Boundary Layer Flow and Heat Transfer of a Dusty Fluid over a Stretching Vertical Surface

Author(s)
Bijjanal Jayanna Gireesha,
Gosikere Kenchappa Ramesh,
Hatti Jayappa Lokesh,
Channabasappa Shanthappa Bagewadi

ABSTRACT

This paper presents the study of convective heat transfer characteristics of an incompressible dusty fluid past a vertical stretching sheet. The governing partial differential equations are reduced to nonlinear ordinary differential equations by using similarity transformation. The transformed equations are solved numerically by applying Runge Kutta Fehlberg fourth-fifth order method (RKF45 Method). Here obtained non-dimensional velocity and temperature profiles has been carried out to study the effect of different physical parameters such as fluid-particle interaction parameter, Grashof number, Prandtl number, Eckert number. Comparison of the obtained numerical results is made with previously published results.

This paper presents the study of convective heat transfer characteristics of an incompressible dusty fluid past a vertical stretching sheet. The governing partial differential equations are reduced to nonlinear ordinary differential equations by using similarity transformation. The transformed equations are solved numerically by applying Runge Kutta Fehlberg fourth-fifth order method (RKF45 Method). Here obtained non-dimensional velocity and temperature profiles has been carried out to study the effect of different physical parameters such as fluid-particle interaction parameter, Grashof number, Prandtl number, Eckert number. Comparison of the obtained numerical results is made with previously published results.

KEYWORDS

Boundary Layer Flow, Dusty Fluid, Stretching Sheet, Grashof Number, Fluid-Particle Interaction Parameter, Numerical Solution

Boundary Layer Flow, Dusty Fluid, Stretching Sheet, Grashof Number, Fluid-Particle Interaction Parameter, Numerical Solution

Cite this paper

nullB. Gireesha, G. Ramesh, H. Lokesh and C. Bagewadi, "Boundary Layer Flow and Heat Transfer of a Dusty Fluid over a Stretching Vertical Surface,"*Applied Mathematics*, Vol. 2 No. 4, 2011, pp. 475-481. doi: 10.4236/am.2011.24061.

nullB. Gireesha, G. Ramesh, H. Lokesh and C. Bagewadi, "Boundary Layer Flow and Heat Transfer of a Dusty Fluid over a Stretching Vertical Surface,"

References

[1] B. C. Sakiadis, “Boundary Layer Behaviour on Continuous Solid Surface,” AIChE Journal, Vol. 7, No. 1, 1961, pp. 26-28. doi:10.1002/aic.690070108

[2] 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

[3] H. I. Anderson, K. H. Bech and B. S. Dandapat, “Magnetohydrodynamic Flow of a Power-Law Fluid over a Stretching Sheet,” International Journal of Non-Linear Mechanics, Vol. 27, No. 6, 1992, pp. 929-936. doi:10.1016/0020-7462(92)90045-9

[4] A. Chakrabarti and A. S. Gupta, “Hydromagnetic Flow and Heat Transfer over a Stretching Sheet,” Quarterly of Applied Mathematics, Vol. 37, No. 1, 1979, pp. 73-78.

[5] L. J. Grubka and K. M. Bobba, “Heat Transfer Characteristics of a Continuous Stretching Surface with Variable Temperature,” Journal of Heat Transfer, Vol. 107, No. 1, 1985, pp. 248-250. doi:10.1115/1.3247387

[6] R. Cortell, “A Note on Magnetohydrodynamic Flow of a Power-Law Fluid over a Stretching Sheet,” Applied Mathematics and Computation, Vol. 168, No. 1, 2005, pp. 557-56. doi:10.1016/j.amc.2004.09.046

[7] C. H. Chen, “MHD Mixed Convection of a Power Law Fluid Past a Strtching Surface in the Presence of Thermal Radiation and Internal Heat Generation/Absorption,” International Journal of Nonlinear Mechanics, Vol. 44, No. 6, 2009, pp. 596-603.

