MHD stagnation point flow of Carreau fluid toward a permeable shrinking sheet: Dual solutions

Akbar, Noreen Sher; Nadeem, S.; Haq, Rizwan Ul; Ye, Shiwei

doi:10.1016/j.asej.2014.05.006

Cited by 116 publications

(62 citation statements)

References 17 publications

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“…Chiam [15] discussed the steady viscous flow near a stagnation point and found that near the plate no boundary is formed when the velocities of stagnation flow and stretching plate are equal in the viscous free stream. Also, the following authors studied the magnetohydrodynamic flows over a stretching sheet and channel, like the magnetohydrodynamic boundary layer flow of a Carreau fluid due to shrinking surface with suction/injection is considered by Akbar et al [16]. In this study the authors analyzed the dual solutions on boundary later flow and noted that the velocity profiles are depreciated by of power index parameter for both solutions.…”

Section: Introductionmentioning

confidence: 98%

Analysis of Arrhenius activation energy in magnetohydrodynamic Carreau fluid flow through improved theory of heat diffusion and binary chemical reaction

Kumar

Raju

et al. 2018

J. Phys. Commun.

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In this work, we addressed the characterization of stagnation-point Carreau fluid flow induced due to stretching of chemically reactive surface. The energy expression is incorporated with a new theory of heat diffusion named Cattaneo-Christov, which is an advanced form of Fourier's heat flux formula. The additional term of thermal relaxation time is arisen in Cattaneo-Christov model of heat diffusion. We considered modified Arrhenius energy function with chemical reaction effect. The theory of boundary layer is employed to govern the mathematical phenomenon. The ordinary differential system is obtained by the implementation of suitable similarity variables. The governing system of mathematical expressions is solved by using Runge-Kutta based MATLAB bvp4c package. The derived solutions are sketched for various values of physical constraints on quantities of interest. A comparative study is presented for validating the results. It is found that the larger value of the thermal relaxation parameter act as non-conductor. It also noted that the destructive binary reaction is favorable to enhance the species concentration.

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Section: Introductionmentioning

confidence: 98%

Analysis of Arrhenius activation energy in magnetohydrodynamic Carreau fluid flow through improved theory of heat diffusion and binary chemical reaction

Kumar

Raju

et al. 2018

J. Phys. Commun.

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“…Nazar (2016) and Akbar et al (2014), as shown in (0) f  for first solution. As noted by Naganthran and Nazar (2016), the first solution is stable and physically realizable, while the second solution is unstable.…”

Section: Resultsmentioning

confidence: 99%

Slip Effects on MHD Stagnation-Point Flow of Carreau Fluid Past a Permeable Shrinking Sheet

Arifin

Yusof

Ismail

2017

mijst

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“…Meanwhile, the first study on MHD flow of non-Newtonian fluid was done by Sarpkaya (1961). Later, Akbar et al (2014) studied the MHD stagnationpoint flow of Carreau fluid over a permeable linearly shrinking sheet. Dual solutions were obtained in this study.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of MHD Carreau Fluid Flow over a Permeable Shrinking Sheet with Thermal Radiation

Yahaya¹,

Arifin²,

Isa³

2019

JSM

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Dual solutions are discovered in the problem of magnetohydrodynamics (MHD) boundary layer flow of Carreau fluid over a permeable shrinking sheet with thermal radiation. Therefore, a stability analysis is carried out to identify the stable solution of this problem. For the stability analysis, the problem is considered to be unsteady with time derivative introduced into the governing equations. Next, time-dependent solutions are substituted into these equations to form linear eigenvalue equations. The smallest eigenvalue of these equations is then computed using the bvp4c solver in MATLAB. The results showed that the first solution is stable, while the second solution is unstable. The first solution is physically meaningful and realizable in practice, and thus significant to the problem. ABSTRAK Penyelesaian dual telah diperoleh dalam masalah aliran lapisan sempadan magnetohidrodinamik (MHD) bendalirCarreau terhadap permukaan telap mengecut dengan radiasi terma. Sehubungan dengan itu, analisis kestabilan dilakukan bagi mengenal pasti penyelesaian yang stabil dalam masalah ini. Bagi analisis kestabilan tersebut, masalah ini telah dipertimbangkan sebagai masalah yang tidak stabil dengan memperkenalkan terbitan masa ke dalam persamaan menakluk. Kemudian, penyelesaian bersandar masa digantikan ke dalam persamaan tersebut untuk menghasilkan persamaan nilai eigen linear. Nilai eigen terkecil bagi persamaan ini kemudiannya dihitung menggunakan solver bvp4c di MATLAB. Keputusannya menunjukkan bahawa penyelesaian pertama adalah stabil sementara penyelesaian kedua tidak stabil. Penyelesaian pertama adalah bermakna secara fizikal dan boleh direalisasikan dalam amalan sebenar. Oleh itu, penyelesaian pertama adalah penting bagi masalah ini.

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MHD stagnation point flow of Carreau fluid toward a permeable shrinking sheet: Dual solutions

Cited by 116 publications

References 17 publications

Analysis of Arrhenius activation energy in magnetohydrodynamic Carreau fluid flow through improved theory of heat diffusion and binary chemical reaction

Analysis of Arrhenius activation energy in magnetohydrodynamic Carreau fluid flow through improved theory of heat diffusion and binary chemical reaction

Slip Effects on MHD Stagnation-Point Flow of Carreau Fluid Past a Permeable Shrinking Sheet

Stability Analysis of MHD Carreau Fluid Flow over a Permeable Shrinking Sheet with Thermal Radiation

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