Boundary Layer Flow of an Unsteady Dusty Fluid and Heat Transfer Over a Stretching Sheet with Non-Uniform Heat Source/Sink

Bijjanal J. Gireesha, Govinakovi S. Roopa, Channabasappa S. Bagewadi

.

DOI: 10.4236/eng.2011.37087                

Abstract

An analysis has been carried out to study the effect of hydrodynamic laminar boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface in the presence of non-uniform heat source/sink. Heat transfer characteristics are examined for two different kinds of boundary conditions, namely 1) variable wall temperature and 2) variable heat flux. The governing partial differential equations are transformed to system of ordinary differential equations. These equations are solved numerically by applying RKF-45 method. The effects of various physical parameters such as magnetic parameter, dust interaction parameter, number density, Prandtl number, Eckert number, heat source/sink parameter and unsteadiness parameter on velocity and temperature profiles are studied.

Keywords

Unsteady Flow, Heat Transfer, Boundary Layer Flow, Stretching Surface, Dusty Fluid, Fluid-Particle Interaction Parameter and Non-Uniform Heat Source/Sink

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	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
[2]	L. J. Grubka and K. M. Bobba, “Heat Transfer Characteristics of a Continuous, Stretching Surface with Variable Temperature,” International Journal of Heat and Mass Transfer, Vol. 107, No. 1, 1985, pp. 248-250.
[3]	L. J. Crane, “Flow Past a Stretching Plate,” Zeitschrift fr angewandte Mathematik und Physik (ZAMP), Vol. 21, No. 4, 1970, pp. 645-647.
[4]	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
[5]	C. H. Chen, “Laminar Mixed Convection Adjacent to Vertical Continuously Stretching Sheets,” Heat Mass Transfer, Vol. 33, No. 5-6, 1998, pp. 471-476. doi:10.1007/s002310050217
[6]	M. S. Abel, P. G. Siddeshwar and M. M. Nandeppanavar, “Heat Transfer in a Viscoelastic Boundary Layer Flow over a Stretching Sheet with Viscous Dissipation and Non-Uniform Heat Source,” International Journal of Heat and Mass Transfer, Vol. 50, No. 5-6, 2007, pp. 960-966. doi:10.1016/j.ijheatmasstransfer.2006.08.010
[7]	A. Ishak, R. Nazar and I. Pop, “Hydromagnetic Flow and Heat Transfer Adjacent to a Stretching Vertical Sheet,” Heat Mass Transfer, Vol. 44, No. 8, 2008, pp. 921-927. doi:10.1007/s00231-007-0322-z
[8]	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 Simulation, Vol. 14, No. 4, 2009, pp. 1064-1068. doi:10.1016/j.cnsns.2008.05.003
[9]	E. M. A. Elbashbeshy and M. A. A. Bazid, “Heat Transfer in a Porous Medium over a Stretching Sheet with Internal Generation and Suction or Injection,” Applied Mathematics and Computation, Vol. 158, No. 3, 2004, pp. 799-807. doi:10.1016/j.amc.2003.08.141
[10]	H. I. Andersson, J. B. Aareseth and B. S. Dandapat, “Heat Transfer in a Liquid Film on an Unsteady Stretching Surface,” International Journal of Heat and Mass Transfer, Vol. 43, No. 1, 2000, pp. 69-74. doi:10.1016/S0017-9310(99)00123-4
[11]	E. M. A. Elbashbeshy and M. A. A. Bazid, “Heat Transfer over an Unsteady Stretching Surface,” Heat and Mass Transfer, Vol. 41, No. 1, 2004, pp. 1-4. doi:10.1007/s00231-004-0520-x
[12]	S. Sharidan, T. Mahmood and I. Pop, “Similarity Solutions for the Unsteady Boundary Layer Flow and Heat Transfer Due to a Stretching Sheet,” International Journal of Applied Mechanics and Engineering, Vol. 11, No. 3, 2008, pp. 647-654.
[13]	R. Tsai, K. H. Huang and J. S. Huang, “Flow and Heat Transfer over an Unsteady Stretching Surface with a Non-Uniform 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
[14]	A. Ishak, R. Nazar and I. Pop, “Heat Transfer over an Unsteady Stretching Permeable Surfaec 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
[15]	S. Mukhopadhyay and H. I. Andersson, “Effect of Slip and Heat Transfer Analysis of Flow over an Unsteady Stretching Surface,” Heat Mass Transfer, Vol. 45, No. 11, 2009, pp. 1447-1452. doi:10.1007/s00231-009-0516-7
[16]	D. Pal and P. S. Hiremath, “Computational Modelling of Heat Transfer over an Unsteady Stretching Surface Embedded in a Porous Medium,” Meccanica, Vol. 45, No. 3, 2010, pp. 415-424. doi:10.1007/s11012-009-9254-7
[17]	H. Schlichting, “Boundary Layer Theory,” McGraw-Hill, New York, 1968.