Radiation Effects on Flow past a Stretching Plate with Temperature Dependent Viscosity

Author(s)
Michalis Xenos

Affiliation(s)

Section of Applied Mathematics and Engineering Research, Department of Mathematics, University of Ioannina, Ioannina, Greece.

Section of Applied Mathematics and Engineering Research, Department of Mathematics, University of Ioannina, Ioannina, Greece.

ABSTRACT

The effect of radiation on the flow over a stretching plate of an optically thin gray, viscous and incompressible fluid is studied. The fluid viscosity is assumed to vary as an inverse linear function of the temperature. The partial differential equations (PDEs) and their boundary conditions, describing the problem under consideration, are dimensionalized and the numerical solution is obtained by using the finite volume discretization methodology which is suitable for fluid mechanics applications. The numerical results for the velocity and temperature profiles are shown for different dimensionless parameters entering the problem under consideration, such as the temperature parameter, *θr*, the radiation parameter,* S*, and the Prandtl number, *Pr*. The numerical results indicate a strong influence of these parameters on the non-dimensional velocity and temperature profiles in the boundary layer.

KEYWORDS

Radiation; Stretching Plate; Optically Thin Gray Fluid; Viscosity as a Function of the Temperature

Radiation; Stretching Plate; Optically Thin Gray Fluid; Viscosity as a Function of the Temperature

Cite this paper

M. Xenos, "Radiation Effects on Flow past a Stretching Plate with Temperature Dependent Viscosity,"*Applied Mathematics*, Vol. 4 No. 9, 2013, pp. 1-5. doi: 10.4236/am.2013.49A001.

M. Xenos, "Radiation Effects on Flow past a Stretching Plate with Temperature Dependent Viscosity,"

References

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doi:10.1016/j.enconman.2010.12.006

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doi:10.1615/JPorMedia.v9.i3.60

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doi:10.1016/j.ijthermalsci.2006.03.006

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[22] P. G. Siddheshwar and U. S. Mahabaleswar, “Effects of Radiation and Heat Source on MHD Flow of a Viscoelas tic Liquid and Heat Transfer over a Stretching Sheet,” In ternational Journal of Non-Linear Mechanics, Vol. 40, No. 6, 2005, pp. 807-820.

[23] S. K. Khan, “Heat Transfer in a Viscoelastic Fluid Flow over a Stretching Surface with Heat Source/Sink, Suc tion/Blowing and Radiation,” International Journal of Heat and Mass Transfer, Vol. 49, No. 3-4, 2006, pp. 628-639. doi:10.1016/j.ijheatmasstransfer.2005.07.049

[24] A. R. Bestman and S. K. Adjepong, “Unsteady Hydro Magnetic Free-Convection Flow with Radiative Heat Transfer in a Rotating Fluid. Compressible Optically Thin Fluid,” Astrophysics and Space Science, Vol. 143, No. 2, 1988, pp. 217-224. doi:10.1007/BF00637135

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[26] V. Rajesh, “Radiation Effects on MHD Free Convective Flow near a Vertical Plate with Ramped Wall Tempera ture,” International Journal of Applied Mathematics and Mechanics, Vol. 6, No. 21, 2010, pp. 60-77.

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[28] A. Raptis, “Free Convective Oscillatory Flow and Mass Transfer past a Porous Plate in the Presence of Radiation for an Optically Thin Fluid,” Thermal Science, Vol. 15, No. 3, 2011, pp. 849-857.

doi:10.2298/TSCI101208032R

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[31] M. Xenos, S. Dimas and A. Raptis, “MHD Free Convec tive Flow of Water near 4°C past a Vertical Moving Plate with Constant Suction,” Applied Mathematics, Vol. 4, No. 1, 2013, pp. 52-57.

[32] S. V. Patankar, “Numerical Heat Transfer and Fluid Flow,” McGraw-Hill, New York, 1980.

[1] M. M. Ali, T. S. Chen and B. F. Armaly, “Natural Con vection-Radiation Interaction in Boundary-Layer Flow over Horizontal Surfaces,” AIAA Journal, Vol. 22, No. 12, 1984, pp. 1797-1803.

doi:10.2514/3.8854

[2] M. A. Seddeek and M. S. Abdelmeguid, “Effects of Radi ation and Thermal Diffusivity on Heat Transfer over a Stretching Surface with Variable Heat Flux,” Physics Let ters A, Vol. 348, No. 3-6, 2006, pp. 172-179. doi:10.1016/j.physleta.2005.01.101

[3] A. Raptis and C. J. Toki, “Thermal Radiation in the Pres ence of Free Convective Flow past a Moving Vertical Po rous Plate—An Analytical Solution,” International Jour nal of Applied Mechanics and Engineering, Vol. 14, No. 4, 2009, pp. 1115-1126.