[8] R. Cortell, “Effects of Viscous Dissipation and Work Done by Deformation on the MHD Flow and Heat Transfer of a Viscoelastic Fluid over a Stretching Sheet,” Physics Letters A, Vol. 357, No. 4-5, 2006, pp. 298-305. doi:10.1016/j.physleta.2006.04.051

[9] M. S. Abel, E. Sanjayanand and M. M. Nandeppanavar, “Viscoelastic MHD Flow and Heat Transfer over a Stretching Sheet with Viscous and Ohmic Dissipation,” Communications in Nonlinear Science and Numerical Simulation, Vol. 13, No. 9, 2008, pp. 1808-1821.

[10] M. S. Abel and N. Mahesha, “Heat Transfer in MHD Viscoelastic Fluid Flow over a Stretching Sheet with Variable Thermal Conductivity, Non-Uniform Heat Source and Radiation,” Applied Mathematical Modelling, Vol. 32, No. 10, 2008, pp. 1965-1983. doi:10.1016/j.apm.2007.06.038

[11] R. Tsai, K. H. Huang and J. S. Haung, “Flow and Heat Transfer over an Unsteady Stretching Surface with Nonuniform Heat Source,” International Communications in Heat and Mass Transfer, Vol. 35, No. 10, 2008, pp. 1340-1343. doi:10.1016/j.icheatmasstransfer.2008.07.001

[12] A. Ishak, R. Nazar and I. Pop, “Heat Transfer over an Unsteady Stretching Permeable Surface with Prescribed Wall Temperature,” Non-Linear Analysis, Real World Applications, Vol. 10, No. 5, 2009, pp. 2909-2913. doi:10.1016/j.nonrwa.2008.09.010

[13] A. Ishak, R. Nazar and I. Pop, “Boundary Layer Flow and Heat Transfer over an Unsteady Stretching Vertical Surface,” Meccanica, Vol. 44, No. 4, 2009, pp. 369-375. doi:10.1007/s11012-008-9176-9

[14] F. Aman, A. Ishak and R. Nazar, “Boundary Layer Flow and Heat Transfer Adjacent to a Stretching Vertical Sheet with Prescribed Surface Heat Flux,” Matematika, Vol. 26, No. 2, 2010, pp. 197-206.

[15] S. M. Alharbi, M. A. A. Bazid and M. S. E. Gendy, “Heat and Mass Transfer in MHD Visco-Elastic Fluid Flow through a Porous Medium over a Stretching Sheet with Chemical Reaction,” Applied Mathematics, Vol. 1, No. 6, 2010, pp. 446-455. doi:10.4236/am.2010.16059

[16] I. Olajuwon, “Heat and Mass Transfer in MHD Visco-Elastic Fluid Flow through a Porous Medium over a Stretching Sheet with Chemical Reaction,” International Journal of Nonlinear Science, Vol. 7, No. 1, 2009, pp. 50-56.

[17] K. M. Chakrabarti, “Note on Boundary Layer in a Dusty Gas,” AIAA Journal, Vol. 12, No. 8, 1974, pp. 1136-1137. doi:10.2514/3.49427

[18] N. Datta and S. K. Mishra, “Boundary Layer Flow of a Dusty Fluid over a Semi-Infinite Flat Plate,” Acta Mechanica, Vol. 42, No. 1-2, 1982, pp. 71-83. doi:10.1007/BF01176514

[19] E. S. Asmolov and S. V. Manuilovich, “Stability of a Dusty Gas Laminar Boundary Layer on a Flat Plate,” Journal of Fluid Mechanics, Vol. 365, No. 1, 1998, pp. 137-170. doi:10.1017/S0022112098001256

[20] M.-L. Xie, J.-Z. Lin and F.-T. Xing, “On the Hydrodynamic Stability of a Particleladen Flow in Growing Flat Plate Boundary Layer,” Journal of Zhejiang University SCIENCE A (Springer), Vol. 8, No. 2, 2007, pp. 275-284. doi:10.1631/jzus.2007.A0275

