Dual Solutions in Magnetohydrodynamic Stagnation-Point Flow and Heat Transfer Over a Shrinking Surface With Partial Slip

Mahapatra, Tapas Ray; Nandy, Samir Kumar; Pop, Ioan

doi:10.1115/1.4024592

Cited by 20 publications

(15 citation statements)

References 36 publications

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“…The idea and procedure to determine the stability of the solutions obtained has been triggered by Merkin (1985). This analysis later was continued by Weidman et al (2006), Harris et al (2009), Mahapatra andNandy (2011), Sharma et al (2014), Hafidzuddin et al (2015), Najib et al (2016) and Yasin et al (2017). They concluded that the upper branch solution is always stable and physically realizable, while the lower branch solution is not.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of a Rotating Flow Toward a Shrinking Permeable Surface in Nanofluid

Salleh

Bachok

Arifin

2019

MJS

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The rotating boundary layer flow over a shrinking permeable surface in nanofluid is numerically studied. The similarity transformation is used to transform the partial differential equations into nonlinear ordinary differential equations. Later, these equations are determined by using bvp4c package in the MATLAB software. The numerical results reveal that there is more than one solution called dual solutions obtained for a certain range of the rotation and suction parameters. A stability analysis is performed to determine which solution is stable by depending on the sign of the eigenvalues. Based on this analysis, the results indicate that the upper branch solution (first solution) is linearly stable, while the lower branch solution (second solution) is linearly unstable. ABSTRAKAliran putaran lapisan sempadan terhadap permukaan mengecut yang telap di dalam nanobendalir dikaji. Penjelmaan keserupaan digunakan untuk menjelmakan persamaan perbezaan separa kepada persamaan perbezaan biasa tak linear. Kemudian, persamaan ini diselesaikan dengan menggunakan pakej bvp4c dalam perisian MATLAB. Keputusan menunjukkan bahawa terdapat lebih daripada satu penyelesaian yang disebut penyelesaian dwi diperolehi untuk julat tertentu bagi parameter putaran dan sedutan. Analisis kestabilan dijalankan untuk menentukan penyelesaian mana yang stabil dengan bergantung kepada tanda nilai eigen. Berdasarkan analisis ini, keputusan menunjukkan bahawa penyelesaian cabang atas (penyelesaian pertama) adalah stabil, sementara penyelesaian cabang bawah (penyelesaian kedua) adalah tidak stabil.

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Section: Introductionmentioning

confidence: 99%

Stability Analysis of a Rotating Flow Toward a Shrinking Permeable Surface in Nanofluid

Salleh

Bachok

Arifin

2019

MJS

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“…Dual solutions are categorized as first solution (upper branch solution) and second solution (lower branch solution). Weidman et al [49], Weidman and Ali [50], Roşca and Pop [51], Mahapatra and Nandy [52], Nazar et al [53], and Rahman et al [28] have performed stability analysis to determine which solution is stable and physically realizable. They have established that the first solution is the stable solution and second one is unstable [28].…”

Section: Resultsmentioning

confidence: 99%

Dual Solutions of Non-Newtonian Casson Fluid Flow and Heat Transfer over an Exponentially Permeable Shrinking Sheet with Viscous Dissipation

Zaib

Bhattacharyya

Uddin

et al. 2016

Modelling and Simulation in Engineering

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The two-dimensional boundary layer flow of a non-Newtonian Casson fluid and heat transfer due to an exponentially permeable shrinking sheet with viscous dissipation is investigated. Using similarity transformations, the governing momentum and energy equations are transformed to self-similar nonlinear ODEs and then those are solved numerically by very efficient shooting method. The analysis explores many important aspects of flow and heat transfer of the aforesaid non-Newtonian fluid flow dynamics. For the steady flow of non-Newtonian Casson fluid, more amount of wall mass suction through the porous sheet is required in comparison to that of Newtonian fluid flow. Dual similarity solutions are obtained for velocity and temperature. The viscous dissipation effect has major impact on the heat transfer characteristic. In fact, heat absorption at the surface occurs and it increases due to viscous dissipation. For higher Prandtl number, the temperature inside the boundary layer reduces, but with larger Eckert number (viscous dissipation) it is enhanced.

