Soret-Dufour Effects on the MHD Flow and Heat Transfer of Microrotation Fluid over a Nonlinear Stretching Plate in the Presence of Suction

Affiliation(s)

Department of Mathematics, Comilla University, Comilla, Bangladesh.

Department of Accounting and Information System, University of Chittagong, Chittagong, Bangladesh.

Department of Mathematics, Comilla University, Comilla, Bangladesh.

Department of Accounting and Information System, University of Chittagong, Chittagong, Bangladesh.

ABSTRACT

In this work, the Micropolar fluid flow and heat and mass transfer past a horizontal nonlinear stretching sheet through porous medium is studied including the Soret-Dufour effect in the presence of suction. A uniform magnetic field is applied transversely to the direction of the flow. The governing differential equations of the problem have been transformed into a system of non-dimensional differential equations which are solved numerically by Nachtsheim-Swigert iteration technique along with the sixth order Runge-Kutta integration scheme. The velocity, microrotation, temperature and concentration profiles are presented for different parameters. The present problem finds significant applications in hydromagnetic control of conducting polymeric sheets, magnetic materials processing, etc.

In this work, the Micropolar fluid flow and heat and mass transfer past a horizontal nonlinear stretching sheet through porous medium is studied including the Soret-Dufour effect in the presence of suction. A uniform magnetic field is applied transversely to the direction of the flow. The governing differential equations of the problem have been transformed into a system of non-dimensional differential equations which are solved numerically by Nachtsheim-Swigert iteration technique along with the sixth order Runge-Kutta integration scheme. The velocity, microrotation, temperature and concentration profiles are presented for different parameters. The present problem finds significant applications in hydromagnetic control of conducting polymeric sheets, magnetic materials processing, etc.

KEYWORDS

Heat Transfer; Micropolar Fluid; Porous Media; Stretching Sheet; Soret Number; Dufour Number

Heat Transfer; Micropolar Fluid; Porous Media; Stretching Sheet; Soret Number; Dufour Number

Cite this paper

M. Mahbub, N. Nasu, S. Aktar and Z. Rahman, "Soret-Dufour Effects on the MHD Flow and Heat Transfer of Microrotation Fluid over a Nonlinear Stretching Plate in the Presence of Suction,"*Applied Mathematics*, Vol. 4 No. 6, 2013, pp. 864-875. doi: 10.4236/am.2013.46119.

M. Mahbub, N. Nasu, S. Aktar and Z. Rahman, "Soret-Dufour Effects on the MHD Flow and Heat Transfer of Microrotation Fluid over a Nonlinear Stretching Plate in the Presence of Suction,"

References

[1] S. Ostrach, “An Analysis of Laminar Free-Convection Flow and Heat Transfer about a Flat Plate Parallel to the Direction of the Generating Body Force,” Technical Note, nACA Report, Washington DC, 1952. http://naca.central.cranfield.ac.uk/report.php?NID=5021

[2] R. M. Goody, “The Influence of Radiative Transfer on Cellular Convection,” Journal of Fluid Mechanics, Vol. 1, No. 4, 1956, pp. 424-435. doi:10.1017/S0022112056000263

[3] B. C. Sakiadis, “Boundary-Layer Behavior on Continuous Solid Surfaces: I. Boundary-Layer Equations for Two-Dimensional and Axisymmetric Flow,” AIChE Journal, Vol. 7, No. 1, 1961, pp. 26-28. doi:10.1002/aic.690070108

[4] A. C. Eringen, “Theory of Micropolar Fluids,” Journal of Mathematics and Mechanics, Vol. 16, No. 1, 1966, pp. 1-18.

[5] L. J. Crane, “Flow past a Stretching Sheet,” Zeitschrift für Angewandte Mathematik und Physik (ZAMP), Vol. 21, No. 4, 1970, pp. 645-647. doi:10.1007/BF01587695

[6] E. M. Sparrow, “Radiation Heat Transfer,” Augmented Edition, Hemisphere Publishing Corp., Washington DC, 1978.