[4] P. Malekzadeh, M. A. Moghimi and M. Nickaeen, “The Radiation and Variable Viscosity Effects on Electrically Conducting Fluid over a Vertically Moving Plate Sub jected to Suction and Heat Flux,” Energy Conversion and Management, Vol. 52, No. 5, 2011, pp. 2040-2047.

doi:10.1016/j.enconman.2010.12.006

[5] A. J. Chamkha, M. Mujtaba, A. Quadri and C. Issa, “Ther mal Radiation Effects on MHD Forced Convection Flow Adjacent to a Non-Isothermal Wedge in the Presence of a Heat Source or Sink,” Heat and Mass Transfer, Vol. 39, No. 4, 2003, pp. 305-312.

[6] A. Raptis, C. Perdikis and H. S. Takhar, “Effect of Ther mal Radiation on MHD Flow,” Applied Mathematics and Computation, Vol. 153, No. 3, 2004, pp. 645-649. doi:10.1016/S0096-3003(03)00657-X

[7] H. M. Duwairi, “Viscous and Joule Heating Effects on Forced Convection Flow from Radiate Isothermal Porous Surfaces,” International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 15, No. 5-6, 2005, pp. 429 440. doi:10.1108/09615530510593620

[8] M. E. M. Ouaf, “Exact Solution of Thermal Radiation on MHD Flow over a Stretching Porous Sheet,” Applied Mathematics and Computation, Vol. 170, No. 2, 2005, pp. 1117-1125.

doi:10.1016/j.amc.2005.01.010

[9] M. Abd-El Aziz, “Thermal Radiation Effects on Magne Tohydrodynamic Mixed Convection Flow of a Micropo lar Fluid past a Continuously Moving Semi-Infinite Plate for High Temperature Differences,” Acta Mechanica, Vol. 187, No. 1-4, 2006, pp. 113-127. doi:10.1007/s00707-006-0377-9

[10] D. Pal and H. Mondal, “Effects of Soret Dufour, Chem ical Reaction and Thermal Radiation on MHD Non-Darcy Unsteady Mixed Convective Heat and Mass Transfer over a Stretching Sheet,” Communications in Nonlinear Sci ence and Numerical Simulation, Vol. 16, No. 4, 2011, pp. 1942-1958.

doi:10.1016/j.cnsns.2010.08.033

[11] G. C. Shit and R. Haldar, “Effects of Thermal Radiation on MHD Viscous Fluid Flow and Heat Transfer over Non-Linear Shrinking Porous Sheet,” Applied Mathemat ics and Mechanics-English Edition, Vol. 32, No. 6, 2011, pp. 677-688. doi:10.1007/s10483-011-1448-6

[12] P. V. S. N. Murthy, S. Mukherjee, D. Srinivasacharya, and P. V. S. S. S. R. Krishna, “Combined Radiation and Mixed Convection from a Vertical Wall with Suction/In jection in a Non-Darcy Porous Medium,” Acta Mechanica, Vol. 168, No. 3-4, 2004, pp. 145-156. doi:10.1007/s00707-004-0084-3

[13] S. M. Al-Harbi, “Numerical Study of Natural Convection Heat Transfer with Variable Viscosity and Thermal Radi ation from a Cone and Wedge in Porous Media,” Applied Mathematics and Computation, Vol. 170, No. 1, 2005, pp. 64-75. doi:10.1016/j.amc.2004.10.093

[14] M. Q. Al-Odat, F. M. S. Al-Hussien and R. A. Damseh, “Influence of Radiation on Mixed Convection over a We dge in Non-Darcy Porous Medium,” Forschung Im Inge nieurwesen-Engineering Research, Vol. 69, No. 4, 2005, pp. 209-215. doi:10.1007/s10010-005-0004-2

[15] A. Raptis and C. Perdikis, “Flow through a High Poros ity Medium in the Presence of Radiation,” Journal of Porous Media, Vol. 9, No. 2, 2006, pp. 169-175. doi:10.1615/JPorMedia.v9.i2.60

[16] H. M. Duwairi. “Radiation Effects on Mixed Convection over a Nonisothermal Cylinder and Sphere in a Porous Media,” Journal of Porous Media, Vol. 9, No. 3, 2006, pp. 251-259.

