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Analysis of Flow of Nanofluid through a Porous Channel with Expanding or Contracting Walls using Chebychev Spectral Collocation Method | ||
| Journal of Computational Applied Mechanics | ||
| مقاله 8، دوره 48، شماره 2، اسفند 2017، صفحه 225-232 اصل مقاله (696.05 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jcamech.2017.240097.179 | ||
| نویسندگان | ||
| George Oguntala* ؛ Raed Abd-Alhameed؛ Zubair Oba Mustapha؛ Eya Nnabuike | ||
| School of Electrical Engineering and Computer Science, Faculty of Engineering and Informatics, University of Bradford, West Yorkshire, UK. | ||
| چکیده | ||
| In this work, we applied Chebychev spectral collocation method to analyze the unsteady two-dimensional flow of nanofluid in a porous channel through expanding or contracting walls with large injection or suction. The solutions are used to study the effects of various parameters on the flow of the nanofluid in the porous channel. From the analysis, It was established that increase in expansion ratio and Reynolds number decreases the axial velocity at the center of the channel during the expansion while the axial velocity increases near the surface of the channel during contraction. Moreover, it was also established that an increase in injection rate leads to a higher axial velocity near the center and the lower axial velocity near the wall. On the verification of the results, it is shown that the results obtained from Chebychev spectral collocation method are in good agreement when compared to the results obtained using other numerical methods. | ||
| کلیدواژهها | ||
| Nanofluid, Porous Channel؛ Expanding or Contracting walls, Chebychev Spectral Collocation method | ||
| مراجع | ||
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[1] Berman A. S., 1953, Laminar flow in channels with porous walls, Journal of Applied Physics, Vol. 24: 1232 - 1235.
[2] Terrill R. M., 1964, Laminar flow in a uniformly porous channel, The Aeronautical Quarterly, Vol. 15, 299 – 310.
[3] Terrill R. M., 1965, Laminar flow in a uniformly porous channel with large injection, Aeronautical Quarterly, Vol. 16, 323 - 332.
[4] Dauenhauer E. C., Majdalani, J., 2003, Exact self-similarity solution of the Navier-Stokes equations for a porous channel with orthogonally moving walls, Physics of Fluids, Vol. 15, No. 6, 1485–1495.
[5] Majdalani, J., 2001, The oscillatory channel flow with arbitrary wall injection, Zeitschrift fur Angewandte Mathematik und Physik, Vol. 52, No. 1, 33–61.
[6] Majdalani J., Roh, T-S., 2000, The oscillatory channel flow with large wall injection, Proceedings of the Royal Society of London. Series A, Vol. 456, No. 1999, 625–1657.
[7]Majdalani, J., van Moorhem, W. K., 1997, Multiple-scales solution to the acoustic boundary layer in solid rocket motors, Journal of Propulsion and Power, Vol. 13, No. 2, 186–193.
[8] Oxarango, L., Schmitz, P., Quintard, M., 2004, Laminar flow in channels with wall suction or injection: a new model to study multi-channel filtration systems, Chemical Engineering Science, Vol. 59, No.5, 1039–1051.
[9] Jankowski, T. A., Majdalani, J., 2006, Symmetric solutions for the oscillatory channel flow with arbitrary suction,” Journal of Sound and Vibration, Vol. 294, No. 4, pp. 880–893.
[10] Jankowski, A., Majdalani, J., 2002, Laminar flow in a porous channel with large wall suction and a weakly oscillatory pressure, Physics of Fluids, Vol. 14, No. 3, 1101–1110.
[11] Zhou, C., Majdalani, J., 2002, Improved mean-flow solution for slab rocket motors with regressing walls, Journal of Propulsion and Power, Vol. 18, No. 3, 703–711.
[12] Majdalani, J., Zhou, C., 2003, Moderate-to-large injection and suction driven channel flows with expanding or contracting walls, Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 83, No. 3,181–196.
[13]Robinson, W. A., 1976, The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls, J. Eng. Math. 23–40.
[14] Zaturska, M. B., Drazin, P. G., Banks, W. H., 1988, On the flow of a viscous fluid driven along a channel by suction at porous walls, Fluid Dynamics Research, Vol. 4, No. 3, 151–178.
[15] Si, X. H., Zheng, L. C., Zhang, X. X., Chao, Y., 2011, Existence of multiple solutions for the laminar flow in a porous channel with suction at both slowly expanding or contracting walls. Int. J. Miner. Metal. Mater. 11, 494-501.
[16] Si, X. H., Zheng, L. C., Zhang, X. X., Chao, Y., 2011, Multiple solutions for the laminar flow in a porous pipe with suction at slowly expanding or contracting wall. Applied. Math. Comput. 218, 3515-3521.
