×

Slip MHD liquid flow and heat transfer over non-linear permeable stretching surface with chemical reaction. (English) Zbl 1219.80098

Summary: In the present study the magnetohydrodynamic (MHD) liquid flow and heat transfer over non-linear permeable stretching surface has been presented in the presence of chemical reactions and partial slip. By means of proper similarity variables, the fundamental equations of the boundary layer are transformed to ordinary differential equations which for the fixed values of the \(x\)-coordinate along the plate local similarity solution would be valid appropriately. The ordinary differential equations are solved numerically using an explicit Runge-Kutta (4, 5) formula, the Dormand-Prince pair and shooting method. As a result, the velocity profiles, the concentration profiles, temperature profiles, the wall shear stress, the local Sherwood number and the local Nusselt number for the various values of the involved parameters of the problem are presented and discussed in details.

MSC:

80A20 Heat and mass transfer, heat flow (MSC2010)
76W05 Magnetohydrodynamics and electrohydrodynamics
76V05 Reaction effects in flows
76D05 Navier-Stokes equations for incompressible viscous fluids
76M25 Other numerical methods (fluid mechanics) (MSC2010)
80M25 Other numerical methods (thermodynamics) (MSC2010)
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Gad-El-Hak, M.: MEMS applications, (2006)
[2] Tanaka, M.: An industrial and applied review of new MEMS devices features, Microelectron. eng. 84, 1341-1344 (2007)
[3] Nisar, A.; Afzulpurkar, N.; Mahaisavariya, B.; Tuantranont, A.: Review MEMS-based micropumps in drug delivery and biomedical applications, Sens. actuators 130, 917-942 (2008)
[4] Gal-El-Hak, M.: The fluid mechanics of microdevices – the freeman scholar lecture, J. fluids eng. Trans. ASME 121, 5-33 (1999)
[5] Matthews, M. T.; Hill, J. M.: Nano boundary layer equation with nonlinear Navier boundary condition, Ames special issue J. Math. anal. Appl. 333, 381-400 (2007) · Zbl 1207.76050
[6] Enderle, J.; Bronzino, J. D.; Blanchard, S. M.: Introduction to biomedical engineering, (2005)
[7] C.H. Chen, L.S. Jang, Recent patents on micromixing technology and micromixers, Recent Patents Mech. Eng. 2 (2009) 240 – 247.
[8] Afify, A. A.: MHD free convective flow and mass transfer over a stretching sheet with chemical reaction, Heat mass transfer 40, 495-500 (2004)
[9] Cortell, R.: Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to suction and to a transverse magnetic field, Int. J. Heat mass transfer 49, 1851-1856 (2006) · Zbl 1189.76778
[10] Cortell, R.: Effects of viscous dissipation and work done by deformation on the MHD flow and heat transfer of a viscoelastic fluid over a stretching sheet, Phys. lett. A 357, 298-305 (2006) · Zbl 1236.76087
[11] Hayat, T.; Sajid, M.: Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet, Int. J. Heat mass transfer 50, 75-84 (2007) · Zbl 1104.80006
[12] Cortell, R.: Toward an understanding of the motion and mass transfer with chemically reactive species for two classes of viscoelastic fluid over a porous stretching sheet, Chem. eng. Process. 46, 982-989 (2007)
[13] Cortell, R.: Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet, Phys. lett. A 372, 631-636 (2008) · Zbl 1217.76028
[14] Ishak, A.; Nazar, R.; Pop, I.: Heat transfer over an unsteady stretching permeable surface with prescribed wall temperature, Nonlinear anal. Real world appl. 10, 2909-2913 (2009) · Zbl 1162.76017
[15] Ziabakhsh, Z.; Domairry, G.; Mozaffari, M.; Mahbobifar, M.: Analytical solution of heat transfer over an unsteady stretching permeable surface with prescribed wall temperature, J. Taiwan inst. Chem. eng. 41, 169-177 (2010)
[16] Yao, S.; Fang, T.; Zhong, Y.: Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions, Commun. nonlinear sci. Numer. simul. 16, 752-760 (2011) · Zbl 1221.76062
