Stability analysis of stagnation point flow in nanofluid over stretching/shrinking sheet with slip effect using buongiorno's model

Najwa Najib; Norfifah Bachok; Norihan Md Arifin; Fadzilah Md Ali

doi:10.3934/naco.2019041

Article Contents

2019, Volume 9, Issue 4: 423-431. Doi: 10.3934/naco.2019041

This issue Previous Article Onset of Benard-Marangoni instabilities in a double diffusive binary fluid layer with temperature-dependent viscosity Next Article Numerical solutions of Volterra integro-differential equations using General Linear Method

Stability analysis of stagnation point flow in nanofluid over stretching/shrinking sheet with slip effect using buongiorno's model

1.
Institute for Mathematical Research, Universiti Putra Malaysia, 43400, Serdang, Selangor, Malaysia
2.
Department of Mathematics, Universiti Putra Malaysia, 43400, Serdang, Selangor, Malaysia

^* Corresponding author: najwamohdnajib@ymail.com
^* Corresponding author: najwamohdnajib@ymail.com

The reviewing process of the paper is handled by Gafurjan Ibragimov, Siti Hasana Sapar and Siti Nur Iqmal Ibrahim

Received: January 2018

Revised: September 2018

Published: November 2019

The first author is supported by Putra grant of Universiti Putra Malaysia.

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Abstract

The study on stagnation boundary layer flow in nanofluid over stretching/shrinking sheet with the effect of slip at the boundary was considered by applying the Buongiorno's model. The partial differential equations of the governing equations were transformed into ordinary differential equations by using appropriate similarity transformation in order to obtain the similarity equations. The equations then were substituted into bvp4c code in Matlab software to get the numerical results. The results of skin friction coefficient, heat transfer coefficient as well as mass transfer coefficient on the governing parameters such as slip parameter, Brownian motion parameter, and thermophoresis parameter are shown graphically. The presence of slip parameter is significantly affected the skin friction, heat and mass transfer coefficient. The smallest number of Brownian motion is sufficient to increase the heat transfer coefficient while largest number of thermophoresis parameter is required to increase mass transfer coefficient. The stability analysis results expressed that the first solution is stable and physically realizable whereas the second solution is not.

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Mathematics Subject Classification: 76D10.

Citation:

FullText(HTML)

Figure 1. Skin friction coefficient $ f''(0) $, heat transfer coefficient $ -\theta'(0) $ and mass transfer coefficient $ -\phi'(0) $ vs $ \varepsilon $ for different $ \sigma $

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Figure 2. Heat transfer coefficient $ -\theta'(0) $ and mass transfer coefficient $ -\phi'(0) $ vs $ \varepsilon $ for different $ Nb $

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Figure 3. Heat transfer coefficient $ -\theta'(0) $ and mass transfer coefficient $ -\phi'(0) $ vs $ \varepsilon $ for different $ Nt $

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Figure 4. Velocity profile $ f'(\eta) $, temperature profile $ \theta(\eta) $ and concentration profile $ \phi(\eta) $ for different $ \varepsilon $

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Table 1. Smallest eigenvalues $ \gamma $ for selected values of $ \varepsilon $ with different $ \sigma $

$ \sigma $	$ \varepsilon $	First solution	Second solution
0	-1.246	0.0622	-0.0614
	-1.24	0.2121	-0.2036
	-1.2	0.5780	-0.5172
0.2	-1.388	0.0802	-0.0791
	-1.38	0.2390	-0.2300
	-1.3	0.7707	-0.6783
0.4	-1.582	0.0719	-0.0712
	-1.58	0.1273	-0.1251
	-1.5	0.6936	-0.6301

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