Stagnation Point Flow of a Micropolar Fluid over a Stretching/Shrinking Sheet with Second-Order Velocity Slip
Publication: Journal of Aerospace Engineering
Volume 29, Issue 5
Abstract
The steady stagnation point flow of a micropolar fluid over a stretching/shrinking sheet with second-order velocity slip is studied. Similarity equations are obtained using similarity transformation, which are then solved numerically using MATLAB routine boundary value problem solver (bvp4c) based on the finite-difference method. Numerical results show that dual solutions exist for a certain range of the shrinking parameter. The dual solutions for velocity and microrotation distribution with first-order, second-order velocity slip parameter and micropolar parameter are shown graphically. It is observed that the range of the stretching/shrinking parameter for which the solution exists increases with the increase of the first-order slip parameter and micropolar parameter, whereas it decreases with the increase of the second-order slip parameter. The linear stability analysis of the obtained results was performed to show that the first solution branch is linearly stable, whereas the other is always unstable.
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References
Abel, M. S., Siddheshwar, P. G., and Mahesha, N. (2011). “Numerical solution of the momentum and heat transfer equations for a hydromagnetic flow due to a stretching sheet of a non-uniform property micropolar liquid.” Appl. Math. Comput., 217(12), 5895–5909.
Ariman, T., Turk, M. A., and Sylvester, N. D. (1974). “Microcontinuum fluid mechanics—A review.” Int. J. Eng. Sci., 12(4), 273–293.
Bachok, N., Ishak, A., and Pop, I. (2010). “Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet.” Phys. Lett. A, 374(40), 4075–4079.
Bhargava, R., Kumar, L., and Takhar, H. S. (2003). “Finite element solution of mixed convection micropolar fluid driven by a porous stretching sheet.” Int. J. Eng. Sci., 41(18), 2161–2178.
Bhargava, R., and Rani, M. (1985). “Heat transfer in micropolar boundary layer flow near a stagnation point.” Int. J. Eng. Sci., 23(12), 1331–1335.
Bhargava, R., Sharma, S., Takhar, H. S., Beg, O. A., and Bhargava, P. (2007). “Numerical solutions for microplar transport phenomena over a nonlinear stretching sheet.” Nonlinear Anal. Modell. Control, 12(1), 45–63.
Bhattacharyya, K., Mukhopadhyay, S., and Layek, G. C. (2011). “Steady boundary layer slip flow and heat transfer over a flat porous plate embedded in a porous media.” J. Pet. Sci. Eng., 78(2), 304–309.
Das, K. (2012a). “Slip effects on heat and mass transfer in MHD micropolar fluid flow over an inclined plate with thermal radiation and chemical reaction.” Int. J. Numer. Methods Fluids, 70(1), 96–113.
Das, K. (2012b). “Slip flow and convective heat transfer of nanofluids over a permeable stretching surface.” Comput. Fluids, 64, 34–42.
Eringen, A. C. (1966). “Theory of micropolar fluids.” J. Math. Mech., 16(1), 1–16.
Fang, T., and Aziz, A. (2010). “Viscous flow with second-order slip velocity over a stretching sheet.” Z. Naturforschung—Sect. A, 65, 1087–1092.
Fang, T., Yao, S., Zhang, J., and Aziz, A. (2010). “Viscous flow over a shrinking sheet with a second order slip flow model.” Commun. Nonlinear Sci. Numer. Simul., 15(7), 1831–1842.
Fang, T., Zhang, J., and Yao, S. (2009). “Slip MHD viscous flow over a stretching sheet-an exact solution.” Commun. Nonlinear Sci. Numer. Simul., 14(11), 3731–3737.
Harris, S. D., Ingham, D. B., and Pop, I. (2009). “Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip.” Transp. Porous Med., 77(2), 267–285.
Ishak, A., Nazar, R., and Pop, I. (2008). “Mixed convection stagnation point flow of a micropolar fluid towards a stretching sheet.” Meccanica, 43(4), 411–418.
Kelson, N. A., and Desseaux, A. (2001). “Effect of surface condition on flow of micropolar fluid driven by a porous stretching sheet.” Int. J. Eng. Sci., 39(16), 1881–1897.
Lok, Y. Y., Phang, P., Amin, N., and Pop, I. (2003). “Unsteady boundary layer flow of a micropolar fluid near the forward stagnation point of a plane surface.” Int. J. Eng. Sci., 41(2), 173–186.
MATLAB [Computer software]. MathWorks, Natick, MA.
