×

Effects of slip, viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet. (English) Zbl 1397.76182

Summary: The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective numerical scheme is adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and temperature fields. It is interesting to find that the slip increases the momentum and thermal boundary layer thickness. As the slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid. The presence of a magnetic field has also substantial effects on velocity and temperature fields.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
80A20 Heat and mass transfer, heat flow (MSC2010)
76A05 Non-Newtonian fluids
76A10 Viscoelastic fluids
76M20 Finite difference methods applied to problems in fluid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Sakiadis, B. C. Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow. AIChE Journal 7(1), 26–28 (1961)
[2] Blasius, H. Grenzschichten in flüssigkeiten mit kleiner reibung. Z. Angew. Math. Phys. 56, 1–37 (1908) · JFM 39.0803.02
[3] Crane, L. J. Flow past a stretching sheet. Z. Angew. Math. Phys. 21(4), 645–647 (1970)
[4] Cortell, R. Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet. Phys. Letters A 372(5), 631–636 (2008) · Zbl 1217.76028
[5] Vajravelu, K. and Cannon, J. R. Fluid flow over a nonlinearly stretching sheet. Appl. Math. Comput. 181(1), 609–618 (2006) · Zbl 1143.76024
[6] Ariel, P. D. Generalized three-dimensional flow due to a stretching sheet. ZAMM 83(12), 844–852 (2003) · Zbl 1047.76019
[7] Ariel, P. D. Axisymmetric flow due to a stretching sheet with partial slip. Comput. Math. Appl. 54(7–8), 1169–1183 (2007) · Zbl 1138.76030
[8] Ariel, P. D. On computation of the three-dimensional flow past a stretching sheet. Appl. Math. Comput. 188(2), 1244–1250 (2007) · Zbl 1114.76056
[9] Wang, C. Y. The three-dimensional flow due to a stretching at surface. Phys. Fluids 27(8), 1915–1917 (1984) · Zbl 0545.76033
[10] Sajid, M., Hayat, T., Asghar, S., and Vajravelu, K. Analytic solution for axisymmetric flow over a nonlinearly stretching sheet. Arch. Appl. Mech. 78(2), 127–134 (2007) DOI 10.1007/s00419-007-0146-9 · Zbl 1161.76460
[11] Sajid, M., Ahmad, I., Hayat, T., and Ayub, M. Series solution for unsteady axisymmetric flow and heat transfer over a radially stretching sheet. Communications in Nonlinear Science and Numerical Simulation 13(10), 2193–2202 (2008) · Zbl 1155.76304
[12] Rajagopal, K. R., Na, T. Y., and Gupta, A. S. Flow of a viscoelastic fluid over a stretching sheet. Rheo. Acta 23(2) 213–215 (1984)
[13] Andersson, H. I. MHD flow of a viscoelastic fluid past a stretching surface. Acta Mech. 95(1–4), 227–230 (1992) · Zbl 0753.76192
[14] Ariel, P. D. MHD flow of a viscoelastic fluid past a stretching sheet with suction. Acta Mech. 105(1–4), 49–56 (1994) · Zbl 0814.76086
[15] Liu, I. C. Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to a transverse magnetic field. Int. J. Heat Mass Transfer 47(19–20), 4427–4437 (2004) · Zbl 1111.76336
[16] Sahoo, B. and Sharma, H. G. Existence and uniqueness theorem for flow and heat transfer of a non-Newtonian fluid over a stretching sheet. Journal of Zhejiang University Science A 8(5), 766–771 (2007) · Zbl 1144.80347
[17] Ariel, P. D. Axisymmetric flow of a second grade fluid past a stretching sheet. Int. J. Eng. Sci. 39(5), 529–553 (2001) · Zbl 1210.76127
[18] Hayat, T. and 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(1–2), 75–84 (2007) · Zbl 1104.80006
[19] Hayat, T., Sajid, M., and Pop, I. Three-dimensional flow over a stretching surface in a viscoelastic fluid. Nonl. Anal. Real World Appl. 9(4), 1811–1822 (2008) · Zbl 1154.76315
[20] Navier, C. L. M. H. Mémoire sur les lois du mouvement des fluides. Mem. Acad. R. Sci. Inst. Fr. 6, 389–440 (1823)
[21] Wang, C. Y. Flow due to a stretching boundary with partial slip-an exact solution of the Navier-Stokes equation. Chem. Eng. Sci. 57(17), 3745–3747 (2002)
[22] Andersson, H. I. Slip flow past a stretching surface. Acta Mech. 158(1–2), 121–125 (2002) · Zbl 1013.76020
[23] Wang, C. Y. Analysis of viscous flow due to a stretching sheet with surface slip and suction. Nonl. Anal. Real World Appl. 10(1), 375–380 (2009) · Zbl 1154.76330
[24] Ariel, P. D., Hayat, T., and Asghar, S. The flow of an elastico-viscous fluid past a stretching sheet with partial slip. Acta Mech. 187(1–4), 29–35 (2006) · Zbl 1103.76010
[25] Hayat, T., Javed, T., and Abbas, Z. Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous space. Int. J. Heat Mass Transfer 51(17–18), 4528–4534 (2008) · Zbl 1144.80316
[26] Sahoo, B. Effects of partial slip on axisymmetric flow of an electrically conducting viscoelastic fluid past a stretching sheet. Cent. Eur. J. Phys. (2009) DOI 10.2478/s11534-009-0105-x
[27] Truesdell, C. and Noll, W. The Non-Linear Field Theories of Mechanics, 3rd Ed., Springer (2004) · Zbl 1068.74002
[28] Shercliff, J. A. A Text Book of Magnetohydrodynamics, Pergamon Press, Oxford (1965) · Zbl 0134.22101
[29] Sahoo, B. and Sharma, H. G. MHD flow and heat transfer from a continuous surface in a uniform free stream of a non-Newtonian fluid. Appl. Math. Mech. -Engl. Ed. 28(11), 1467–1477 (2007) DOI 10.1007/s10483-007-1106-z · Zbl 1231.34015
[30] Sahoo, B. and Sharma, H. G. Effects of partial slip on the steady Von Karman flow and heat transfer of a non-Newtonian fluid. Bull. Braz. Math. Soc. 38(4), 595–609 (2007) · Zbl 1133.76003
[31] Sahoo, B. Hiemenz flow and heat transfer of a non-Newtonian fluid. Comm. Nonl. Sci. Num. Sim. 14(3), 811–826 (2009)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.