The exact effects of radiation and joule heating on magnetohydrodynamic Marangoni convection over a flat surface

Khaled, S. M.

doi:10.2298/tsci151005050k

Cited by 23 publications

(15 citation statements)

References 22 publications

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“…which is the same result that was obtained by Khaled [8]. The mass transfer equation in a Jeffrey fluid in the presence of heat source/sink was given in Qasim [18] as:…”

Section: Magnetohydrodynamic Marangonisupporting

confidence: 76%

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Analytic Solution of a Class of Singular Second-Order Boundary Value Problems with Applications

et al. 2019

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Recently, it was observed that the concentration/heat transfer of pure/nano fluids are finally governed by singular second-order boundary value problems with exponential coefficients. These coefficients were transformed into polynomials and therefore the governing equations become singular in a new independent variable. Unfortunately, the published approximate solutions in the literature suffer from some weaknesses as showed by one of the present coauthors. Hence, the exact solution for such types of problems becomes a challenge. In this paper, a straightforward approach is presented to obtaining the exact solution for such class of singular second-order boundary value problems. The results are also applied to some selected problems within the literature. Accordingly, the published solutions are recovered as special cases of the present ones.

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“…which is the same result that was obtained by Khaled [8]. The mass transfer equation in a Jeffrey fluid in the presence of heat source/sink was given in Qasim [18] as:…”

Section: Magnetohydrodynamic Marangonisupporting

confidence: 76%

“…This is also the exact solution of Equations (45) and (46) which were verified by substitution. It may be useful to end this section by observing that the exact solution reported by Qasim [18] is given as:…”

Section: Magnetohydrodynamic Marangonimentioning

confidence: 99%

Analytic Solution of a Class of Singular Second-Order Boundary Value Problems with Applications

et al. 2019

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“…, which is the same obtained result in Ref. [21]. As shown in the previous subsection, the solution (4.8) converges if l 1 = (j + 1) ∀ j ∈ Z + .…”

Section: Exact Solution and Convergence Analysissupporting

confidence: 89%

Applicable Solution for a Class of Ordinary Differential Equations with Singularity

Ahamad

2020

ijaa

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Boundary value problems arise in many real applications such as nanofluids and other areas of applied sciences. The temperature/nanoparticles concentration are usually expressed as singular 2 ndorder ODEs. So, it is a challenge to obtain the exact solution of these problems due to the difficulty of the singularity encountered in the governing equations. By means of a suitable transformation, a direct approach is introduced to solve a general class of 2 nd-order ODEs. The efficiency of the obtained results is validated through selected problems in the literature. It is found that several existing solutions can be deduced as special cases of our generalized one. Moreover, the present results may be invested for similar future problems in fluid mechanics, especially nanofluids.

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“…Moreover, such approximate methods, sometimes, lead to inaccurate results as pointed out in Refs. [20][21][22][23][24]. Regarding, the authors [20] mentioned that there were great differences between their exact results and those approximately obtained in Ref.…”

Section: Introductionmentioning

confidence: 84%

Applications of a Generalized Singular Boundary Value Problem for the Exact Solutions of Some Temperature/Concentration Equations

Ebaid

Alharbi

2020

PSIJ

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In the field of fluid mechanics, the temperature distribution and the nanoparticles concentration are usually described by singular boundary value problems (SBVPs). Such SBVPs are also used to describe various models with applications in engineering and other areas. Generally, obtaining the analytic solutions of such kind of problems is a challenge due to the singularity involved in the governing equations. In this paper, a class of SBVPs is analyzed. The solution of this class is analyzed and investigated through developing several theorems and lemmas. In addition, the theoretical results are invested to construct several solutions for various models/problems in fluid mechanics in the literature. Moreover, the published results are recovered as special cases of our analysis.

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The exact effects of radiation and joule heating on magnetohydrodynamic Marangoni convection over a flat surface

Cited by 23 publications

References 22 publications

Analytic Solution of a Class of Singular Second-Order Boundary Value Problems with Applications

Analytic Solution of a Class of Singular Second-Order Boundary Value Problems with Applications

Applicable Solution for a Class of Ordinary Differential Equations with Singularity

Applications of a Generalized Singular Boundary Value Problem for the Exact Solutions of Some Temperature/Concentration Equations

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