MHD Stagnation Point Flow Towards a Heated Shrinking Surface Subject to Heat Generation/Absorption
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摘要: 分析了微极流体朝向加热伸展平面的磁流体动力学(MHD)驻点流动,考虑了粘性耗散和内部产热/吸热对流动的影响.讨论了指定表面温度(PST)和指定热通量(PHF)两种情况,采用同伦分析方法(HAM)求解边界层流动和能量方程.通过图表的显示,研究了感兴趣物理量的变化.注意到高伸展参数时解的存在与外加应用磁场密切相关.Abstract: The magnetohydrodynamic (MHD) stagnation point flow of micropolar fluid towards a heated shrinking surface was analyzed. The effects of viscous dissipation and internal heat generation/absorption were taken into account. Two explicit cases of prescribed surface temperature (PST) and prescribed heat flux (PHF) were discussed. The boundary layer flow and energy equations were solved by employing a homotopy analysis method (HAM). The quantities of physical interest were examined through the presentation of plots/tabulated values. It was noticed that existing of solution for high shrinking parameter was associated closely with the applied magnetic filed.
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Key words:
- stagnation point flow /
- micropolar fluid /
- shrinking sheet /
- convergence
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[1] Mahapatra T R, Gupta A S. Magnetohydrodynamics stagnation point flow towards a stretching sheet[J]. Acta Mechanica, 2001, 152(1/4): 191-196. [2] Nazar R, Amin N, Filip D, Pop I. Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet[J]. International Journal of Engineering Science, 2004, 42(11/12): 1241-1253. [3] Lok Y Y, Amin N, Pop I. Unsteady mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface[J]. International Journal of Thermal Sciences, 2006, 45(12): 1149-1157. [4] Yian L Y, Amin N, Pop I. Mixed convection flow near a non-orthogonal stagnation point towards a stretching vertical plate[J]. International Journal of Heat and Mass Transfer, 2007, 50(23/24): 4855-4863. [5] Wang C Y. Off-centered stagnation flow towards a rotating disc[J]. International Journal of Engineering Science, 2008, 46(4): 391-396. [6] Xu H, Liao S J, Pop I. Series solution of unsteady boundary layer flow of a micropolar fluid near the forward stagnation point of a plane surface[J]. Acta Mechanica, 2006, 184(14): 87-101. [7] Nadeem S, Hussain M, Naz M. MHD stagnation flow of a micropolar fluid through a porous medium[J]. Meccanica, 2010, 45(6) :869-880. [8] Kumari M, Nath G. Steady mixed convection stagnation-point flow of upper convected Maxwell fluids with magnetic field[J]. International Journal of Non-Linear Mechanics, 2009, 44(10): 1048-1055. [9] Hayat T,Abbas Z,Sajid M. MHD stagnation-point flow of an upper-convected Maxwell fluid over a stretching surface[J]. Chaos, Solitons & Fractals, 2009, 39(2): 840-848. [10] Labropulu F, Li D, Pop I. Non-orthogonal stagnation-point flow towards a stretching surface in a non-Newtonian fluid with heat transfer[J]. International Journal of Thermal Sciences, 2010, 49(6) :1042-1050. [11] Miklavic M, Wang C Y. Viscous flow due to a shrinking sheet[J]. Quarterly Applied Mathematics, 2006, 64(2): 283-290. [12] Fang T. Zhong Y. Viscous flow over a shrinking sheet with an arbitrary surface velocity[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(12): 3768-3776. [13] Cortell R. On a certain boundary value problem arising in shrinking sheet flows[J]. Applied Mathematics and Computation, 2010, 217(8): 4086-4093. [14] Nadeem S, Awais M. Thin film flow of an unsteady shrinking sheet through porous medium with variable viscosity[J]. Physics Letters A, 2008, 372(30): 4965-4972. [15] Hayat T, Iram S, Javed T, Asghar S. Shrinking flow of second grade fluid in a rotating frame: an analytic solution[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(10): 2932-2941. [16] Eringen A C. Theory of micropolar fluids[J]. J Math Mech, 1966, 16(1): 1-18. [17] Eringen A C. Microcontinuum Field Theories―Ⅱ: Fluent Media[M]. New York: Springer, 2001. [18] Devakar M, Iyengar T K V. Stokes’ first problem for a micropolar fluid through state-space approach[J]. Applied Mathematical Modelling, 2009, 33(2): 924-936. [19] Ali N, Hayat T. Peristaltic flow of a micropolar fluid in an asymmetric channel[J]. Computers & Mathematics With Applications, 2008, 55(4): 589-608. [20] Magyari E, Kumaran V. Generalized Crane flows of micropolar fluids[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(11): 3237-3240. [21] Ariman T, Turk M A, Sylvester N D. Microcontinuum fluid mechanics―a review[J]. International Journal of Engineering Science, 2010, 11(8): 905-930. [22] Hoyt J W, Fabula A F. The effect of additives on fluid friction [23] [R]. US Naval Ordinance Test station Report, 1964. [24] Power H. Micropolar fluid model for the brain fluid dynamics[C]Int Confer Bio-Fluid Mech, UK, 1998. [25] Abbasbandy S. Homotopy analysis method for the Kawahara equation[J]. Nonlinear Analysis: Real World Applications, 2010, 11(1): 307-312. [26] LIU Cheng-shi. The essence of the homotopy analysis method[J]. Applied Mathematics and Computation, 2010, 216(4): 1299-1303. [27] Liao S J. Beyond Perturbation: Introductin to Homotopy Analysis Method[M]. Boca Raton: Chapman & Hall/CRC Press, 2003. [28] LIAO Shi-jun. A short review on the homotopy analysis method in fluid mechanics[J]. Journal of Hydrodynamics, Ser B, 2010, 22(5): 882-884. [29] Hayat T, Naz R, Sajid M. On the homotopy solution for Poiseuille flow of a fourth grade fluid[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(3): 581-589. [30] Hayat T, Qasim M, Abbas Z. Homotopy solution for the unsteady three-dimensional MHD flow and mass transfer in a porous space[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(9): 2375-2387. [31] Dinarvand S, Doosthoseini A, Doosthoseini E, Rashidi M M. Series solutions for unsteady laminar MHD flow near forward stagnation point of an impulsively rotating and translating sphere in presence of buoyancy forces[J]. Nonlinear Analysis: Real World Applications, 2010, 11(2): 1159-1169. [32] Hayat T, Javed T. On analytic solution for generalized three-dimensional MHD flow over a porous stretching sheet[J]. Physics Letters A, 2007, 370(3/4): 243-250. [33] Abbasbandy S, Yurusoy M, Pakdemirli M. The analysis approach of boundary layer equations of power-law fluids of second grade[J]. Z Naturforsch A, 2008, 63: 564-570. [34] Tan Y, Abbasbandy S. Homotopy analysis method for quadratic Riccati differential equation[J]. Communications in Nonlinear Science and Numerical Simulation, 2008, 13(3): 539-546. [35] Hayat T, Iqbal Z, Sajid M, Vajravelu K. Heat transfer in pipe flow of a Johnson-Segalman fluid[J]. International Communications in Heat and Mass Transfer, 2008, 35(10): 1297-1301. [36] Rees D A S, Pop I. Free convection boundary layer flow of a micropolar fluid from a vertical flat plate[J]. IMA Journal of Applied Mathematics, 1998, 61(2): 179-197.
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