doi:10.1615/JPorMedia.v9.i3.60

[17] I. A. Badruddin, Z. A. Zainal, P. A. A. Narayana and K. N. Seetharamu, “Numerical Analysis of Convection Con duction and Radiation Using a Non-Equilibrium Model in a Square Porous Cavity,” International Journal of Ther mal Sciences, Vol. 46, No. 1, 2007, pp. 20-29.

doi:10.1016/j.ijthermalsci.2006.03.006

[18] F. G. Awad, P. Sibanda, S. S. Motsa and O. D. Makinde, “Convection from an Inverted Cone in a Porous Medium with Cross-Diffusion Effects,” Computers & Mathemat ics with Applications, Vol. 61, No. 5, 2011, pp. 1431-1441. doi:10.1016/j.camwa.2011.01.015

[19] A. Raptis, “Radiation and Viscoelastic Flow,” Internatio nal Communications in Heat and Mass Transfer, Vol. 26, No. 6, 1999, pp. 889-895.

[20] P. S. Datti, K. V. Prasad, M. S. Abel and A. Joshi, “MHD Visco-Elastic Fluid Flow over a Non-Isothermal Stretching Sheet,” International Journal of Engineering Science, Vol. 42, No. 8-9, 2004, pp. 935-946. doi:10.1016/j.ijengsci.2003.09.008

[21] S. Abel, K. V. Prasad and A. Mahaboob, “Buoyancy Force and Thermal Radiation Effects in MHD Boundary Layer Visco-Elastic Fluid Flow over Continuously Moving Stre tching Surface,” International Journal of Thermal Scienc es, Vol. 44, No. 5, 2005, pp. 465-476. doi:10.1016/j.ijthermalsci.2004.08.005

[22] P. G. Siddheshwar and U. S. Mahabaleswar, “Effects of Radiation and Heat Source on MHD Flow of a Viscoelas tic Liquid and Heat Transfer over a Stretching Sheet,” In ternational Journal of Non-Linear Mechanics, Vol. 40, No. 6, 2005, pp. 807-820.

[23] S. K. Khan, “Heat Transfer in a Viscoelastic Fluid Flow over a Stretching Surface with Heat Source/Sink, Suc tion/Blowing and Radiation,” International Journal of Heat and Mass Transfer, Vol. 49, No. 3-4, 2006, pp. 628-639. doi:10.1016/j.ijheatmasstransfer.2005.07.049

[24] A. R. Bestman and S. K. Adjepong, “Unsteady Hydro Magnetic Free-Convection Flow with Radiative Heat Transfer in a Rotating Fluid. Compressible Optically Thin Fluid,” Astrophysics and Space Science, Vol. 143, No. 2, 1988, pp. 217-224. doi:10.1007/BF00637135

[25] A. Raptis and C. Perdikis, “Thermal Radiation of an Opti cally Thin Gray Gas,” International Journal of Applied Mechanics and Engineering, Vol. 8, No. 1, 2003, pp. 131-134.

[26] V. Rajesh, “Radiation Effects on MHD Free Convective Flow near a Vertical Plate with Ramped Wall Tempera ture,” International Journal of Applied Mathematics and Mechanics, Vol. 6, No. 21, 2010, pp. 60-77.

[27] U. S. Rajput and S. Kumar, “Rotation and Radiation Ef fects on MHD Flow past an Impulsively Started Vertical Plate with Variable Temperature,” International Journal of Mathematical Analysis, Vol. 5, No 24, 2011, pp. 1155-1163.

[28] A. Raptis, “Free Convective Oscillatory Flow and Mass Transfer past a Porous Plate in the Presence of Radiation for an Optically Thin Fluid,” Thermal Science, Vol. 15, No. 3, 2011, pp. 849-857.

doi:10.2298/TSCI101208032R

[29] F. C. Lai and F. A. Kulacki, “The Effect of Variable Visco sity on Convective Heat-Transfer Along a Vertical Sur face in a Saturated Porous-Medium,” International Jour nal of Heat and Mass Transfer, Vol. 33, No. 5, 1990, pp. 1028-1031. doi:10.1016/0017-9310(90)90084-8

[30] Wolfram-Research, “Mathematica Edition: Version 8.0,” Wolfram-Research, Inc., Champaign, 2010.

[31] M. Xenos, S. Dimas and A. Raptis, “MHD Free Convec tive Flow of Water near 4°C past a Vertical Moving Plate with Constant Suction,” Applied Mathematics, Vol. 4, No. 1, 2013, pp. 52-57.

[32] S. V. Patankar, “Numerical Heat Transfer and Fluid Flow,” McGraw-Hill, New York, 1980.