[7] O. Aydin and I. Pop, “Natural Convection from a Discrete Heater in Enclosures Filled with a Micropolar Fluid,” International Journal of Engineering Science, Vol. 43, No. 19-20, 2005, pp. 1409-1418. doi:10.1016/j.ijengsci.2005.06.005

[8] M.-I. Char and C.-L. Chang, “Effect of Wall Conduction on Natural Convection Flow of Micropolar Fluids along a Flat Plate,” International Journal of Heat and Mass Transfer, Vol. 40, No. 15, 1997, pp. 3641-3652. doi:10.1016/S0017-9310(97)00006-9

[9] H. A. M. El-Arabawy, “Effect of Suction/Injection on the Flow of a Micropolar Fluid past a Continuously Moving Plate in the Presence of Radiation,” International Journal of Heat and Mass Transfer, Vol. 46, No. 8, 2003, pp. 1471-1477. doi:10.1016/S0017-9310(02)00320-4

[10] A. Ishak, R. Nazar and I. Pop, “The Schneider Problem for a Micropolar Fluid,” Fluid Dynamics Research, Vol. 38, No. 7, 2006, pp. 489-502. doi:10.1016/j.fluiddyn.2006.03.004

[11] M. E. Karim, M. A. Samad and M. A. Sattar, “Steady MHD Free Convection Flow with Thermal Radiation past a Vertical Porous Plate Immersed in a Porous Medium,” Research Journal of Mathematics and Statistics, Vol. 3, No. 4, 2011, pp. 141-147. http://www.maxwellsci.com/print/rjms/v3-141-147.pdf

[12] Y. Y. Lok, N. Amin and I. Pop, “Unsteady Boundary Layer Flow of a Micropolar Fluid near the Rear Stagnation Point of a Plane Surface,” International Journal of Thermal Sciences, Vol. 42, No. 11, 2003, pp. 995-1001. doi:10.1016/S1290-0729(03)00079-6

[13] R. Nazar, A. Ishak and I. Pop, “Unsteady Boundary Layer Flow over a Stretching Sheet in a Micropolar Fluid,” International Journal of Mathematical, Physical and Engineering Sciences, Vol. 2, No. 3, 2008, pp. 161-165.

[14] M. M. Rahman, M. A. Rahman, M. A. Samad and M. S. Alam, “Heat Transfer in a Micropolar Fluid along a NonLinear Stretching Sheet with a Temperature-Dependent Viscosity and Variable Surface Temperature,” International Journal of Thermophysics, Vol. 30, No. 5, 2009, pp. 1649-1670.

[15] M. M. Rahman, M. J. Uddin and A. Aziz, “Convective Flow of Micropolar Fluid in a Porous Medium with Variable Electric Conductivity, Surface Heat Flux and NonUniform Heat Source (or Sink),” International Journal of Energy & Technology, Vol. 25, No. 2, 2010, pp. 1-18.

[16] H. S. Takhar, R. Bhargava, R. S. Agrawal and A. V. S. Balaji, “Finite Element Solution of a Micropolar Fluid Flow and Heat Transfer between Two Porous Disks,” International Journal of Engineering Science, Vol. 38, No. 17, 2000, pp. 1907-1922. doi:10.1016/S0020-7225(00)00019-7

[17] E. R. G. Eckert and R. M. Drake, “Analysis of Heat and Mass Transfer,” McGraw-Hill, New York, 1972.