Merkin, J. H. (1985). “On dual solutions occurring in mixed convection in a porous medium.” J. Eng. Math., 20(2), 171–179.
Mishra, S. R., Pattnaik, P. K., and Dash, G. C. (2015). “Effect of heat source and double stratification on MHD free convection in a micropolar fluid.” Alexandria Eng. J., 54(3), 681–689.
Mohammadein, A. A., and Gorla, R. S. R. (2001). “Heat transfer in a micropolar fluid over a stretching sheet with viscous dissipation and internal heat generation.” Int. J. Numer. Methods Heat Fluid Flow, 11(1), 50–58.
Mohanty, B., Mishra, S. R., and Pattnaik, H. B. (2015). “Numerical investigation on heat and mass transfer effect of micropolar fluid over a stretching sheet through porous media.” Alexandria Eng. J., 54(2), 223–232.
Nandeppanavar, M. M., Vajravelu, K., Abel, M. S., and Siddalingappa, M. N. (2012). “Second order slip flow and heat transfer over a stretching sheet with non-linear Navier boundary condition.” Int. J. Therm. Sci., 58, 143–150.
Noghrehabadi, A., Pourrajab, R., and Ghalambaz, M. (2012). “Effect of partial slip boundary condition on the flow and heat transfer of nanofluids past stretching sheet prescribed constant wall temperature.” Int. J. Therm. Sci., 54, 253–261.
Rosali, H., Ishak, A., and Pop, I. (2012). “Micropolar fluid flow towards a stretching/shrinking sheet in a porous medium with suction.” Int. Commun. Heat Mass Transfer, 39(6), 826–829.
Sahoo, B., and Poncet, S. (2011). “Flow and heat transfer of a third grade fluid past an exponentially stretching sheet with partial slip boundary condition.” Int. J. Heat Mass Transfer, 54(23–24), 5010–5019.
Sajid, M., Ali, N., Abbas, Z., and Javed, T. (2010). “Stretching flows with general slip boundary condition.” Int. J. Mod. Phys. B, 24(30), 5939–5947.
Sharma, R. (2014). “Element free Galerkin modeling of radiative hydromagnetic micropolar flow saturated Darcy medium with heat transfer over a stretching sheet with Joule heating.” ASIA-Pac. J. Chem. Eng., 9(1), 50–62.
Sharma, R., Bhargava, R., and Singh, I. V. (2010). “Combined effect of magnetic field and heat absorption on unsteady free convection and heat transfer flow in a micropolar fluid past a semi-infinite moving plate with viscous dissipation using element free Galerkin method.” Appl. Math. Comput., 217(1), 308–321.
Sharma, R., Ishak, A., and Pop, I. (2013). “Partial slip flow and heat transfer over a stretching sheet in a nanofluid.” Math. Probl. Eng., 2013, 724547.
Shidlovskiy, V. P. (1967). Introduction to the dynamics of rarefied gases, Elsevier, New York.
Wang, C. Y. (2002). “Flow due to a stretching boundary with partial slip-an exact solution of the Navier-Stokes equations.” Chem. Eng. Sci., 57(17), 3745–3747.
Wang, C. Y. (2008). “Stagnation flow towards a shrinking sheet.” Int. J. Non-Linear Mech., 43(5), 377–382.
Wang, C. Y. (2009). “Analysis of viscous flow due to a stretching sheet with surface slip and suction.” Nonlinear Anal. Real World Appl., 10(1), 375–380.
Weidman, P. D., Kubitschek, D. G., and Davis, A. M. J. (2006). “The effect of transpiration on self-similar boundary layer flow over moving surface.” Int. J. Eng. Sci., 44(11–12), 730–737.
Wu, L. (2008). “A slip model for rarefied gas flows at arbitrary Knudsen number.” Appl. Phys. Lett., 93(25), 253103.
Yoshimura, A., and Prudhomme, R. K. (1988). “Wall slip corrections for Couette and parallel disc viscometers.” J. Rheol., 32(1), 53–67.
Zheng, L., Niu, J., Zhang, X., and Gao, Y. (2012). “MHD flow and heat transfer over a porous shrinking surface with velocity slip and temperature jump.” Math. Comput. Modell., 56(5–6), 133–144.
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Published In
Journal of Aerospace Engineering
Volume 29 • Issue 5 • September 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Mar 19, 2014
Accepted: Dec 16, 2015
Published online: Mar 17, 2016
Discussion open until: Aug 17, 2016
Published in print: Sep 1, 2016
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