Boundary layer flow of Oldroyd-B fluid by exponentially stretching sheet

doi:10.1007/s10483-016-2072-8

摘要/Abstract

摘要：

The present paper investigates the steady flow of an Oldroyd-B fluid. The fluid flow is induced by an exponentially stretched surface. Suitable transformations reduce a system of nonlinear partial differential equations to a system of ordinary differential equations. Convergence of series solution is discussed explicitly by a homotopy analysis method (HAM). Velocity, temperature and heat transfer rates are examined for different involved parameters through graphs. It is revealed that for a larger retardation time constant, the velocity is enhanced and the temperature is lowered. It is noted that relaxation time constant and the Prandtl number enhance the heat transfer rate.

关键词: homotopy analysis method (HAM), exponentially stretching sheet, Oldroyd-B fluid

Abstract:

Key words: homotopy analysis method (HAM), Oldroyd-B fluid, exponentially stretching sheet

中图分类号:

T. HAYAT, M. IMTIAZ, A. ALSAEDI. Boundary layer flow of Oldroyd-B fluid by exponentially stretching sheet[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(5): 573-582.

参考文献

[1] Hayat, T., Khan, M., and Ayub, M. Exact solutions of flow problems of an Oldroyd-B fluid. Applied Mathematics and Computation, 151, 105–119 (2004)
[2] Vieru, D., Fetecau, C., and Fetecau, C. Flow of a generalized Oldroyd-B fluid due to a constantly accelerating plate. Applied Mathematics and Computation, 201, 834–842 (2008)
[3] Qi, H. and Jin, H. Unsteady helical flows of a generalized Oldroyd-B fluid with fractional derivative. Nonlinear Analysis: Real World Applications, 10(5), 2700–2708 (2009)
[4] Fetecau, C., Akhtar, W., Imran, M. A., and Vieru, D. On the oscillating motion of an Oldroyd-B fluid between two infinite circular cylinders. Computers and Mathematics with Applications, 59, 2836–2845 (2010)
[5] Fetecau, C., Hayat, T., Zierep, J., and Sajid, M. Energetic balance for the Rayleigh-Stokes problem of an Oldroyd-B fluid. Nonlinear Analysis: Real World Applications, 12(1), 1–13 (2011)
[6] Jamil, M., Fetecau, C., and Imran, M. Unsteady helical flows of Oldroyd-B fluids. Communications in Nonlinear Science and Numerical Simulation, 16(3), 1378–1386 (2011)
[7] Zheng, L., Liu, Y., and Zhang, X. Exact solutions for MHD flow of generalized Oldroyd-B fluid due to an infinite accelerating plate. Mathematical and Computer Modelling, 54, 780–788 (2011)
[8] Zheng, L., Liu, Y., and Zhang, X. Slip effects on MHD flow of a generalized Oldroyd-B fluid with fractional derivative. Nonlinear Analysis: Real World Applications, 13, 513–523 (2012)
[9] Hayat, T., Zaib, S., Asghar, S., and Hendi, A. A. Exact solutions in generalized Oldroyd- B fluid. Applied Mathematics and Mechanics (English Edition), 33(4), 411–426 (2012) DOI 10.1007/s10483-012-1560-7
[10] Niu, J., Shi, Z. H., and Tan, W. C. The viscoelastic effects on thermal convection of an Oldroyd-B fluid in open-top porous media. Journal of Hydrodynamics, 25, 639–642 (2013)
[11] Hayat, T., Shehzad, S. A., Alsaedi, A., and Alhothuali, M. S. Three-dimensional flow of Oldroyd- B fluid over surface with convective boundary conditions. Applied Mathematics and Mechanics (English Edition), 34(4), 489–500 (2013) DOI 10.1007/s10483-013-1685-9
[12] Shehzad, S. A., Alsaedi, A., Hayat, T., and Alhothuali, M. S. Thermophoresis particle deposition in mixed convection three-dimensional radiative flow of an Oldroyd-B fluid. Journal of the Taiwan Institute of Chemical Engineers, 45(3), 787–794 (2014)
[13] Hayat, T., Hussain, T., Shehzad, S. A., and Alsaed, A. Flow of Oldroyd-B fluid with nanoparticles and thermal radiation. Applied Mathematics and Mechanics (English Edition), 36(1), 69–80 (2015) DOI 10.1007/s10483-015-1896-9
[14] Ramzan, M., Farooq, M., Alhothuali, M. S., Malaikah, H. M., Cui, W., and Haycot, T. Three dimensional flow of an Oldroyd-B fluid with Newtonian heating. International Journal of Numerical Methods for Heat and Fluid Flow, 25(1), 68–85 (2015)
[15] Hayat, T., Imtiaz, M., Alsaedi, A., and Almezal, S. On Cattaneo-Christov heat flux in MHD flow of Oldroyd-B fluid with homogeneous-heterogeneous reactions. Journal of Magnetism and Magnetic Materials, 401, 296–303 (2016)
