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Open AccessArticle

Unsteady Stagnation-Point Flow and Heat Transfer Over a Permeable Exponential Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect: A Stability Analysis

1
Department of Mathematics, Faculty of Computer and Mathematics Sciences, Universiti Teknologi MARA Pahang, Bandar Pusat Jengka 26400, Pahang, Malaysia
2
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang 43400, Selangor, Malaysia
*
Author to whom correspondence should be addressed.
Appl. Sci. 2018, 8(11), 2172; https://doi.org/10.3390/app8112172
Received: 26 September 2018 / Revised: 5 October 2018 / Accepted: 8 October 2018 / Published: 6 November 2018
(This article belongs to the Special Issue Nanofluids and Their Applications)
A model of unsteady stagnation-point flow and heat transfer over a permeable exponential stretching/shrinking sheet with the presence of velocity slip is considered in this paper. The nanofluid model proposed by Tiwari and Das is applied where water with Prandtl number 6.2 has been chosen as the base fluid, while three different nanoparticles are taken into consideration, namely Copper, Alumina, and Titania. The ordinary differential equations are solved using boundary value problem with fourth order accuracy (bvp4c) program in Matlab to find the numerical solutions of the skin friction and heat transfer coefficients for different parameters such as stretching/shrinking, velocity slip, nanoparticle volume fraction, suction/injection, and also different nanoparticles, for which the obtained results (dual solutions) are presented graphically. The velocity and temperature profiles are presented to show that the far field boundary conditions are asymptotically fulfilled, and validate the findings of dual solutions as displayed in the variations of the skin friction and heat transfer coefficients. The last part is to perform the stability analysis to determine a stable and physically-realizable solution. View Full-Text
Keywords: stability analysis; stagnation-point flows; exponential stretching/shrinking sheet; nanofluid; velocity slip effect stability analysis; stagnation-point flows; exponential stretching/shrinking sheet; nanofluid; velocity slip effect
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MDPI and ACS Style

Dzulkifli, N.F.; Bachok, N.; Yacob, N.A.; Md Arifin, N.; Rosali, H. Unsteady Stagnation-Point Flow and Heat Transfer Over a Permeable Exponential Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect: A Stability Analysis. Appl. Sci. 2018, 8, 2172. https://doi.org/10.3390/app8112172

AMA Style

Dzulkifli NF, Bachok N, Yacob NA, Md Arifin N, Rosali H. Unsteady Stagnation-Point Flow and Heat Transfer Over a Permeable Exponential Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect: A Stability Analysis. Applied Sciences. 2018; 8(11):2172. https://doi.org/10.3390/app8112172

Chicago/Turabian Style

Dzulkifli, Nor F.; Bachok, Norfifah; Yacob, Nor A.; Md Arifin, Norihan; Rosali, Haliza. 2018. "Unsteady Stagnation-Point Flow and Heat Transfer Over a Permeable Exponential Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect: A Stability Analysis" Appl. Sci. 8, no. 11: 2172. https://doi.org/10.3390/app8112172

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