STABILITY ANALYSIS OF A ROTATING FLOW TOWARD A SHRINKING PERMEABLE SURFACE IN NANOFLUID
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Published:
Feb 28, 2019
Keywords:
Dual solutions Nanofluid rotating flow shrinking sheet stability analysis
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Abstract
The rotating boundary layer flow over a shrinking permeable surface in nanofluid is numerically studied. The similarity transformation is used to transform the partial differential equations into nonlinear ordinary differential equations. Later, these equations are determined by using bvp4c package in the MATLAB software. The numerical results reveal that there is more than one solution called dual solutions obtained for a certain range of the rotation and suction parameters. A stability analysis is performed to determine which solution is stable by depending on the sign of the eigenvalues. Based on this analysis, the results indicate that the upper branch solution (first solution) is linearly stable, while the lower branch solution (second solution) is linearly unstable.
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How to Cite
Salleh, S. N. A., Bachok, N., & Md Arifin, N. (2019). STABILITY ANALYSIS OF A ROTATING FLOW TOWARD A SHRINKING PERMEABLE SURFACE IN NANOFLUID. Malaysian Journal of Science, 38(Sp 1), 19–32. https://doi.org/10.22452/mjs.sp2019no1.2
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ICMSS2018 (Published)
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References
Bachok, N., Ishak, A., & Pop, I. (2010). Boundary-layer flow of nanofluids over a moving surface in a flowing fluid. International Journal of Thermal Sciences, 49:1663-1668.
Bachok, N., Ishak, A., & Pop, I. (2012). Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet. International Journal of Heat and Mass Transfer, 55:2102-2109.
Choi, S. U. S. (1995). Enhancing thermal conductivity of fluids with nanoparticles. ASME Publication, 231:99-105.
Das, K., Duari, P. R., Pop, I., & Kundu, P. K. (2014). Nanofluid flow over an unsteady stretching surface in presence of thermal radiation. Alexandria Engineering Journal, 53:737-745.
Hafidzuddin, E. H., Nazar, R., Arifin, N. M., & Pop, I. (2015). Stability analysis of unsteady three-dimensional viscous flow over a permeable stretching/shrinking surface. Journal of Quality Measurement and Analysis, 11:19-31.
Harris, S. D., Ingham, D. B., & Pop, I. (2009). Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transport Porous Media, 77: 267-285.
Mahapatra, T. R. & Nandy, S. K. (2011). Stability analysis of dual solutions in stagnation-point flow and heat transfer over a power-law shrinking surface. International Journal of Nonlinear Sciences, 12: 86-94.
Merkin, J. H. (1985). On dual solutions occurring in mixed convection in a porous medium. Journal of Engineering Mathematics, 20:171-179.
Nadeem, S., Rehman, A., & Mehmood, R. (2014). Boundary layer flow of rotating two phase nanofluid over a stretching surface. Heat Transfer Asian Research, 45:285-2
Najib, N., Bachok, N., & Ari_n, N. M. (2016). Stability of dual solutions in
boundary layer flow and heat transfer over an exponentially shrinking cylinder. Indian Journal of Science and Technology, 9:1-6.
Naramgari, S. & S ulochana, C. (2016). MHD flow over a permeable stretching/shrinking sheet of a nanofluid with suction/injection. Alexandria Engineering Journal, 55:819-827
Othman, N. A., Yacob, N. A., Bachok, N., Ishak, A., & Pop, I. (2017). Mixed convection boundary-layer stagnation point flow past a vertical stretching/ shrinking surface in a nanofluid. Applied Thermal Engineering, 115:1412-1417.
Oztop, H. F. & Abu-Nada, E. (2008). Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International Journal of Heat Fluid Flow, 29:1326-1336.
Reddy, C. R., Murthy, P. V. S. N., Chamkha, A. J., & Rashad, A. M. (2013). Soret effect on mixed convection flow in a nanofluid under convective boundary condition. International Journal of Heat and Mass Transfer, 64:384-392.
Rosca, N. C. & Pop, I. (2014). Unsteady boundary layer flow of a nanofluid past a moving surface in an external uniform free stream using Buongiorno’s model. Computers and Fluids, 95:49-55.
