The effect of vertical throughflow in Rivlin–Ericksen elasticoviscous nanofluid in a nonDarcy porous medium
https://doi.org/10.17586/22208054201785606612
Abstract
The instability of convection in a Rivlin–Ericksen elasticoviscous nanofluid with vertical throughflow is investigated using the linear stability theory. A modified Brinkman model is employed and singleterm Galerkin method is used to solve the conservation equations. Nine dominating parameters are extracted from the analysis. Due to the combined effect of vertical throughflow, Brownaian motion, and thermophoresis, the Rayleigh number is reduced by a substantial amount. It is found that through flow delays the convection while other nanofluid parameter enhance the convection. The thermal capacity ratio, kinematics viscoelasticity, and Vadasz number do not govern stationary convection. Using the convective component of nanoparticle flux, the critical wave number is a function of nanofluid parameters as well as throughflow parameter. Major trends are investigated briefly by plotting the graphs.
About the Authors
S. Saini
Department of Mathematics, National Institute of Technology Hamirpur
India
India
Hamirpur (H.P.), India177005
Y. D. Sharma
Department of Mathematics, National Institute of Technology Hamirpur
India
India
Hamirpur (H.P.), India177005
References
1. Rivlin R., Ericksen J. StressDeformation Relations for Isotropic Materials. J. Ration Mec.h Anal., 1955, 4(2), P. 323–425.
2. Rudraiah N., Kaloni P.N., Radhadevi P.V. Oscillatory convection in a viscoelastic fluid through a porous layer heated from below. Rheologica Acta., 1989, 28(1), P. 48–53.
3. Kim M.C., Lee S.B., Chung B.J. Thermal instability of viscoelastic fluids in porous media. Int. J. Heat Mass Transf., 2003, 46, P. 5065– 5072.
4. Sharma R.C., Kumar P. Effect of Rotation on Thermal Instability in RivlinEricksen elasticoviscous Fluid. Zeitschrift f¨ur Naturforschung A., 1996, 51(7), P. 821–824.
5. Sharma R.C., Kumar P. Thermal Instability in RivlinEricksen elasticoviscous Fluid in Hydromagnetic. Z. Naturforsch., 1997, 52a, P. 369–371.
6. Sheu L.J. Thermal Instability in a Porous Medium Layer Saturated with a ViscoElastic Nanofluid. Transp. Porous Med., 2011, 88, P. 461–477.
7. Sheu L.J. Linear Stability of Convection in a Visco Elastic Nanofluid Layer. World Acad. Sci. Eng. Technol., 2011, 58, P. 289–295.
8. Choi S. Enhancing Thermal Conductivity of Fluids with Nanoparticles in Developments and Applications of NonNewtonian Flows. ASME, 1995, 66, P. 99–105.
9. Buongiorno J. Connective Transport in nanofluids. J. Heat Transf., 2006, 128, P. 240–250.
10. Nield D.A., Kuznetsov A.V. Thermal instability in a porous medium layer saturated by a nanofluid. Int .J. Heat Mass Transf., 2009, 52, P. 5796–5801.
11. Nield D.A., Kuznetsov A.V. The onset of convection in a horizontal layer of finite depth. Eur. J. Mech. B/Fluids, 2010, 29, P. 217–223.
12. Homsy G.M., Sherwood A.E. Convective instabilities in porous media with throughflow. AIChE J., 1976, 22, P. 168–174.
13. Jones M.C., Persichetti J.M. Convective instability in packed beds with throughflow. AIChE J., 1986, 32, P. 1555–1557.
14. Nield D.A. Convective instability in porous media with throughflow. AIChE J., 1987, 33, P.1222–1224.
15. Barletta A., di Schio E. R., Storesletten L. Convective roll instabilities of vertical throughflow with viscous dissipation in a horizontal porous layer. Transp. Porous Med., 1986, 81, P. 461–77.
16. Nield D.A., Kuznetsov A.V. The effect of vertical through flow on thermal instability in a porous medium layer saturated by a nanofluid. Transp. Porous Med., 2011, 87, P. 765–775.
17. Nield D.A., Kuznetsov A.V. The onset of convection in a layered porous medium with vertical throughflow. Transp. Porous Med. 2013, 98, P. 363–376.
18. Nield D.A., Kuznetsov A.V. The effect of vertical throughflow on thermal instability in a porous medium layer saturated by a nanofluid: a revised model. ASME J. Heat Transf., 2015, 137, P. 052601.
19. Khalili A., Shivakumara I.S. Onset of convection in a porous layer with net throughflow and internal heat generation. Phys Fluids, 1998, 10, P. 315.
20. Nield D.A., Kuznetsov A.V. The effects of combined horizontal and vertical heterogeneity on the onset of convection in a porous medium with horizontal throughflow. Int. J. Heat Mass Transf., 2010, 54, P. 5595–5601.
Review
For citations:
Saini S., Sharma Y.D. The effect of vertical throughflow in Rivlin–Ericksen elasticoviscous nanofluid in a nonDarcy porous medium. Nanosystems: Physics, Chemistry, Mathematics. 2017;8(5):606-612. https://doi.org/10.17586/22208054201785606612
Views:
8
Email this article 