[18] T. Hayat and F. A. Hendi, “Thermal-Diffusion and Diffusion-Thermo Effects on MHD Three-Dimensional Axisymmetric Flow with Hall and Ion-Slip Currents,” Journal of American Science, Vol. 8, No. 1, 2012, pp. 284-294. http://www.jofamericanscience.org/journals/am-sci/am0801/042_7833am0801_284_294.pdf

[19] O. D. Makinde and P. O. Olanrewaju, “Unsteady Mixed Convection with Soret and Dufour Effects past a Porous Plate Moving through a Binary Mixture of Chemical Reacting Fluid,” Chemical Engineering Communications, Vol. 198, No. 7, 2011, pp. 920-938. doi:10.1080/00986445.2011.545296

[20] S. Shateyi, S. S. Motsa and P. Sibanda, “The Effects of Thermal Radiation, Hall Currents, Soret, and Dufour on MHD Flow by Mixed Convection over a Vertical Surface in Porous Media,” Mathematical Problems in Engineering, Vol. 2010, No. 1, 2010, pp. 1-20. doi:10.1155/2010/627475

[21] D. Srinivasacharya and K. Kaladhar, “Mixed Convection in a Couple Stress Fluid with Soret and Dufour Effects,” Internatioanl Journal of Applied Mathematics and Mechanics, Vol. 7, No. 20, 2011, pp. 59-71.

[22] P. R. Nachtsheim and P. Swigert, “Satisfaction of the Asymptotic Boundary Conditions in Numerical Solution of the Systems of Non-Linear Equations of Boundary Layer Type,” Ph.D. Thesis, NASA TN D-3004, Washington DC, 1965. http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19650026350_1965026350.pdf

[1] S. Ostrach, “An Analysis of Laminar Free-Convection Flow and Heat Transfer about a Flat Plate Parallel to the Direction of the Generating Body Force,” Technical Note, nACA Report, Washington DC, 1952. http://naca.central.cranfield.ac.uk/report.php?NID=5021

[2] R. M. Goody, “The Influence of Radiative Transfer on Cellular Convection,” Journal of Fluid Mechanics, Vol. 1, No. 4, 1956, pp. 424-435. doi:10.1017/S0022112056000263

[3] B. C. Sakiadis, “Boundary-Layer Behavior on Continuous Solid Surfaces: I. Boundary-Layer Equations for Two-Dimensional and Axisymmetric Flow,” AIChE Journal, Vol. 7, No. 1, 1961, pp. 26-28. doi:10.1002/aic.690070108

[4] A. C. Eringen, “Theory of Micropolar Fluids,” Journal of Mathematics and Mechanics, Vol. 16, No. 1, 1966, pp. 1-18.

[5] L. J. Crane, “Flow past a Stretching Sheet,” Zeitschrift für Angewandte Mathematik und Physik (ZAMP), Vol. 21, No. 4, 1970, pp. 645-647. doi:10.1007/BF01587695

[6] E. M. Sparrow, “Radiation Heat Transfer,” Augmented Edition, Hemisphere Publishing Corp., Washington DC, 1978.

[7] O. Aydin and I. Pop, “Natural Convection from a Discrete Heater in Enclosures Filled with a Micropolar Fluid,” International Journal of Engineering Science, Vol. 43, No. 19-20, 2005, pp. 1409-1418. doi:10.1016/j.ijengsci.2005.06.005

[8] M.-I. Char and C.-L. Chang, “Effect of Wall Conduction on Natural Convection Flow of Micropolar Fluids along a Flat Plate,” International Journal of Heat and Mass Transfer, Vol. 40, No. 15, 1997, pp. 3641-3652. doi:10.1016/S0017-9310(97)00006-9

[9] H. A. M. El-Arabawy, “Effect of Suction/Injection on the Flow of a Micropolar Fluid past a Continuously Moving Plate in the Presence of Radiation,” International Journal of Heat and Mass Transfer, Vol. 46, No. 8, 2003, pp. 1471-1477. doi:10.1016/S0017-9310(02)00320-4

[10] A. Ishak, R. Nazar and I. Pop, “The Schneider Problem for a Micropolar Fluid,” Fluid Dynamics Research, Vol. 38, No. 7, 2006, pp. 489-502. doi:10.1016/j.fluiddyn.2006.03.004

