Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T03:21:11.316Z Has data issue: false hasContentIssue false
  • English
  • Français

Poiseuille-Couette Flow and Heat Transfer in an Inclined Channel for Composite Porous Medium

Published online by Cambridge University Press:  22 March 2012

I-C. Liu ,
H.-H. Wang  and
J. C. Umavathi
I-C. Liu*
Affiliation:
Department of Civil Engineering, National Chi Nan University, Nantou, Taiwan 54561, R.O.C.
H.-H. Wang
Affiliation:
Department of Civil Engineering, National Chi Nan University, Nantou, Taiwan 54561, R.O.C.
J. C. Umavathi
Affiliation:
Department of Mathematics, Gulbarga University, Gulbarga, Karnataka 585106, India
*
*Corresponding author ([email protected])
Get access

Abstract

Convective flow and heat transfer in an inclined channel bounded by two rigid plates is studied, where the lower plate is fixed and upper plate is moving with a constant velocity. One of the regions filled with clear viscous fluid and the other region filled with the porous matrix saturated with a viscous fluid different from the fluid in the first region are considered. The coupled nonlinear equations are mainly solved numerically using finite difference method. It is found that the presence of porous matrix in one of the region reduces the velocity and temperature. Both the velocity and temperature profiles enhance as the values of buoyancy parameter GP, height ratio h, Brinkman number Br, density ratio n and thermal expansion ratio b increase but reduce as the values of porous parameter σ, viscosity ratio λand thermal conductivity ratio λT increase. The Nusselt numbers at upper plate diminish as GP, h and Br increase, whereas they increase as σ, λ and λT increase. The lower plate Nusselt numbers are reversely affected by the relevant parameters. The effect of σ and GP on shear stress profiles are drawn and discussed.

Keywords

Inclined channelPoiseuille-Couette flowHeat transferImmiscible fluidsViscous dissipation
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 1 , March 2012 , pp. 171 - 178
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Poulikakos, D., Bejan, A., Selimos, B. and Blake, K. R., “High Rayleigh Number Convection in a Fluid Overlaying a Porous Bed,” International Journal of Heat and Fluid Flow, 7, pp. 109–116 (1986).CrossRefGoogle Scholar
2. Sathe, S. B., Lin, W. Q. and Tong, T. W., “Natural Convection in Enclosures Containing an Insulation with a Permeable Fluid-Porous Interface,” International Journal of Heat and Fluid Flow, 9, pp. 389–395 (1988).Google Scholar
3. Beckermann, C., Viskanta, R. and Ramadhyani, S., “Natural Convection in Vertical Enclosures Containing Simultaneously Fluid and Porous Layers,” Journal of Fluid Mechanics, 186, pp. 257–284 (1988).Google Scholar
4. Beckermann, C., Ramadhyani, S. and Viskanta, R., “Natural Convection Flow and Heat Transfer Between a Fluid Layer and a Porous Layer Inside a Rectangular Enclosure,” Journal of Heat Transfer, ASME, 109, pp. 363–370 (1987).CrossRefGoogle Scholar
5. Prasad, V., “Convective Flow Interaction and Heat Transfer Between Fluid and Porous Layers,” Proceedings of NATO, ASI Convective Heat and Mass Transfer in Porous Medium, Izmir, Turkey, pp. 563–615 (1991).CrossRefGoogle Scholar
6. Beavers, G. S. and Joseph, D. D., “Boundary Conditions at a Naturally Permeable Wall,” Journal of Fluid Mechanics, 30, pp. 197–207 (1967).Google Scholar
7. Neale, G. and Nader, W., “Practical Significance of Brinkman's Extension of Darcy's Law: Coupled Parallel Flows Within a Channel and a Bounding Porous Medium,” Canadian Journal of Chemical Engineering, 52, pp. 475–478 (1974).CrossRefGoogle Scholar
8. Vafai, K. and Kim, S. J., “Fluid Mechanics of the Interface Region Between a Porous Medium and a Fluid Layer—An Exact Solution,” International Journal of Heat and Fluid Flow, 11, pp. 254–256 (1990).CrossRefGoogle Scholar
9. Vafai, K. and Thiyagaraja, R., “Analysis of Flow and Heat Transfer at the Interface Region of a Porous Medium,” International Journal of Heat and Mass Transfer, 30, pp. 1391–1405 (1987).CrossRefGoogle Scholar
10. Alazmi, B. and Vafai, K., “Analysis of Fluid Flow and Heat Transfer Interfacial Conditions Between a Porous Medium and a Fluid Layer,” International Journal of Heat and Mass Transfer, 44, pp. 1735–1749 (2001).CrossRefGoogle Scholar
11. Bhargava, S. K. and Sacheti, N. C., “Heat Transfer in Generalized Couette Flow of Two Immiscible Newtonian Fluids Through a Porous Channel: Use of Brinkman Model,” Indian Journal of Technology, 27, pp. 211–214 (1989).Google Scholar
12. Daskalakis, J., “Couette Flow Through a Porous Medium of a High Prandtl Number Fluid with Temperature-Dependent Viscosity,” International Journal of Energy Research, 14, pp. 21–26 (1990).CrossRefGoogle Scholar
13. Nakayama, A., “Non-Darcy Couette Flow in a Porous Medium Filled with an Inelastic Non-Newtonian Fluid,” Journal of Fluids Engineering, ASME, 114, pp. 642–647 (1992).Google Scholar
14. Kakac, S., Kilkis, B., Kulacki, F. A. and Arnic, F., Convective Heat and Mass Transfer in Porous Media, Kluwer, Boston (1991).Google Scholar
15. Ochoa-Tapia, J. A. and Whitaker, S., “Momentum Transfer at the Boundary Between a Porous Medium and a Homogeneous Fluid-I: Theoretical Development,” International Journal of Heat and Mass Transfer, 38, pp. 2635–2646 (1995).CrossRefGoogle Scholar
16. Ochoa-Tapia, J. A. and Whitaker, S., “Momentum Transfer at the Boundary Between a Porous Medium and a Homogeneous Fluid-II: Comparison with Experiment,” International Journal of Heat and Mass Transfer, 38, pp. 2647–2655 (1995).Google Scholar
17. Kuzentsov, A. K., “Analytical Investigation of Couette Flow in a Composite Channel Partially Filled with a Porous Medium and Partially with a Clear Fluid,” International Journal of Heat and Mass Transfer, 41, pp. 2556–2560 (1998).Google Scholar
18. Malashetty, M. S. and Umavathi, J. C., “Two-Phase Magnetohydrodynamic Flow and Heat Transfer in an Inclined Channel,” International Journal of Multiphase Flow, 23, pp. 545–560 (1997).Google Scholar
19. Umavathi, J. C., Mateen, A., Chamka, A. J. and Al-Mudhaf, A., “Oscillatory Flow and Heat Transfer in a Horizontal Composite Porous Medium,” International Journal of Heat and Technology, 24, pp. 75–86 (2007).Google Scholar
20. Umavathi, J. C., Liu, I.-C. and Kumar, J. P., “Magnetohydrodynamic Poiseuille-Couette Flow and Heat Transfer in an Inclined Channel,” Journal of Mechanics, 26, pp. 525–532 (2010)CrossRefGoogle Scholar
21. Rajagopal, K., Ruzicka, M. and Srinivasa, A. R., “On the Oberbeck-Boussinesq Approximation,” Mathematical Models and Methods in Applied Sciences, 6, pp. 1157–1167 (1996).CrossRefGoogle Scholar