Document Type : Research Paper

Authors

Department of Mathematics, Priyadarshini College of Engineering and Technology, Nellore, Andra Pradesh, India - 524004

Abstract

The present paper was aimed to study the effects of variable thermal conductivity and heat generation on the flow of a viscous incompressible electrically conducting fluid in the presence of a uniform transverse magnetic field, thermal radiation, porous medium, mass transfer, and variable free stream near a stagnation point on a non-conducting stretching sheet. Equations of continuity, momentum, energy, and mass were transformed into ordinary differential equations and solved numerically using shooting method. Velocity, temperature, and concentration distributions were numerically discussed and presented in the graphs. Skin-friction coefficient, the Nusselt number, and Sherwood number on the sheet were derived and discussed numerically. Their numerical values for various values of physical parameters were presented in the tables. It was found that temperature increased with increasing radiation parameter, R, and concentration decreased with increasing the Schmidt number, Sc. The numerical predications were compared with the existing information in the literature and a good agreement was obtained. 

Keywords

Main Subjects

[1] L. J. Crane, “Flow past a stretching plate,” Zeitschrift für Angewandte Mathematik und Physik, Vol. 21, No. 4, pp. 645-647, (1970).
[2] K. B. Pavlov, “Magnetohydrodynamic flow of an incompressible viscous fluid caused by the deformation of a plane surface,” Magnetohydrodynamics, Vol. 10, pp. 146-148, (1974).
[3] H. I. Andersson, “MHD flow of a viscoelastic fluid past a stretching surface,” Acta Mechanica, Vol. 95, No. 1-4, pp. 227-230, (1992).
[4] S. Mukhopadhyay, G. C. Layek and S. A. Samad, “Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity,” International Journal of Heat and Mass Transfer, Vol. 48, No. 21-22, pp. 4460-4466, (2005).
[5] K. Bhattacharyya and G. C. Layek, “Chemically reactive solute distribution in MHD boundary layer flow over a permeable stretching sheet with suction or blowing,” Chemical Engineering Communications, Vol. 197, No. 12, pp. 1527-1540, (2010).
[6] H. Tabaei, M. A. Moghimi, A. Kimiaeifar and M. A. Moghimi, “Homotopy analysis and differential quadrature solution of the problem of free-convective magnetohydrodynamic flow over a stretching sheet with the Hall effect and mass transfer taken into account,” Journal of Applied Mechanics and Technical Physics, Vol. 52, No. 4, pp. 624-636, (2011).
[7] A. M. Salem and R. Fathy, “Effects of variable properties on MHD heat and mass transfer flow near a stagnation point towards a stretching sheet in a porous medium with thermal radiation,” Chinese Physics, Vol. 21, Article ID 054701, (2012).
[8] I. C. Mandal and S. Mukhopadhyay, “Heat transfer analysis for fluid flow over an exponentially stretching porous sheet with surface heat flux in porous medium,” Ain Shams Engineering Journal, Vol. 4, No. 1, pp. 103-110, (2013).
[9] B. C. Sakiadis, “Boundary layer behavior on continuous solid surfaces: I The Boundary layer equations for two-dimensional and axi-symmetric flow”, AIChE J. Vol. 7, No. 1, pp. 26-28, (1961).
[10] L. E. Erickson, L.T. Fan and V. G. Fox, “Heat and mass transfer on a moving continuous flat plate with suction and injection”, Industrial & Engineering Chemistry Fundamentals, Vol. 5, No. 1, pp. 19-25, (1966).
[11] F. K. Tsou, F. M. Sparrow and R. J. Goldstein, “Flow and heat transfer in the boundary layer in continuous moving surface”, International Journal of Heat Mass Transfer, Vol. 10, No. 2, pp. 219-235, (1967).
[12] A. Noghrehabadi, R. Pourrajab and M. Ghalambaz, “Effect of partial slip boundary condition on the flow and heat transfer of nanofluids past stretching sheet prescribed constant wall temperature,” International Journal of Thermal Sciences, Vol. 54, No. 1, pp. 253-261, (2012).
[13] A. Noghrehabadi, R. Pourrajab and M. Ghalambaz, “Flow and heat transfer of nanofluids over stretching sheet taking into account partial slip and thermal convective boundary conditions”. Heat Mass Transfer, Vol. 49, No. 9, pp. 1357-1366, (2013).
