Stability analysis on the flow and heat transfer of nanofluid past a stretching/shrinking cylinder with suction effect

Bakar, Nor Ashikin Abu; Bachok, Norfifah; Arifin, Norihan Md; Pop, Ioan

doi:10.1016/j.rinp.2018.04.056

Cited by 45 publications

(31 citation statements)

References 34 publications

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“…As suction enhances, the velocity increases for first solution and decreases for second solution while S tends to deteriorate the temperature for both solutions. This result is parallel with results published by Bakar et al (2018). The fluid suction may assist the heated fluid towards the surface, boost the thermal boundary layer thickness and subsequently, reduce the fluid temperature.…”

Section: Numerical Proceduressupporting

confidence: 90%

“…In addition, the existence of dual solutions is related to the imposition of wall mass suction. Enough value of suction parameter, such as S > 2 will induce two solutions (Bakar et al 2018;Fang et al 2010;Miklavčič & Wang 2006). A critical/separating value is characterized as a meet point of both first and second solutions where a distinctive or unique solution was obtained at λ = λ c It is apparent that Cu-Al 2 O 3 /water hybrid nanofluid with ϕ 2 = 0.09 has larger value of │λ c │ which can delay the boundary layer separation process.…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…Among the earlier studies on mathematical formulation of stability analysis were examined by Harris et al (2009) Merkin (1986, Roşca and Pop (2013), and Weidman et al (2006). Many recent works also discussed the existence of dual solutions and emphasis on stability analysis (Bakar et al 2018;Dzulkifli et al 2018;Hamid & Nazar 2016;Jamaludin et al 2018;Kamal et al 2019;Naganthran et al 2018;Soid et al 2018). All the reported literatures implemented the bvp4c solver in the MATLAB software to examine the paired and stability solutions.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Numerical Proceduressupporting

confidence: 90%

Section: Numerical Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Khashi’ie¹,

Arifin²,

Pop³

et al. 2020

JSM

Self Cite

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“…Rosca and Pop [4], and Weidman et al [10] have shown that the lower branch solutions are unstable (not physically realizable), while the upper branch solutions are stable (physically realizable). Because of the interesting findings mentioned previously, many works on stability analysis have been performed in order to prove the findings which can be found in [28][29][30][31]. Firstly, we consider the eqs.…”

Section: Stability Solutionsmentioning

confidence: 98%

Dual solutions on boundary-layer flow over a moving surface in a flowing nanofluid with second-order slip

et al. 2020

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The steady boundary-layer flow of a nanofluid past a moving semi-infinite flat plate in a uniform free stream in the presence of second order slip is studied using a second order slip flow model. The governing PDE are transformed into non-linear ODE by using appropriate similarity transformations, which are then solved numerically using bvp4c solver for different values of selected parameters. We found that the solutions existed for dual in a certain range of velocity ratio parameter. Therefore, a stability analysis has been analyzed to show which solutions are stable. The effects of velocity ratio parameter, Lewis number, Prandtl number, Brownian motion parameter, thermopherosis parameter, mass suction, first order slip parameter, and second order slip parameter on the skin friction coefficient, heat transfer coefficient, dimensionless velocity, temperature as well as nanoparticle volume fraction profiles are figured out graphically and discussed. These results reveals that the slip parameters expand the range of the solutions obtained. The increment of slip parameters lead to decrease the skin friction coefficient while increase the heat transfer coefficient. In addition, the value of Lewis nmber, Prandtl number, Brownian motion parameter, and thermopherosis parameter are significantly affected the heat transfer coefficient. Lastly, the first solution is stable and physically relevant, while the second solution is not.

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“…In addition, research works on the zero nanoparticles flux condition were also considered by Rehman et al [20], Rahman et al [21], Uddin et al [22], ur Rahman et al [23] and Jusoh et al [24]. Furthermore, studies on the boundary layer problem utilizing Buongiorno's model of nanofluid were also conducted by these researchers [25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

A Stability Analysis for Magnetohydrodynamics Stagnation Point Flow with Zero Nanoparticles Flux Condition and Anisotropic Slip

et al. 2019

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The numerical study of nanofluid stagnation point flow coupled with heat and mass transfer on a moving sheet with bi-directional slip velocities is emphasized. A magnetic field is considered normal to the moving sheet. Buongiorno’s model is utilized to assimilate the mixed effects of thermophoresis and Brownian motion due to the nanoparticles. Zero nanoparticles’ flux condition at the surface is employed, which indicates that the nanoparticles’ fraction are passively controlled. This condition makes the model more practical for certain engineering applications. The continuity, momentum, energy and concentration equations are transformed into a set of nonlinear ordinary (similarity) differential equations. Using bvp4c code in MATLAB software, the similarity solutions are graphically demonstrated for considerable parameters such as thermophoresis, Brownian motion and slips on the velocity, nanoparticles volume fraction and temperature profiles. The rate of heat transfer is reduced with the intensification of the anisotropic slip (difference of two-directional slip velocities) and the thermophoresis parameter, while the opposite result is obtained for the mass transfer rate. The study also revealed the existence of non-unique solutions on all the profiles, but, surprisingly, dual solutions exist boundlessly for any positive value of the control parameters. A stability analysis is implemented to assert the reliability and acceptability of the first solution as the physical solution.

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Stability analysis on the flow and heat transfer of nanofluid past a stretching/shrinking cylinder with suction effect

Cited by 45 publications

References 34 publications

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

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

Dual solutions on boundary-layer flow over a moving surface in a flowing nanofluid with second-order slip

A Stability Analysis for Magnetohydrodynamics Stagnation Point Flow with Zero Nanoparticles Flux Condition and Anisotropic Slip

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