Viscoelastic Effects on Unsteady Two-Dimensional and Mass Transfer of a Viscoelastic Fluid in a Porous Channel with Radiative Heat Transfer

Utpal Jyoti Das

.

DOI: 10.4236/eng.2013.51011                

Abstract

An analysis of oscillatory flow of a viscoelastic fluid and mass transfer along a porous oscillating channel with radiative heat transfer in presence of first-order chemical reaction is considered. The problem is concerned with the flow through a channel in which the viscoelastic fluid is injected on one boundary of the channel with a constant velocity, while it is sucked off at the other boundary with the same velocity. The two boundaries are considered to be in close contact with the two plates placed parallel to each other. The effect of temperature oscillations at the plate (upper wall) where the suction takes place is taken into consideration. The plates are supposed to be oscillating with a given velocity in their own planes. Analytical expressions for velocity profile, the temperature, concentration profile, wall shear stress on the upper wall are obtained. The profiles of the velocity and skin friction have been presented graphically for different values of the viscoelastic parameters with the combination of the other flow parameters encountered in the problem under investigation. It is observed that velocity decrease with the increasing values of the viscoelastic parameter in comparison with Newtonian fluid. Also, the wall shear stress increase with the increasing values of the viscoelastic parameter.

Keywords

Viscoelastic Fluid; First-Order Chemical Reaction; Porous Wall; Oscillating Channel; Radiative Heat Transfer

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	C. Y. Wang, “Pulsatile Flow in a Porous Channel,” Journal of Applied Mechanics, Vol. 38, No. 2, 1971, pp. 553555. doi:10.1115/1.3408822
[2]	B. C. Bhuyan and G. C. Hazarika, “Effect of Magnetic Field on Pulsatile Flow Blood in a Porous Channel,” BioScience Research Bulletin, Vol. 17, No. 2, 2001, pp. 105112.
[3]	A. Raptis, “Unsteady Free Convective Flow and Mass Transfer through a Porous Medium Bounded by an Infinite Vertical Limiting Surface with Constant Suction and Time-Dependent Temperature,” International Journal of Energy Research, Vol. 7, No. 4, 1983, pp. 385-389. doi:10.1002/er.4440070409
[4]	P. C. Ram, “Effect of Hall Current and Wall Temperature Oscillation on Convective Flow in a Rotating Fluid through Porous Medium,” Heat and Mass Transfer, Vol. 25, No. 4, 1990, pp. 205-208.
[5]	O. D. Makinde and P. Y. Mhone, “Heat Transfer to MHD Oscillatory Flow in a Channel Filled with Porous Medium,” Romanian Journal Physics, Vol. 20, 2005, pp. 931-938.
[6]	J. Prakash and A. Ogulu, “A Study of Pulsatile Blood Flow Modeled as a Power Law Fluid in a Constricted Tube,” International Communications in Heat and Mass Transfer, Vol. 34, No. 6, 2007, pp. 762-768.
[7]	A. Mehmood and A. Ali, “The Effect of Slip Condition on Unsteady MHD Oscillatory Flow of a Viscoelastic Fluid in a Planar Channel,” Romanian Journal Physics, Vol. 52, 2007, pp. 85-91.
[8]	S. D. Adhikary and J. C. Misra, “Unsteady Two-Dimensional Hydromagnetic Flow and Heat Transfer of a Fluid,” International Journal of Applied Mathematics and Mechanics, Vol. 7, No. 4, 2011, pp. 1-20.
[9]	S. K. Ghosh, “Hydromagnetic Fluctuating Flow of a Viscoelastic Fluid in a Porous Channel,” Journal of Applied Mechanics, Vol. 74, No. 2, 2007, pp. 177-180. doi:10.1115/1.2062828
[10]	V. M. Soundalgekar, R. M. Lahurikar, S. G. Pohanerkar and N. S. Birajdar, “Effects of Mass Transfer on the Flow Past an Oscillating Infinite Vertical Plate with Constant Heat Flux,” Thermophysics and Aero Mechanics, Vol. 1, 1994, pp. 119-124.
[11]	Y. J. Kim and J. C. Lee, “Analytical Studies on MHD Oscillatory Flow of a Micropolar Fluid over a Vertical Porous Plate,” Surface and Coating Technology, Vol. 171, No. 1-3, 2003, pp. 187-193. doi:10.1016/S0257-8972(03)00268-8
[12]	A. J. Chamkha, “Unsteady MHD Convective Heat and Mass Transfer Past a Semi-Infinite Vertical Permeable Moving Plate with Heat Absorption,” International Journal of Engineering Sciences, Vol. 42, No. 2, 2004, pp. 217-230. doi:10.1016/S0020-7225(03)00285-4
[13]	B. D. Coleman and H. Markovitz, “Incompressible Second-Order Fluids,” Advances in Applied Mechanics, Vol. 8, 1964, pp. 69-101. doi:10.1016/S0065-2156(08)70353-3
[14]	B. D. Coleman and W. Noll, “An Approximation Theorem for Functionals with Applications in Continuum Mechanics,” Archive for Rational Mechanics Analysis, Vol. 6, No. 1, 1960, pp. 355-374. doi:10.1007/BF00276168
[15]	A. C. L. Cogley, W. G. Vincenti and E. S. Giles, “Differential Approximation for Radiative Heat Transfer in a Non-Linear Equation Grey Gas near Equilibrium,” AIAA Journal, Vol. 6, 2007, pp. 551-553.