[21] G. Palani and P. Ganesan, “Heat Transfer Effects on Dusty Gas Flow past a Semi-Infinite Inclined Plate,” Forsch Ingenieurwes (Springer), Vol. 71, No. 3-4, 2007, pp. 223-230. doi:10.1007/s10010-007-0061-9

[22] V. M. Agranat, “Effect of Pressure Gradient on Friction and Heat Transfer in a Dusty Boundary Layer,” Fluid Dynamics, Vol. 23, No. 5, 1988, pp. 729-732. doi:10.1007/BF02614150

[23] K. Vajravelu and J. Nayfeh, “Hydromagnetic Flow of a Dusty Fluid over a Stretching Sheet,” International Journal of Non-Linear Mechanics, Vol. 27, No. 6, 1992, pp. 937-945. doi:10.1016/0020-7462(92)90046-A

[24] A. Aziz, “A Similarity Solution for Laminar Thermal Boundary Layer over a Flat Plate with a Convective Surface Boundary Condition,” Communications in Nonlinear Science and Numerical, Vol. 14, No. 4, 2009, pp. 1064- 1068. doi:10.1016/j.cnsns.2008.05.003

[25] H. Schlichting, et al., “Boundary Layer Theory,” McGraw-Hill, New York, 1968.

[1] B. C. Sakiadis, “Boundary Layer Behaviour on Continuous Solid Surface,” AIChE Journal, Vol. 7, No. 1, 1961, pp. 26-28. doi:10.1002/aic.690070108

[2] 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

[3] H. I. Anderson, K. H. Bech and B. S. Dandapat, “Magnetohydrodynamic Flow of a Power-Law Fluid over a Stretching Sheet,” International Journal of Non-Linear Mechanics, Vol. 27, No. 6, 1992, pp. 929-936. doi:10.1016/0020-7462(92)90045-9

[4] A. Chakrabarti and A. S. Gupta, “Hydromagnetic Flow and Heat Transfer over a Stretching Sheet,” Quarterly of Applied Mathematics, Vol. 37, No. 1, 1979, pp. 73-78.

[5] L. J. Grubka and K. M. Bobba, “Heat Transfer Characteristics of a Continuous Stretching Surface with Variable Temperature,” Journal of Heat Transfer, Vol. 107, No. 1, 1985, pp. 248-250. doi:10.1115/1.3247387

[6] R. Cortell, “A Note on Magnetohydrodynamic Flow of a Power-Law Fluid over a Stretching Sheet,” Applied Mathematics and Computation, Vol. 168, No. 1, 2005, pp. 557-56. doi:10.1016/j.amc.2004.09.046

[7] C. H. Chen, “MHD Mixed Convection of a Power Law Fluid Past a Strtching Surface in the Presence of Thermal Radiation and Internal Heat Generation/Absorption,” International Journal of Nonlinear Mechanics, Vol. 44, No. 6, 2009, pp. 596-603.

[8] R. Cortell, “Effects of Viscous Dissipation and Work Done by Deformation on the MHD Flow and Heat Transfer of a Viscoelastic Fluid over a Stretching Sheet,” Physics Letters A, Vol. 357, No. 4-5, 2006, pp. 298-305. doi:10.1016/j.physleta.2006.04.051

[9] M. S. Abel, E. Sanjayanand and M. M. Nandeppanavar, “Viscoelastic MHD Flow and Heat Transfer over a Stretching Sheet with Viscous and Ohmic Dissipation,” Communications in Nonlinear Science and Numerical Simulation, Vol. 13, No. 9, 2008, pp. 1808-1821.