[16] Crane, L. J. Flow past a stretching plate. Zeitschrift für Angewandte Mathematik Und Physik, 7, 21–28 (1961)
[17] Magyari, E. and Keller, B. Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface. Journal of Physics D: Applied Physics, 32, 577–585 (1999)
[18] Bhattacharyya, K. and Vajravelu, K. Stagnation-point flow and heat transfer over an exponentially shrinking sheet. Communications in Nonlinear Science and Numerical Simulation, 17, 2728–2734 (2012)
[19] Mukhopadhyay, S. MHD boundary layer flow and heat transfer over an exponentially stretching sheet embedded in a thermally stratified medium. Alexandria Engineering Journal, 52, 259–265 (2013)
[20] Pramanik, S. Casson fluid flow and heat transfer past an exponentially porous stretching surface in presence of thermal radiation. Ain Shams Engineering Journal, 5, 205–212 (2014)
[21] Hayat, T., Imtiaz, M., Alsaedi, A., and Mansoor, R. MHD flow of nanofluids over an exponentially stretching sheet in a porous medium with convective boundary conditions. Chinese Physics B, 23, 054701 (2014)
[22] Rahman, M. M., Rosca, A. V., and Pop, I. Boundary layer flow of a nanofluid past a permeable exponentially shrinking/stretching surface with second order slip using Buongiorno's model. International Journal of Heat and Mass Transfer, 77, 1133–1143 (2014)
[23] Nagalakshmi, C., Nagendramma, V., Sreelakshmi, K., and Sarojamma, G. Effects of Hall currents on the boundary layer flow induced by an exponentially stretching surface. Procedia Engineering, 127, 440–446 (2015)
[24] Khan, J. A., Mustafa, M., Hayat, T., and Alsaedi, A. Numerical study of Cattaneo-Christov heat flux model for viscoelastic flow due to an exponentially stretching surface, PLoS One, 10(9), e0137363 (2015)
[25] Mustafa, M., Mushtaq, A., Hayat, T., and Alsaedi, A. Radiation effects in three-dimensional flow over a bi-directional exponentially stretching sheet. Journal of the Taiwan Institute of Chemical Engineers, 47, 43–49 (2015)
[26] Turkyilmazoglu, M. Solution of the Thomas-Fermi equation with a convergent approach. Communications in Nonlinear Science and Numerical Simulation, 17, 4097–4103 (2012)
[27] Hatami, M., Nouri, R., and Ganji, D. D. Forced convection analysis for MHD Al2O3-water nanofluid flow over a horizontal plate. Journal of Molecular Liquids, 187, 294–301 (2013)
[28] Rashidi, M. M., Ali, M., Freidoonimehr, N., Rostami, B., and Hossian, A. Mixed convection heat transfer for viscoelastic fluid flow over a porous wedge with thermal radiation. Advances in Mechanical Engineering, 204, 735939 (2014)
[29] Abbasbandy, S., Yurusoy, M., and Gulluce, H. Analytical solutions of non-linear equations of power-law fluids of second grade over an infinite porous plate. Mathematical and Computational Applications, 19, 124–133 (2014)
[30] Abolbashari, M. H., Freidoonimehr, N., Nazari, F., and Rashidi, M. M. Entropy analysis for an unsteady MHD flow past a stretching permeable surface in nanofluid. Powder Technology, 267, 256–267 (2014)
[31] Xu, H. and Pop, I. Mixed convection flow of a nanofluid over a stretching surface with uniform free stream in the presence of both nanoparticles and gyrotactic microorganisms. International Journal of Heat and Mass Transfer, 75, 610–623 (2014)
[32] Hayat, T., Imtiaz, M., and Alsaedi, A. Partial slip effects in flow over nonlinear stretching surface. Applied Mathematics and Mechanics (English Edition), 36, 1513–1526 (2015) DOI 10.1007/s10483-015-1999-7
[33] Hayat, T., Shafiq, A., Nawaz, M., and Alsaedi, A. MHD axisymmetric flow of third grade fluid between porous disks with heat transfer. Applied Mathematics and Mechanics (English Edition), 33(6), 749–764 (2012) DOI 10.1007/s10483-012-1584-9
[34] Sui, J., Zheng, L., Zhang, X., and Chen, G. Mixed convection heat transfer in power law fluids over a moving conveyor along an inclined plate. International Journal of Heat and Mass Transfer, 85, 1023–1033 (2015)
[35] Farooq, U., Zhao, Y. L., Hayat, T., Alsaedi, A., and Liao, S. J. Application of the HAM-based mathematica package BVPh 2.0 on MHD Falkner-Skan flow of nanofluid. Computers and Fluids, 111, 69–75 (2015)