Stability analysis on the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet with heat source effect

Fatinnabila Kamal, Khairy Zaimi, Anuar Mohd Ishak, Ioan Pop

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Purpose: This paper aims to analyze the behavior of the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet in the presence of the viscous dissipation and heat source effects. Design/methodology/approach: The governing partial differential equations are converted into ordinary differential equations by similarity transformations before being solved numerically using the bvp4c function built in Matlab software. Effects of suction/injection parameter and heat source parameter on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented in the forms of tables and graphs. A temporal stability analysis will be conducted to verify which solution is stable for the dual solutions exist for the shrinking case. Findings: The analysis indicates that the skin friction coefficient and the local Nusselt number as well as the velocity and temperature were influenced by suction/injection parameter. In contrast, only the local Nusselt number, which represents heat transfer rate at the surface, was affected by heat source effect. Further, numerical results showed that dual solutions were found to exist for the certain range of shrinking case. Then, the stability analysis is performed, and it is confirmed that the first solution is linearly stable and has real physical implication, while the second solution is not. Practical implications: In practice, the study of the steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet in the presence of heat source effect is very crucial and useful. The problems involving fluid flow over stretching or shrinking surfaces can be found in many industrial manufacturing processes such as hot rolling, paper production and spinning of fibers. Owing to the numerous applications, the study of stretching/shrinking sheet was subsequently extended by many authors to explore various aspects of skin friction coefficient and heat transfer in a fluid. Besides that, the study of suction/injection on the boundary layer flow also has important applications in the field of aerodynamics and space science. Originality/value: Although many studies on viscous fluid has been investigated, there is still limited discoveries found on the heat source and suction/injection effects. Indeed, this paper managed to obtain the second (dual) solutions and stability analysis is performed. The authors believe that all the results are original and have not been published elsewhere.

Original languageEnglish
Pages (from-to)2650-2663
Number of pages14
JournalInternational Journal of Numerical Methods for Heat and Fluid Flow
Volume28
Issue number11
DOIs
Publication statusPublished - 5 Nov 2018

Fingerprint

Stagnation Point Flow
Heat Source
Shrinking
Stretching
Heat Transfer
Stability Analysis
Suction
Heat transfer
Dual Solutions
Skin Friction
Skin friction
Injection
Nusselt number
Friction Coefficient
Hot Rolling
Viscous Dissipation
Fluids
Heat Transfer Coefficient
Boundary layer flow
Similarity Transformation

Keywords

  • Heat source
  • Heat transfer
  • Stability analysis
  • Stagnation point flow
  • Stretching/shrinking sheet
  • Suction/injection

ASJC Scopus subject areas

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

Cite this

Stability analysis on the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet with heat source effect. / Kamal, Fatinnabila; Zaimi, Khairy; Mohd Ishak, Anuar; Pop, Ioan.

In: International Journal of Numerical Methods for Heat and Fluid Flow, Vol. 28, No. 11, 05.11.2018, p. 2650-2663.

Research output: Contribution to journalArticle

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