Green-Naghdi fluid with non-thermal equilibrium effects

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 466, Issue 2119, 2010, Pages 2021-2032

  Straughan, B ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Green Naghdi fluid; Nanofluid suspension; Thermal convection; Thermal instability

Indexed keywords

CONTINUUM MECHANICS; ELASTICITY; ETHYLENE; ETHYLENE GLYCOL; FLUIDS; HEAT CONVECTION; NON NEWTONIAN FLOW; NUMERICAL ANALYSIS; SUSPENSIONS (FLUIDS); THERMODYNAMIC STABILITY; VORTICITY;

GREEN-NAGHDI; GREEN-NAGHDI FLUID; NANOFLUID SUSPENSIONS; THERMAL CONVECTIONS; THERMAL INSTABILITIES;

NANOFLUIDICS;

EID: 77955209962     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2009.0523     Document Type: Article

References (43)

1. Accuratus 2009 Aluminum oxide, Al2O3. See http://www.accuratus.com/ alumox.html
2. Banu, N. & Rees, D. A. S. 2002 Onset of Darcy-Bénard convection using a thermal non-equilibrium model. Int. J. Heat Mass Transf. 45, 2221-2228. (doi:10.1016/S0017-9310(01)00331-3)
3. Bleustein, J. L. & Green, A. E. 1967 Dipolar fluids. Int. J. Eng. Sci. 5, 323-340. (doi:10.1016/ 0020-7225(67)90041-9)
4. Chandrasekhar, S. 1981 Hydrodynamic and hydromagnetic stability. New York, NY: Dover.
5. Chandrasekharaiah, D. S. 1998 Hyperbolic thermoelasticity: a review of recent literature. Appl. Mech. Rev. 51, 705-729. (doi:10.1115/1.3098984)
6. Dongarra, J. J., Straughan, B. & Walker, D. W. 1996 Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems. Appl. Numer. Math. 22, 399-435. (doi:10.1016/S0168-9274(96)00049-9) (Pubitemid 126375600)
7. Dow 2009 Ethylene glycols: physical properties. See http://www.dow.com/ ethyleneglycol/about/ properties.htm
8. Engineering Toolbox 2009 Water: thermal properties. See http://www.engineeringtoolbox.com/ water-thermal-properties-d-162.html
9. Frohlich, H. & Sack, R. 1946 Theory of the rheological properties of dispersions. Proc. R. Soc. Lond. A 185, 415-430. (doi:10.1098/rspa.1946.0028)
10. Green, A. E. & Naghdi, P. M. 1991 A re-examination of the basic postulates of thermomechanics. Proc. R. Soc. Lond. A 432, 171-194. (doi:10.1098/rspa.1991.0012)
11. Green, A. E. & Naghdi, P. M. 1995a A unified procedure for construction of theories of deformable media. I. Classical continuum mechanics. Proc. R. Soc. Lond. A 448, 335-356. (doi:10.1098/ rspa.1995.0020)
12. Green, A. E. & Naghdi, P. M. 1995b A unified procedure for construction of theories of deformable media. II. Generalised continua. Proc. R. Soc. Lond. A 448, 357-377. (doi:10.1098/ rspa.1995.0021)
13. Green, A. E. & Naghdi, P. M. 1995c A unified procedure for construction of theories of deformable media. III. Mixtures of interacting continua. Proc. R. Soc. Lond. A 448, 379-388. (doi:10.1098/rspa.1995.0022)
14. Green, A. E. & Naghdi, P. M. 1996 An extended theory for incompressible viscous fluid flow. J. Non-Newton. Fluid Mech. 66, 233-255.
15. Green, A. E. & Rivlin, R. S. 1964 Multipolar continuum mechanics. Arch. Ration. Mech. Anal. 17, 113-147. (doi:10.1007/BF00253051)
16. Hetnarsky, R. B. & Ignaczak, J. 1999 Generalized thermoelasticity. J. Therm. Stresses 22, 451-476. (doi:10.1080/014957399280832)
17. Hwang, K. S., Lee, J. H., Jang, S. P. 2007 Buoyancy-driven heat transfer of water-based Al2O3 nanofluids in a rectangular cavity. Int. J. Heat Mass Transf. 50, 4003-4010. (doi:10.1016/ j.ijheatmasstransfer.2007.01.037)
18. Jordan, P. M. & Puri, P. 2002 Exact solutions for the unsteady plane Couette flow of a dipolar fluid. Proc. R. Soc. Lond. A 458, 1245-1272. (doi:10.1098/rspa.2001.0917)
19. Kim, S. H., Choi, S. R. & Kim, D. 2007 Thermal conductivity of metal-oxide nanofluids: particle size dependence and effect of laser irradiation. Trans. ASME 129, 298-307. (doi:10.1115/1.2427071) (Pubitemid 47315820)
20. Kulkarni, D. P., Vajjha, R. S., Das, D. K. & Oliva, D. 2008 Application of aluminium oxide nanofluids in diesel electric generator as jacket water coolant. Appl. Therm. Eng. 28, 1774-1781. (doi:10.1016/j.applthermaleng. 2007.11.017)