Sharma, R., Ishak, A., & Pop, I. (2014). Stability analysis of magnetohydrodynamic stagnation-point flow toward a stretching/shrinking sheet. Computers and Fluids, 102:94-98.
Weidman, P. D., Kubitschek, D. G., & Davis, A. M. J. (2006). The effect of transpiration on self-similar boundary layer flow over moving surfaces. International Journal of Engineering Sciences, 44:730-737.
Yasin, M. H. M., Ishak, A., & Pop, I. (2017). Boundary layer flow and heat transfer past a permeable shrinking surface embedded in a porous medium with a second-order slip: A stability analysis. Applied Thermal Engineering, 115:1407-1]
Bachok, N., Ishak, A., & Pop, I. (2012). Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet. International Journal of Heat and Mass Transfer, 55:2102-2109.
Choi, S. U. S. (1995). Enhancing thermal conductivity of fluids with nanoparticles. ASME Publication, 231:99-105.
Das, K., Duari, P. R., Pop, I., & Kundu, P. K. (2014). Nanofluid flow over an unsteady stretching surface in presence of thermal radiation. Alexandria Engineering Journal, 53:737-745.
Hafidzuddin, E. H., Nazar, R., Arifin, N. M., & Pop, I. (2015). Stability analysis of unsteady three-dimensional viscous flow over a permeable stretching/shrinking surface. Journal of Quality Measurement and Analysis, 11:19-31.
Harris, S. D., Ingham, D. B., & Pop, I. (2009). Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transport Porous Media, 77: 267-285.
Mahapatra, T. R. & Nandy, S. K. (2011). Stability analysis of dual solutions in stagnation-point flow and heat transfer over a power-law shrinking surface. International Journal of Nonlinear Sciences, 12: 86-94.
Merkin, J. H. (1985). On dual solutions occurring in mixed convection in a porous medium. Journal of Engineering Mathematics, 20:171-179.
Nadeem, S., Rehman, A., & Mehmood, R. (2014). Boundary layer flow of rotating two phase nanofluid over a stretching surface. Heat Transfer Asian Research, 45:285-2
Najib, N., Bachok, N., & Ari_n, N. M. (2016). Stability of dual solutions in
boundary layer flow and heat transfer over an exponentially shrinking cylinder. Indian Journal of Science and Technology, 9:1-6.
Naramgari, S. & S ulochana, C. (2016). MHD flow over a permeable stretching/shrinking sheet of a nanofluid with suction/injection. Alexandria Engineering Journal, 55:819-827
Othman, N. A., Yacob, N. A., Bachok, N., Ishak, A., & Pop, I. (2017). Mixed convection boundary-layer stagnation point flow past a vertical stretching/ shrinking surface in a nanofluid. Applied Thermal Engineering, 115:1412-1417.
Oztop, H. F. & Abu-Nada, E. (2008). Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International Journal of Heat Fluid Flow, 29:1326-1336.
Reddy, C. R., Murthy, P. V. S. N., Chamkha, A. J., & Rashad, A. M. (2013). Soret effect on mixed convection flow in a nanofluid under convective boundary condition. International Journal of Heat and Mass Transfer, 64:384-392.
Rosca, N. C. & Pop, I. (2014). Unsteady boundary layer flow of a nanofluid past a moving surface in an external uniform free stream using Buongiorno’s model. Computers and Fluids, 95:49-55.
Sharma, R., Ishak, A., & Pop, I. (2014). Stability analysis of magnetohydrodynamic stagnation-point flow toward a stretching/shrinking sheet. Computers and Fluids, 102:94-98.
Weidman, P. D., Kubitschek, D. G., & Davis, A. M. J. (2006). The effect of transpiration on self-similar boundary layer flow over moving surfaces. International Journal of Engineering Sciences, 44:730-737.
Yasin, M. H. M., Ishak, A., & Pop, I. (2017). Boundary layer flow and heat transfer past a permeable shrinking surface embedded in a porous medium with a second-order slip: A stability analysis. Applied Thermal Engineering, 115:1407-1]