Unsteady Mixed Convective Heat Transfer of Two Immiscible Fluids Confined Between a Long Vertical Wavy Wall and a Parallel Flat Wall

J.C.Umavathi; LIU I-chung; M.Shekar

doi:10.3879/j.issn.1000-0887.2012.07.008

Volume 33 Issue 7

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2012 > 33(7): 877-895

J.C.Umavathi, LIU I-chung, M.Shekar. Unsteady Mixed Convective Heat Transfer of Two Immiscible Fluids Confined Between a Long Vertical Wavy Wall and a Parallel Flat Wall[J]. Applied Mathematics and Mechanics, 2012, 33(7): 877-895. doi: 10.3879/j.issn.1000-0887.2012.07.008

Citation:

PDF( 2533 KB)

Unsteady Mixed Convective Heat Transfer of Two Immiscible Fluids Confined Between a Long Vertical Wavy Wall and a Parallel Flat Wall

doi: 10.3879/j.issn.1000-0887.2012.07.008

¹Department of Mathematics, Gulbarga University, Gulbarga, Karnataka 585 106, India;²Department of Civil Engineering,National Chi Nan University, University Road, Puli, Nantou54561, Taiwan, China

Received Date: 2011-05-18
Rev Recd Date: 2011-12-28
Publish Date: 2012-07-15

Abstract

Abstract

An analysis on the combined effects of thermal and mass convection of viscous incompressible, immiscible fluids through a vertical wavy wall and a smooth flat wall was performed. The dimensionless governing equations were perturbed into: mean part (zeroth order) and a perturbed part (first order). The first order quantities were obtained by perturbation series expansion for short wavelength, in which terms of exponential order arise. Analytical expressions for the zeroth order, first order and the total solutions were obtained.The numerical computations were presented graphically to show salient features of the fluid flow and heat transfer characteristics. Separate solutions were matched at the interface by using suitable matching conditions. The shear stress and the Nusselt number were also analyzed for different variations of the governing parameters. It is observed that Grashof number, viscosity ratio, width ratio and conductivity ratio promote the velocity parallel to the flow direction. A reversal effect is observed for the velocity perpendicular to the flow direction.
- mixed convection,
- wavy wall,
- immiscible fluids,
- perturbation method

FullText(HTML)

References(29)