[10] M. S. Abel and N. Mahesha, “Heat Transfer in MHD Viscoelastic Fluid Flow over a Stretching Sheet with Variable Thermal Conductivity, Non-Uniform Heat Source and Radiation,” Applied Mathematical Modelling, Vol. 32, No. 10, 2008, pp. 1965-1983. doi:10.1016/j.apm.2007.06.038

[11] R. Tsai, K. H. Huang and J. S. Haung, “Flow and Heat Transfer over an Unsteady Stretching Surface with Nonuniform Heat Source,” International Communications in Heat and Mass Transfer, Vol. 35, No. 10, 2008, pp. 1340-1343. doi:10.1016/j.icheatmasstransfer.2008.07.001

[12] A. Ishak, R. Nazar and I. Pop, “Heat Transfer over an Unsteady Stretching Permeable Surface with Prescribed Wall Temperature,” Non-Linear Analysis, Real World Applications, Vol. 10, No. 5, 2009, pp. 2909-2913. doi:10.1016/j.nonrwa.2008.09.010

[13] A. Ishak, R. Nazar and I. Pop, “Boundary Layer Flow and Heat Transfer over an Unsteady Stretching Vertical Surface,” Meccanica, Vol. 44, No. 4, 2009, pp. 369-375. doi:10.1007/s11012-008-9176-9

[14] F. Aman, A. Ishak and R. Nazar, “Boundary Layer Flow and Heat Transfer Adjacent to a Stretching Vertical Sheet with Prescribed Surface Heat Flux,” Matematika, Vol. 26, No. 2, 2010, pp. 197-206.

[15] S. M. Alharbi, M. A. A. Bazid and M. S. E. Gendy, “Heat and Mass Transfer in MHD Visco-Elastic Fluid Flow through a Porous Medium over a Stretching Sheet with Chemical Reaction,” Applied Mathematics, Vol. 1, No. 6, 2010, pp. 446-455. doi:10.4236/am.2010.16059

[16] I. Olajuwon, “Heat and Mass Transfer in MHD Visco-Elastic Fluid Flow through a Porous Medium over a Stretching Sheet with Chemical Reaction,” International Journal of Nonlinear Science, Vol. 7, No. 1, 2009, pp. 50-56.

[17] K. M. Chakrabarti, “Note on Boundary Layer in a Dusty Gas,” AIAA Journal, Vol. 12, No. 8, 1974, pp. 1136-1137. doi:10.2514/3.49427

[18] N. Datta and S. K. Mishra, “Boundary Layer Flow of a Dusty Fluid over a Semi-Infinite Flat Plate,” Acta Mechanica, Vol. 42, No. 1-2, 1982, pp. 71-83. doi:10.1007/BF01176514

[19] E. S. Asmolov and S. V. Manuilovich, “Stability of a Dusty Gas Laminar Boundary Layer on a Flat Plate,” Journal of Fluid Mechanics, Vol. 365, No. 1, 1998, pp. 137-170. doi:10.1017/S0022112098001256

[20] M.-L. Xie, J.-Z. Lin and F.-T. Xing, “On the Hydrodynamic Stability of a Particleladen Flow in Growing Flat Plate Boundary Layer,” Journal of Zhejiang University SCIENCE A (Springer), Vol. 8, No. 2, 2007, pp. 275-284. doi:10.1631/jzus.2007.A0275

[21] G. Palani and P. Ganesan, “Heat Transfer Effects on Dusty Gas Flow past a Semi-Infinite Inclined Plate,” Forsch Ingenieurwes (Springer), Vol. 71, No. 3-4, 2007, pp. 223-230. doi:10.1007/s10010-007-0061-9

[22] V. M. Agranat, “Effect of Pressure Gradient on Friction and Heat Transfer in a Dusty Boundary Layer,” Fluid Dynamics, Vol. 23, No. 5, 1988, pp. 729-732. doi:10.1007/BF02614150

[23] K. Vajravelu and J. Nayfeh, “Hydromagnetic Flow of a Dusty Fluid over a Stretching Sheet,” International Journal of Non-Linear Mechanics, Vol. 27, No. 6, 1992, pp. 937-945. doi:10.1016/0020-7462(92)90046-A

[24] A. Aziz, “A Similarity Solution for Laminar Thermal Boundary Layer over a Flat Plate with a Convective Surface Boundary Condition,” Communications in Nonlinear Science and Numerical, Vol. 14, No. 4, 2009, pp. 1064- 1068. doi:10.1016/j.cnsns.2008.05.003

[25] H. Schlichting, et al., “Boundary Layer Theory,” McGraw-Hill, New York, 1968.