[14] K. Hiemenz, “Die grenzschicht an einem in den gleich formigen flussigkeitsstrom eingetauchten geraden kreiszlinder”. Dingler’s. Polytech. Journal, Vol. 326, pp. 321-328, (1911).
[15] F. Homann, “Der Einfluss grosser Zahigkeit bei der Stromung um den Zylinder und um die Kugel”. Zeitschrift Angewandte Mathematik und Mechanik, Vol. 16, No. 3, pp. 153-164, (1936).
[16] S. I. Pai, “Viscous Flow Theory I: Laminar Flow”, D Van Nostrand Company, Inc., New York, (1956).
[17] H. Schlichting, “Boundary Layer Theory. McGraw- Hill Book Company, New York, (1968).
[18] J. L. Bansal, “Viscous Fluid Dynamics”. Oxford & IBH Publisher Company, New Delhi, (1977).
[19] T. C. Chiam, “Stagnation-point flow towards a stretching plate,” Journal of the Physical Society of Japan, Vol. 63, No. 6, pp. 2443-2444, (1994).
[20] T. R. Mahapatra and A. S. Gupta, “Magnetohydrodynamic stagnation point flow towards a stretching surface”. Acta Mechanica, Vol. 152, No. 1-4, pp. 191-196, (2001).
[21] R. Nazar, N. Amin, D. Filip and I. Pop, “Unsteady boundary layer flow in the region of  the stagnation point on a stretching sheet”. International Journal of Engineering &. Science, Vol. 42, No. 11-12, pp. 1241-1253, (2004).
[22] W. M. Kay, “Convective Heat and Mass Transfer”, McGraw-Hill Book Company, New York, (1966).
[23] M. Arunachalam and N. R. Rajappa, “Forced convection in liquid metals with variable thermal conductivity and capacity”. Acta Mechanica, Vol. 31, No. 1-2, pp. 25-3, (1978).
[24] L. J. Grubka and K. M. Bobba, “Heat transfer characteristics of a continuously stretching surface with variable temperature”. Transactions of ASME Journal of Heat and Mass Transfer , Vol. 107, pp. 248-250, (1985).
[25] T. C. Chaim, “Heat transfer in a fluid with variable thermal conductivity over stretching sheet”. Acta Mechanica, Vol. 129, No. 1-2, pp. 63-72, (1998).
[26] S. R. Pop, T. Grosan and I. Pop, “Radiation effect on the flow near the stagnation point of a stretching sheet”, Technische Mechanik, Vol. 25, No. 2, pp. 100-106, (2004).
[27] M. A. Hossain and H. S. Takhar, “Radiation effect on mixed convection along a vertical plate with uniformsurface temperature,” Heat and Mass Transfer, Vol. 31, No. 4, pp. 243-248, (1996).
[28] D. Pal, “Heat and mass transfer in stagnation-point flow towards a stretching surface in the presence of buoyancy force and thermal radiation”, Meccanica, Vol. 44, No. 2, pp. 145-158, (2009).
[29] P. Vyas and N.  Srivastava,”  Radiative MHD flow over a non-isothermal stretching sheet in a porous medium”, Applied Mathematical Sciences, Vol. 4, No. 50, pp. 2475-2484, (2010).
[30] H. A. Attia, “Stagnation point flow towards a stretching surface through a porous medium with heat generation”. Turkish Journal of Engineering and Environmental Sciences, Vol. 30, No. 5, pp. 299-306, (2006).
[31] P. R. Sharma and G. Singh, “Effects of variable thermal conductivity and heat source/sink on MHD flow near a stagnation point on a linearly stretching sheet”. Journal of Applied Fluid Mechanics, Vol. 2, No. 1, pp. 13-21, (2009).
[32] N. S. Al-Sudais, “Thermal radiation effects on MHD fluid flow near stagnation point of linear stretching sheet with variable thermal conductivity”. International Mathematical Forum, Vol. 7, No. 51, pp. 2525-2544. (2012).
[33] A. Noghrehabadi, M. R. Saffarian, R. Pourrajab and M. Ghalambaz, “Entropy analysis for nanofluid flow over a stretching sheet in the presence of heat generation/absorption and partial slip”, Journal of Mechanical Science and Technology, Vol. 27, No. 3, pp. 927-937, (2013).
[34] M. Q. Brewster, “Thermal radiative transfer and properties”. New York: John Wiley & Sons, (1992).
[35] S. D. Conte and C. Boor, “Elementary Numerical Analysis”, McGraw-Hill Book Company, New York, (1981).
[36] M. K. Jain, “Numerical Solution of Differential Equations”, Wiley Eastern Ltd., New Delhi, India, (1984).
[37] M. K. Jain, S. R. Iyengar and R. K. Jain, “Numerical Methods for Scientific and Engineering Computation”. Wiley Eastern Ltd., New Delhi, India, (1985).
[38] E. V. Krishnamurthy and S. K. Sen, “Numerical Algorithms”, Affiliated East-West Press Pvt. Ltd., New Delhi, India, (1986).
CAPTCHA Image