial differential equations (PDEs)) are converted into a set of nonlinear ordinary differential equations (ODEs) using similarity transformations. The approximate relative error between present results (using the boundary value problem with fourth order accuracy (bvp4c) function) and previous studies in few limiting cases is sufficiently small (0% to 0.3694%). Numerical solutions are graphically displayed for several physical parameters namely suction, magnetic, thermal relaxation, thermal and solutal stratifications on the velocity, temperature and nanoparticles volume fraction profiles. The non-Fourier energy equation gives a different estimation of heat and mass transfer rates as compared to the classical energy equation. The heat transfer rate approximately elevates 5.83% to 12.13% when the thermal relaxation parameter is added for both shrinking and stretching cases. Adversely, the mass transfer rate declines within the range of 1.02% to 2.42%. It is also evident in the present work that the augmentation of suitable wall mass suction will generate dual solutions. The existence of two solutions (first and second) are noticed in all the profiles as well as the local skin friction, Nusselt number and Sherwood number graphs within the considerable range of parameters. The implementation of stability analysis asserts that the first solution is the real solution.

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Section: Resultssupporting

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Dual Stratified Nanofluid Flow Past a Permeable Shrinking/Stretching Sheet Using a Non-Fourier Energy Model

et al. 2019

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“…Further, Zaimi et al 14 examined the effect of suction on the unsteady flow over a shrinking cylinder and found the dual solutions exist for a certain range of suction and unsteadiness parameters. Besides, Soomro et al 15 examined the nanofluid flow along a permeable shrinking vertical cylinder with slip effects. Other than that, some other useful studies to simulate the flow over a cylinder under different conditions can be found in the literature [16][17][18][19][20][21] .…”

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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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“…It is perceptible that these nanomaterials are considered ultrafine (1–50 nm order of length); hence, the nanoliquids appeared to conduct further as a single-phase liquid than a suspension of solid–liquid. Comprehensive monographs regarding the nanofluids in conjunction with several applications can be seen in Tiwari and Das ( 2007 ), Chamkha et al ( 2012 ), El-Kabeir et al ( 2015 ), Wakif et al ( 2018 ), Sheikholeslami ( 2019 ), Soomro et al ( 2019 ), Mebarek-Oudina et al ( 2020 ), and Raza et al ( 2020 ). More precisely, the magnetic nanoliquid (ferroliquids), which is colloidally deferred of magnetic nanomaterials like ferrite, cobalt, and magnetite, is suspended in non-conducting fluids like heptanes, water, hydrocarbons, and kerosene.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Mixed Convection Squeezing Flow of a Hybrid Nanofluid Containing Magnetized Ferroparticles in 50%:50% of Ethylene Glycol–Water Mixture Base Fluids Between Two Disks With the Presence of a Non-linear Thermal Radiation Heat Flux

et al. 2020

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Ferroliquids are an example of a colloidal suspension of magnetic nanomaterials and regular liquids. These fluids have numerous applications in medical science such as cell separation, targeting of drugs, magnetic resonance imaging, etc. The hybrid nanofluid is composed by scattering the magnetic nanomaterial of more than one type nanoparticles suspended into the base fluid. It has different scientific applications such as heat dissipation, dynamic sealing, damping, etc. Owing to the vast ferrofluid applications, the time-dependent squeezed flow of hybrid ferroliquids under the impact of non-linear radiation and mixed convection within two disks was explored for the first time in this analysis. Here, the cobalt and magnetite ferrofluids are considered and scattered in a 50%:50% mixture of water–EG (ethylene glycol). The similarity technique is used to reduce the leading PDEs into coupled non-linear ODEs. The transmuted equations together with recommended boundary restrictions are numerically solved via Matlab solver bvp4c. The opposing and assisting flows are considered. The impacts of an emerging parameter on fluid velocity and temperature field of hybrid ferroliquids are examined through the different graphical aids. The results showed that the opposite trend is scrutinized due to the magnetic influence on the temperature and velocity in the case of assisting and opposing flows. The velocity augments due to the volume fraction of nanoparticles in the assisting flow and declines in the opposing flow, while the opposite direction is noticed in the temperature field.

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Dual nature solution of water functionalized copper nanoparticles along a permeable shrinking cylinder: FDM approach

Cited by 68 publications

References 27 publications

Dual Stratified Nanofluid Flow Past a Permeable Shrinking/Stretching Sheet Using a Non-Fourier Energy Model

Dual Stratified Nanofluid Flow Past a Permeable Shrinking/Stretching Sheet Using a Non-Fourier Energy Model

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

Numerical Simulation of Mixed Convection Squeezing Flow of a Hybrid Nanofluid Containing Magnetized Ferroparticles in 50%:50% of Ethylene Glycol–Water Mixture Base Fluids Between Two Disks With the Presence of a Non-linear Thermal Radiation Heat Flux

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