21. Kuznetsov, A. V. & Nield, D. A. 2010 Thermal instability in a porous medium layer saturated by a nanofluid: Brinkman model. Transport Porous Media 81, 409-422. (doi:10.1007/ s11242-009-9413-9422)
22. Kuznetsov, A. V. & Nield, D. A. In press. Effect of thermal non-equilibrium on the onset of convection in a porous medium layer saturated by a nanofluid. Transport Porous Media (doi:10.1007/s11242-009-9452-8)
23. Kwak, K. & Kim, C. 2005 Viscosity and thermal conductivity of copper oxide nanofluid dispersed in ethylene glycol. Korea Aust. Rheol. J. 17, 35-40.
24. Maïga, S. E. B., Palm, S. J., Nguyen, C. T., Roy, G. & Galanis, N. 2005 Heat transfer enhancement by using nanofluids in forced convection flows. Int. J. Heat Fluid Flow 26, 530-546. (doi:10.1016/j.ijheatfluidflow.2005. 02.004) (Pubitemid 40960334)
25. Malashetty, M. S., Shivakumara, I. S. & Kulkarni, S. 2005 The onset of Lapwood-Brinkman convection using a non-equilibrium model. Int. J. Heat Mass Transf. 48, 1155-1163. (doi:10.1016/j.ijheatmasstransfer.2004.09.027) (Pubitemid 40231276)
26. Marshall, J. S. & Naghdi, P. M. 1989a A thermodynamical theory of turbulence. I. Basic developments. Proc. R. Soc. Lond. A 327, 415-448. (doi:10.1098/rsta.1989.0001)
27. Marshall, J. S. & Naghdi, P. M. 1989b A thermodynamical theory of turbulence. II. Determination of constitutive coefficients and illustrative examples. Proc. R. Soc. Lond. A 327, 449-475. (doi:10.1098/rsta.1989.0002)
28. Masoumi, M., Sohrabi, N. & Behzadmehr, A. 2009 A new model for calculating the effective viscosity of nanofluids. J. Phys. D Appl. Phys. 42, 055 501.
29. Nield, D. A. 2002 A note on the modeling of local thermal non-equilibrium in a saturated porous medium. Int. J. Heat Mass Transf. 45, 4367-4368. (doi:10.1016/S0017-9310(02)00138-2) (Pubitemid 34878024)
30. Nield, D. A. & Bejan, A. 2006 Convection in porous media, 3rd edn. New York, NY: Springer.
31. Nield, D. A. & Kuznetsov, A. V. 1999 Local thermal non-equilibrium effects in forced convection in a porous medium channel: a conjugate problem. Int. J. Heat Mass Transf. 42, 3245-3252. (doi:10.1016/S0017-9310(98)00386-X) (Pubitemid 29388809)
32. Puri, P. & Jordan, P. M. 2006 On the steady shear flow of a dipolar fluid in a porous half-space. Int. J. Eng. Sci. 44, 227-240. (doi:10.1016/j.ijengsci.2005.08.006)
33. Putra, N., Roetzel, W. & Das, S. K. 2003 Natural convection of nano-fluids. Heat Mass Transf. 39, 775-784. (doi:10.1007/s00231-002-0382-z)
34. Quintanilla, R. & Straughan, B. 2005 Bounds for some non-standard problems in porous flow and viscous Green-Naghdi fluids. Proc. R. Soc. A 461, 3159-3168. (doi:10.1098/rspa.2005.1508)
35. Savino, R. & Paterna, D. 2008 Thermodiffusion in nanofluids under different gravity conditions. Phys. Fluids 20, 017 101.
36. Straughan, B. 2006 Global nonlinear stability in porous convection with a thermal non-equilibrium model. Proc. R. Soc. A 462, 409-418. (doi:10.1098/rspa.2005.1555) (Pubitemid 44922141)
37. Travis, K. P., Todd, B. D. & Evans, D. J. 1997 Poiseuille flow of molecular liquids. Physica A 240, 315-327. (doi:10.1016/S0378-4371(97)00155-6)
38. Tzou, D. Y. 2008 Thermal instability of nanofluids in natural convection. Int. J. Heat Mass Transf. 51, 2967-2979. (doi:10.1016/j.ijheatmasstransfer. 2007.09.014) (Pubitemid 351514731)
39. Vadasz, P. 2006 Heat conduction in nanofluid suspensions. ASME J. Heat Transf. 128, 465-477. (doi:10.1115/1.2175149) (Pubitemid 43821493)
40. Vadasz, J. J., Govender, S. & Vadasz, P. 2005 Heat transfer enhancement in nanofluid suspensions: possible mechanisms and explanations. Int. J. Heat Mass Transf. 48, 2673-2683. (doi:10.1016/ j.ijheatmasstransfer.2005.01. 023)
41. Wong, K. F. V. & Kurma, T. 2008 Transport properties of alumina nanofluids. Nanotechnology 19, 345 702.
42. Xuan, Y. & Roetzel, W. 2000 Conceptions for heat transfer correlation of nanofluids. Int. J. Heat Mass Transf. 43, 3701-3707. (doi:10.1016/S0017- 9310(99)00369-5) (Pubitemid 30605120)
43. Xuan, Y., Li, Q. & Hu, W. 2003 Aggregation structure and thermal conductivity of nanofluids. AIChE J. 49, 1038-1043. (doi:10.1002/aic.690490420) (Pubitemid 36504566)