[17] Robert, A.; Gorder, Van; Vajravelu, K.: Convective heat transfer in a conducting fluid over a permeable stretching surface with suction and internal heat generation/absorption, Appl. math. Comput. 217, 5810-5821 (2011) · Zbl 1388.76349
[18] T. Javed, Z. Abbas, M. Sajid, N. Ali, Heat transfer analysis for a hydromagnetic viscous fluid over a non-linear shrinking sheet, Int. J. Heat Mass Transfer (in press), doi:10.1016/j.ijheatmasstransfer.2010.12.025. · Zbl 1217.80044
[19] M.J. Martin, I.D. Boyd, Blasius boundary layer solution with slip flow conditions, Presented at the 22nd Rarefied Gas Dynamics Symposium, Sydney, Australia, 2000.
[20] Martin, M. J.; Boyd, I. D.: Momentum and heat transfer in a laminar boundary layer with slip flow, J. thermophys. Heat transfer 20, No. 4, 710-719 (2006)
[21] Latif, M. J.: Heat convection, (2006)
[22] Matthews, M. T.; Hill, J. M.: A note on the boundary layer equations with linear slip boundary conditions, Appl. math. Lett. 21, 810-813 (2008) · Zbl 1148.76019
[23] Matthews, M. T.; Hill, J. M.: Newtonian flow with nonlinear Navier boundary condition, Acta mechanica 191, 195-217 (2007) · Zbl 1117.76024
[24] Ariel, P. D.: Axisymmetric flow due to a stretching sheet with partial slip, Comput. math. Appl. 54, 1169-1183 (2007) · Zbl 1138.76030
[25] M.H. Yazdi, S. Abdullah, I. Hashim, A. Zaharim, K. Sopian, Friction and heat transfer in slip flow boundary layer at constant heat flux boundary conditions, in: Proceedings of the 10th WSEAS International Conference on Mathematical Methods, Computational Techniques and Intelligent Systems, Corfu, Greece, 2008, pp. 207 – 214. · Zbl 1341.80022
[26] Wang, C. Y.: Analysis of viscous flow due to a stretching sheet with surface slip and suction, Nonlinear anal. Real. world appl. 10, No. 1, 375-380 (2009) · Zbl 1154.76330
[27] M.H. Yazdi, S. Abdullah, I. Hashim, M.N. Zulkifli, A. Zaharim, K. Sopian, Convective heat transfer of slip liquid flow past horizontal surface within the porous media at constant heat flux boundary conditions, in: Proceedings of the American Conference on Applied Mathematics, Cambridge, USA, 2010, pp. 527 – 533. · Zbl 1341.80022
[28] Van Gorder, R. A.; Sweet, E.; Vajravelu, K.: Nano boundary layers over stretching surfaces, Commun. nonlinear sci. Numer. simul. 15, 1494-1500 (2010) · Zbl 1221.76024
[29] Kechil, S. A.; Hashim, I.: Series solution of flow over nonlinearly stretching sheet with chemical reaction and magnetic field, Phys. lett. A 372, 2258-2263 (2008) · Zbl 1220.76029
[30] Fang, T.; Zhang, J.; Yao, S.: Slip MHD viscous flow over a stretching sheet – an exact solution, Commun. nonlinear sci. Numer. simul. 14, 3731-3737 (2009)
[31] Bejan, A.: Convection heat transfer, (1995) · Zbl 0599.76097
[32] Cortell, R.: Viscous flow and heat transfer over a nonlinearly stretching sheet, Appl. math. Comput. 184, 864-873 (2007) · Zbl 1112.76022
[33] Cortell, R.: MHD flow and mass transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet with chemically reactive species, Chem. eng. Process. 46, 721-728 (2007)
[34] Ali, M. E.: Heat transfer characteristics of a continuous stretching surface, Waerme stoffuebertrag 29, 227-234 (1994)
[35] Takhar, H. S.; Chamkha, A. J.; Nath, G.: Flow and mass transfer on a stretching sheet with a magnetic field and chemically reactive species, Int. J. Eng. sci. 38, 1303-1314 (2000) · Zbl 1210.76205
[36] T. Hayat, M. Qasim, MHD flow and heat transfer over permeable stretching sheet with slip conditions, Int. J. Numer. Meth. Fluids (in press), doi:10.1002/fld.2294. · Zbl 1285.76044
[37] Dormand, J. R.; Prince, P. J.: A family of embedded Runge – Kutta formulae, J. comp. Appl. math. 6, 19-26 (1980) · Zbl 0448.65045
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.