[11] M. E. Karim, M. A. Samad and M. A. Sattar, “Steady MHD Free Convection Flow with Thermal Radiation past a Vertical Porous Plate Immersed in a Porous Medium,” Research Journal of Mathematics and Statistics, Vol. 3, No. 4, 2011, pp. 141-147. http://www.maxwellsci.com/print/rjms/v3-141-147.pdf

[12] Y. Y. Lok, N. Amin and I. Pop, “Unsteady Boundary Layer Flow of a Micropolar Fluid near the Rear Stagnation Point of a Plane Surface,” International Journal of Thermal Sciences, Vol. 42, No. 11, 2003, pp. 995-1001. doi:10.1016/S1290-0729(03)00079-6

[13] R. Nazar, A. Ishak and I. Pop, “Unsteady Boundary Layer Flow over a Stretching Sheet in a Micropolar Fluid,” International Journal of Mathematical, Physical and Engineering Sciences, Vol. 2, No. 3, 2008, pp. 161-165.

[14] M. M. Rahman, M. A. Rahman, M. A. Samad and M. S. Alam, “Heat Transfer in a Micropolar Fluid along a NonLinear Stretching Sheet with a Temperature-Dependent Viscosity and Variable Surface Temperature,” International Journal of Thermophysics, Vol. 30, No. 5, 2009, pp. 1649-1670.

[15] M. M. Rahman, M. J. Uddin and A. Aziz, “Convective Flow of Micropolar Fluid in a Porous Medium with Variable Electric Conductivity, Surface Heat Flux and NonUniform Heat Source (or Sink),” International Journal of Energy & Technology, Vol. 25, No. 2, 2010, pp. 1-18.

[16] H. S. Takhar, R. Bhargava, R. S. Agrawal and A. V. S. Balaji, “Finite Element Solution of a Micropolar Fluid Flow and Heat Transfer between Two Porous Disks,” International Journal of Engineering Science, Vol. 38, No. 17, 2000, pp. 1907-1922. doi:10.1016/S0020-7225(00)00019-7

[17] E. R. G. Eckert and R. M. Drake, “Analysis of Heat and Mass Transfer,” McGraw-Hill, New York, 1972.

[18] T. Hayat and F. A. Hendi, “Thermal-Diffusion and Diffusion-Thermo Effects on MHD Three-Dimensional Axisymmetric Flow with Hall and Ion-Slip Currents,” Journal of American Science, Vol. 8, No. 1, 2012, pp. 284-294. http://www.jofamericanscience.org/journals/am-sci/am0801/042_7833am0801_284_294.pdf

[19] O. D. Makinde and P. O. Olanrewaju, “Unsteady Mixed Convection with Soret and Dufour Effects past a Porous Plate Moving through a Binary Mixture of Chemical Reacting Fluid,” Chemical Engineering Communications, Vol. 198, No. 7, 2011, pp. 920-938. doi:10.1080/00986445.2011.545296

[20] S. Shateyi, S. S. Motsa and P. Sibanda, “The Effects of Thermal Radiation, Hall Currents, Soret, and Dufour on MHD Flow by Mixed Convection over a Vertical Surface in Porous Media,” Mathematical Problems in Engineering, Vol. 2010, No. 1, 2010, pp. 1-20. doi:10.1155/2010/627475

[21] D. Srinivasacharya and K. Kaladhar, “Mixed Convection in a Couple Stress Fluid with Soret and Dufour Effects,” Internatioanl Journal of Applied Mathematics and Mechanics, Vol. 7, No. 20, 2011, pp. 59-71.

[22] P. R. Nachtsheim and P. Swigert, “Satisfaction of the Asymptotic Boundary Conditions in Numerical Solution of the Systems of Non-Linear Equations of Boundary Layer Type,” Ph.D. Thesis, NASA TN D-3004, Washington DC, 1965. http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19650026350_1965026350.pdf