# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
The onset of convection in a couple stress fluid saturated porous layer using a thermal non-equilibrium model. (English) Zbl 1227.76059
Summary: The stability of a couple stress fluid saturated horizontal porous layer heated from below and cooled from above when the fluid and solid phases are not in local thermal equilibrium is investigated. The Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the solid and fluid phases separately. The linear stability theory is employed to obtain the condition for the onset of convection. The effect of thermal non-equilibrium on the onset of convection is discussed. It is shown that the results of the thermal non-equilibrium Darcy model for the Newtonian fluid case can be recovered in the limit as couple stress parameter $C\to 0$. We also present asymptotic analysis for both small and large values of the inter phase heat transfer coefficient $H$. We found an excellent agreement between the exact solutions and asymptotic solutions when $H$ is very small.
##### MSC:
 76R10 Free convection (fluid mechanics) 76S05 Flows in porous media; filtration; seepage 76A05 Non-Newtonian fluids
##### References:
 [1] , Transport phenomena in porous media (1998) [2] , Transport phenomena in porous media, vol. III (2005) [3] , Handbook of porous media (2000) [4] , Handbook of porous media (2005) [5] Nield, D. A.; Bejan, A.: Convection in porous media, (2006) [6] Rees, D. A. S.; Pop, I.: J. porous media, J. porous media 3, 31 (2000) [7] Rees, D. A. S.; Pop, I.: J. appl. Math. phys., J. appl. Math. phys. 53, 1 (2002) [8] Banu, N.; Rees, D. A. S.: Int. J. Heat mass transfer, Int. J. Heat mass transfer 45, 2221 (2002) [9] Rees, D. A. S.; Pop, I.: D.b.inghami.poptransport phenomena in porous media, vol. III, Transport phenomena in porous media, vol. III, 147-173 (2005) [10] Baytas, A. C.; Pop, I.: Int. J. Thermal sci., Int. J. Thermal sci. 41, 861 (2002) [11] Baytas, A. C.: Int. J. Energy res., Int. J. Energy res. 27, 975 (2003) [12] Saeid, N. H.: Int. J. Heat mass transfer, Int. J. Heat mass transfer 47, 5619 (2004) [13] Malashetty, M. S.; Shivakumara, I. S.; Sridhar, K.: Int. J. Heat mass transfer, Int. J. Heat mass transfer 48, 1155 (2005) [14] Malashetty, M. S.; Shivakumara, I. S.; Sridhar, K.: Transp. porous media, Transp. porous media 60, 199 (2005) [15] Straughan, B.: Proc. R. Soc. London A, Proc. R. Soc. London A 462, 409 (2006) [16] Malashetty, M. S.; Shivakumara, I. S.; Sridhar, K.; Mahantesh, S.: Transp. porous media, Transp. porous media 64, 123 (2006) [17] Shivakumara, I. S.; Malashetty, M. S.; Chavaraddi, K. B.: Can. J. Phys., Can. J. Phys. 84, 973 (2006) [18] Sheu, L. J.: Chaos solitons fractals, Chaos solitons fractals 30, 672 (2006) [19] Malashetty, M. S.; Swamy, M.; Sridhar, K.: Phys. fluids, Phys. fluids 19, No. 5, 054102 (2007) [20] Stokes, V. K.: Phys. fluids, Phys. fluids 9, 1709 (1966) [21] Sharma, R. C.; Thakur, K. D.: Czech J. Phys., Czech J. Phys. 50, No. 6, 7753 (2000) [22] Sunil; Sharma, R. C.; Chandel, R. S.: Z. naturforsch., Z. naturforsch. 57a, 955 (2002) [23] Sharma, R. C.; Sharma, M.: Indian J. Pure appl. Math., Indian J. Pure appl. Math. 35, 973 (2004) [24] Horton, C. W.; Rogers, F. T.: J. appl. Phys., J. appl. Phys. 16, 367 (1945) [25] Lapwood, E. R.: Proc. Cambridge philos. Soc., Proc. Cambridge philos. Soc. 44, 508 (1948)