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“…The obtained advantage manifests iteself most vividly in complicated cases. Thus, in [8], when examining the magnetohydrodynamic flows, using the similarity transformations, it was possible to reduce the Navier-Stokes equations to ordinary differential equations. Such a result is possible due to the representation, when rendering dimensionless, all terms of equations in the uniform form and obtaining the possibility of running a fractional analysis.…”

Section: A Simplified Methods For the Numerical Calculation Of Nonstatmentioning

confidence: 99%

“…Similar to the previos case, let us substitute (8) in (7), divide all terms of the equation by λ/δx. As a result, taking into account (1), we shall obtain…”

Section: Methods For Constructing the Discrete Analogmentioning

confidence: 99%

A simplified method for the numerical calculation of nonstationary heat transfer through a flat wall

Brunetkin

Maksymov

Lysiuk

2017

EEJET

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4process. But at the same time, its application is cumbersome and covers only particular cases. As a rule, they are confined by the description of the process of heating-cooling the bodies of simple shapes: infinite plate, cylinder, and sphere. Such solutions have been known for a long time, but up to now they have been applied only for a similar kind of processes. Only the object of application has changed in favor of contemporary equipment as, for example, in [3], where the problem on cooling a display is solved. Article [4] examines a process of cooling the plate with an internal heat source. The difference is that the examined plate is a multilayer one. A special feature of paper [5] is the application, instead of the frequently utilized Fourier expansion, the Trefftz functions. In this case, only the approximate solution is obtained. The problem of nonstationary heat transfer is of practical interest and it does not have the analytical solution.Numerical methods are more universal and can be used to solve any problems on heat transfer. From the above enumeration of simple shapes of bodies, a plate appears the most important one. It has two surfaces, which corresponds to the process of heat transfer. Furthermore, for the case of coaxial cylinders (a pipe) at the ratio between outer and inside diameters of d 2 /d 1 <2, heat transfer through the cylindrical wall with an error less than 4 % can be described using the model for a flat wall. Such a relationship of diameters corresponds to the majority of variants of tubular heat exchangers. Heat transfer is predetermined by taking account of the combined processes of heat exchange at the surfaces of a plate. These IntroductionThe use in energy equipment of fuel with variable composition [1, 2] instead of the certified constant formulation leads to an increase in the number of transient modes. A change in calorific fuel capacity, amount of products of combustion, their thermophysical properties predetermines the non-stationary processes of heating-cooling the elements of power equipment design, as well as nonstationary processes of heat transfer through the heat exchange surfaces. As a consequence, in the processes of energy conversion a more important role is played by its variable accumulation -release in all equipment components in contact with the combustion products. The accumulation of energy (heating -cooling) affects inertness in the processes of heat transfer and, therefore, manageability of the process of energy transformations. In turn, the magnitude of energy accumulation is determined by temperature of the elements of design. Thus, determining the non-stationary temperature and, as a result, the nonstationary magnitude of energy accumulation, is an important element in solving the problem on optimal control of power equipment under conditions of using a non-certified fuel of variable composition. Literature review and problem statementAnalytical solution is a reliable and universal means to calculate parameters of the nonstationary heat exchange O ....

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Dual Solutions in Magnetohydrodynamic Stagnation-Point Flow and Heat Transfer Over a Shrinking Surface With Partial Slip

Cited by 20 publications

References 36 publications

Stability Analysis of a Rotating Flow Toward a Shrinking Permeable Surface in Nanofluid

Stability Analysis of a Rotating Flow Toward a Shrinking Permeable Surface in Nanofluid

Dual Solutions of Non-Newtonian Casson Fluid Flow and Heat Transfer over an Exponentially Permeable Shrinking Sheet with Viscous Dissipation

A simplified method for the numerical calculation of nonstationary heat transfer through a flat wall

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