[17] Majdalani, J., Zhou, C., Dawson, C. A., 2011, Two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability, Journal of Biomechanics, Vol. 35, No. 10, 1399–1403.
[18] Dinarvand, S., Doosthoseini, A., Doosthoseini, E., Rashidi, M. M., 2008, Comparison of HAM and HPM methods for Berman’s model of two-dimensional viscous flow in porous channel with wall suction or injection, Advances in Theoretical and Applied Mechanics, Vol. 1, No. 7, 337–347.
[19] Xu, J., Lin, Z. L., Liao, S. J., Wu, J. Z., Majdalani, J., 2010, Homotopy based solutions of the Navier-Stokes equations for a porous channel with orthogonally moving walls, Physics of Fluids, Vol. 22, Issue 5, 10.1063/1.3392770.
[20] Dinarvand, S., Rashidi, M. M., 2010, A reliable treatment of a homotopy analysis method for two dimensional viscous flow in a rectangular domain bounded by two moving porous walls, Nonlinear Analysis: Real World Applications, Vol. 11, No. 3, 1502–1512.
[21] Oguntala, G. A., Sobamowo, M. G., 2016, Galerkin’s Method of Weighted Residual for a Convective Straight Fin with Temperature-dependent Conductivity and Internal Heat Generation. International Journal of Engineering and Technology, Vol. 6, No. 12, 432–442.
[22] Sobamowo, M. G., 2016, Thermal Analysis of longitudinal fin with Temperature-dependent properties and Internal Heat generation using Galerkin’s Method of weighted residual. Applied Thermal Engineering 99, 1316–1330.
[23] Gottlieb, D., Orszag, S.A., 1977, Numerical analysis of spectral methods: Theory and applications, in: Regional Conference Series in Applied Mathematics, Vol. 28, SIAM, Philadelphia, pp. 1 - 168.
[24] Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A., 1988, Spectral Methods in Fluid Dynamics, Springer-Verlag, New York.
[25] Peyret, R., 2002, Spectral Methods for Incompressible Viscous Flow, Springer Verlag, New York, 2002.
[26] F.B. Belgacem, M. Grundmann, Approximation of the wave and electromagnetic diffusion equations by spectral methods, SIAM Journal on Scientific Computing 20 (1), (1998), 13–32.
[27] Shan, X.W., Montgomery, D., Chen, H.D., 1991, Nonlinear magnetohydrodynamics by Galerkin-method computation, Physical Review A 44 (10), 6800–6818.
[28] Shan, X.W., 1994, Magnetohydrodynamic stabilization through rotation, Physical Review Letters 73 (12), 1624–1627.
[29] Wang, J.P., 2001, Fundamental problems in spectral methods and finite spectral method, Sinica Acta Aerodynamica 19 (2), 161–171.
[30] Elbarbary, E.M.E., El-kady, M., 2003, Chebyshev Finite difference approximation for the boundary value problems, Applied Mathematics and Computation 139, 513–523.
[31] Huang, Z.J., Zhu, Z.J., 2009, Chebyshev spectral collocation method for solution of Burgers’ equation and laminar natural convection in two-dimensional cavities, Bachelor Thesis, University of Science and Technology of China, Hefei, China.
[32] Eldabe, N.T., Ouaf, M.E.M., 2006, Chebyshev finite difference method for heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching surface with Ohmic heating and viscous dissipation, Applied Mathematics and Computation 177, 561–571.
[33] Khater, A.H., Temsah, R.S., Hassan, M.M., 2008, A Chebyshev spectral collocation method for solving Burgers'-type equations, Journal of Computational and Applied Mathematics, Vol. 222, Issue 2, 333–350.
[34] Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A., 1998, Spectral Methods in Fluid Dynamics, Springer, New York.
[35] Doha, E.H., Bhrawy, A.H., 2008, Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials, Applied Numerical Mathematics, Vol. 58, Issue 8, 1224–1244.
[36] Doha, E.H., Bhrawy, A.H., 2009, Jacobi spectral Galerkin method for the integrated forms of fourth-order elliptic differential equations, Numerical Methods for Partial Differential Equations, Wiley Online Library, Vol. 25, Issue, 712–739.
[37] Doha, E.H., Bhrawy, A.H., Hafez, R.M., 2011, A Jacobi–Jacobi dual-Petrov–Galerkin method for third- and fifth-order differential equations, Mathematical and Computer Modelling, Vol. 53, Issue 9 – 10, 1820–1832.
[38] Doha, E.H., Bhrawy, A.H., Ezzeldeen, S.S., 2011, Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations, Applied Mathematical Modelling, Vol. 35, Issue 12, 5662 – 5672.
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