The effect of vertical throughflow on the boundary layer flow of a nanofluid past a stretching/shrinking sheet

A revised model

Ioan Pop, Kohilavani Naganthran, Roslinda Mohd. Nazar, Anuar Mohd Ishak

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Purpose - The purpose of this paper is to study the effects of vertical throughflow on the boundary layer flow and heat transfer of a nanofluid driven by a permeable stretching/shrinking surface. Design/methodology/approach - Similarity transformation is used to convert the system of boundary layer equations into a system of ordinary differential equations. The system of governing similarity equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. The generated numerical results are presented graphically and discussed based on some governing parameters. Findings - It is found that dual solutions exist in both cases of stretching and shrinking sheet situations. Stability analysis is performed to determine which solution is stable and valid physically. Originality/value - Dual solutions are found for positive and negative values of the moving parameter. A stability analysis has also been performed to show that the first (upper branch) solutions are stable and physically realizable, while the second (lower branch) solutions are not stable and, therefore, not physically possible.

Original languageEnglish
Pages (from-to)1910-1927
Number of pages18
JournalInternational Journal of Numerical Methods for Heat and Fluid Flow
Volume27
Issue number9
DOIs
Publication statusPublished - 2017

Fingerprint

Nanofluid
Boundary layer flow
Boundary Layer Flow
Shrinking
Stretching
Dual Solutions
Vertical
Stability Analysis
Branch
Similarity Transformation
First order differential equation
System of Ordinary Differential Equations
Design Methodology
Convert
MATLAB
Heat Transfer
Boundary Layer
Ordinary differential equations
Model
Valid

Keywords

  • Boundary layer
  • Nanofluid
  • Stability analysis
  • Stretching/Shrinking surface
  • Throughflow

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics

Cite this

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title = "The effect of vertical throughflow on the boundary layer flow of a nanofluid past a stretching/shrinking sheet: A revised model",
abstract = "Purpose - The purpose of this paper is to study the effects of vertical throughflow on the boundary layer flow and heat transfer of a nanofluid driven by a permeable stretching/shrinking surface. Design/methodology/approach - Similarity transformation is used to convert the system of boundary layer equations into a system of ordinary differential equations. The system of governing similarity equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. The generated numerical results are presented graphically and discussed based on some governing parameters. Findings - It is found that dual solutions exist in both cases of stretching and shrinking sheet situations. Stability analysis is performed to determine which solution is stable and valid physically. Originality/value - Dual solutions are found for positive and negative values of the moving parameter. A stability analysis has also been performed to show that the first (upper branch) solutions are stable and physically realizable, while the second (lower branch) solutions are not stable and, therefore, not physically possible.",
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author = "Ioan Pop and Kohilavani Naganthran and {Mohd. Nazar}, Roslinda and {Mohd Ishak}, Anuar",
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T2 - A revised model

AU - Pop, Ioan

AU - Naganthran, Kohilavani

AU - Mohd. Nazar, Roslinda

AU - Mohd Ishak, Anuar

PY - 2017

Y1 - 2017

N2 - Purpose - The purpose of this paper is to study the effects of vertical throughflow on the boundary layer flow and heat transfer of a nanofluid driven by a permeable stretching/shrinking surface. Design/methodology/approach - Similarity transformation is used to convert the system of boundary layer equations into a system of ordinary differential equations. The system of governing similarity equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. The generated numerical results are presented graphically and discussed based on some governing parameters. Findings - It is found that dual solutions exist in both cases of stretching and shrinking sheet situations. Stability analysis is performed to determine which solution is stable and valid physically. Originality/value - Dual solutions are found for positive and negative values of the moving parameter. A stability analysis has also been performed to show that the first (upper branch) solutions are stable and physically realizable, while the second (lower branch) solutions are not stable and, therefore, not physically possible.

AB - Purpose - The purpose of this paper is to study the effects of vertical throughflow on the boundary layer flow and heat transfer of a nanofluid driven by a permeable stretching/shrinking surface. Design/methodology/approach - Similarity transformation is used to convert the system of boundary layer equations into a system of ordinary differential equations. The system of governing similarity equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. The generated numerical results are presented graphically and discussed based on some governing parameters. Findings - It is found that dual solutions exist in both cases of stretching and shrinking sheet situations. Stability analysis is performed to determine which solution is stable and valid physically. Originality/value - Dual solutions are found for positive and negative values of the moving parameter. A stability analysis has also been performed to show that the first (upper branch) solutions are stable and physically realizable, while the second (lower branch) solutions are not stable and, therefore, not physically possible.

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KW - Stability analysis

KW - Stretching/Shrinking surface

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