References

[1]	Chiu C P, Chou H M. Transient analysis of natural convection along a vertical wavy surface in micropolar fluids[J]. International Journal of Engineering Science, 1994, 32(1): 19-33.
[2]	Rees D A S, Pop I. A note on free convection along a vertical wavy surface in a porous medium[J]. American Society of Mechanical Engineers Journal of Heat Transfer, 1994, 116(2): 505-508.
[3]	Rees D A S, Pop I. Free convection induced by a vertical wavy surface with uniform heat flux in a porous medium[J]. American Society of Mechanical Engineers Journal of Heat Transfer, 1995, 117(2): 547-550.
[4]	Yang Y T, Chen C K, Lin M T. Natural convection of non-Newtonian fluids along a wavy vertical plate including the magnetic field effect[J]. International Journal of Heat and Mass Transfer, 1996, 39(13): 2831-2842.
[5]	Yao L S. Natural convection along a vertical complex wavy surface[J]. International Journal of Heat and Mass Transfer, 2005, 49 (1/2): 281-286.
[6]	Yao L S. Natural convection along a wavy surface[J]. American Society of Mechanical Engineers Journal of Heat Transfer, 1983, 105: 465-468.
[7]	Yao L S. A note on Prandtl’s transposition theorem[J]. American Society of Mechanical Engineers Journal of Heat Transfer, 1988, 110: 503-507.
[8]	Yao L S, Moulic S G. Mixed convection along a wavy surface[J]. American Society of Mechanical Engineers Journal of Heat Transfer, 1989, 111: 974-979.
[9]	Vajravelu K, Sastri K S. Free convective heat transfer in a viscous incompressible fluid confined between a long vertical wavy wall and a parallel flat wall[J]. Journal of Fluid Mechanics, 1978, 80(2): 365-383.
[10]	Chen C K, Wang C C. Transient analysis of force convection along a wavy surface in micropolar fluids[J]. American Institute of Aeronautics and Astronautics Journal of Thermophysics and Heat Transfer, 2000, 14(3): 340-347.
[11]	Chen C K, Wang C C. Transient force and free convection along a vertical wavy surface in micropolar fluids[J]. International Journal of Heat and Mass Transfer, 2001, 44(17): 3241-3251.
[12]	Cheng C Y. Natural convection heat and mass transfer near a vertical wavy surface with constant wall temperature and concentration in a porous medium[J]. International Communications in Heat and Mass Transfer, 2000, 27(8): 1143-1154.
[13]	Cheng C Y. Natural convection heat and Mass transfer near a wavy cone with constant wall temperature and concentration in a porous medium[J]. Mechanics Research Communications, 2000, 27(5): 613-620.
[14]	Malashetty M S, Umavathi J C, Leela V. Magnetoconvective flow and heat transfer between vertical wavy wall and a parallel flat wall[J]. International Journal of Applied Mechanics and Engineering, 2001, 6(2): 437-456.
[15]	Fasogbon P F.Analytical studies of heat and mass transfer by free convection in a two-dimensional irregular channel[J]. International Journal of Applied Mechanics and Engineering, 2010, 6(4): 17-37.
[16]	Batchelor G K. An Introduction to Fluid Dynamics[M]. Cambridge: Cambridge University Press, 1967.
[17]	Ishii M. Thermo-Fluid Dynamic Theory of Two-Phase Flow[M]. Paris: Eyrolles,1975.
[18]	Meyer H I, Garder A O. Mechanics of two immiscible fluids in porous media[J]. Journal of Applied Physics, 1954, 25(11): 1400-1406.
[19]	Loharsbi J, Sahai V. Magnetohydrodynamic heat transfer in two phase flow between parallel plates[J]. Applied Scientific Research, 1988, 45(1): 53-66.
[20]	Packham B A, Shail R. Stratified laminar flow of two immiscible fluids[J]. Proceedings of Cambridge Philosophical Society, 1971, 69(3): 443-448.
[21]	Malashetty M S, Leela V. Magnetohydrodynamic heat transfer in two phase flow[J]. International Journal of Engineering Science, 1992, 30(3): 371-377.
[22]	Malashetty M S, Umavathi J C, Prathap Kumar J. Convective flow and heat transfer in an inclined composite porous medium[J]. Journal Porous Media, 2001, 4(1): 15-22.
[23]	Malashetty M S, Umavathi J C, Prathap Kumar J. Two fluid flow and heat transfer in an inclined composite porous and fluid layer[J]. Heat and Mass Transfer, 2004, 40: 871-876.
[24]	Umavathi J C, Chamkha A J, Mateen A, Al-Mudhaf A. Unsteady two fluid flow and heat transfer in a horizontal channel[J]. Heat and Mass Transfer, 2005, 42(2): 81-90.
[25]	Umavathi J C, Chamkha A J, Mateen A, Prathap Kumar J. Unsteady magneto hydrodynamic two fluid flow and heat transfer in a horizontal channel[J]. International Journal of Heat and Technology, 2008, 26: 121-133.
[26]	Umavathi J C, Manjula M H, Pop I, Liu I C. Flow and heat transfer of couple stress viscous fluids in a vertical channel[J]. International Journal of Applied Mechanics and Engineering, 2007, 12(2): 537-555.
[27]	Kumar J P, Umavathi J C, Biradar B M. Mixed convective flow of immiscible viscous fluids in a vertical channel[J]. Heat Transfer—Asian Research, 2011, 40(1): 1-25.
[28]	Soundalgekar V M, Deka R K, Das U N. Transient free convection flow of a viscous incompressible fluid past an infinite vertical plate with periodic heat flux[J]. Indian Journal Engineering and Material Sciences, 2003, 10(5): 390-396.
[29]	Ostrach S. An Analysis of Laminar Free-Convection Flow and Heat Transfer About a Flat Plate Parallel to the Direction of the Generating Body Force[M]. NACA, TN-2635, Accession number -93R12788, Documentation ID-19930083498 ,1952.