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Research Papers: Micro/Nanoscale Heat Transfer

Onset of Convection in a Porous Medium Layer Saturated With an Oldroyd-B Nanofluid

[+] Author and Article Information
J. C. Umavathi

Department of Engineering,
University of Sannio,
Piazza Roma 21,
Benevento 82100, Italy
e-mail: drumavathi@rediffmail.com

J. Prathap Kumar

Department of Mathematics,
Gulbarga University,
Gulbarga 585 106, Karnataka, India
e-mail: p_rathap@yahoo.com

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 4, 2015; final manuscript received May 20, 2016; published online September 13, 2016. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 139(1), 012401 (Sep 13, 2016) (14 pages) Paper No: HT-15-1163; doi: 10.1115/1.4033698 History: Received March 04, 2015; Revised May 20, 2016

A linear and nonlinear stability analysis of a viscoelastic fluid in a porous medium layer saturated by a nanofluid with thermal conductivity and viscosity dependent on the nanoparticle volume fraction is studied. To simulate the momentum equation in porous media, a modified Darcy model has been used. To describe the rheological behavior of viscoelastic nanofluids, an Oldroyd-B type constitutive equation has been used. The onset criterion for stationary and oscillatory convection is derived analytically. The nonlinear theory based on the truncated representation of Fourier series method is used to find the transient heat and mass transfer.

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Figures

Grahic Jump Location
Fig. 1

Neutral curves on the stationary convection for different values of (a) nanoparticle concentration Rayleigh number Rn, (b) Lewis number Ln, (c) viscosity ratio ν, and (d) conductivity ratio η

Grahic Jump Location
Fig. 2

Neutral curves on the oscillatory convection for different values of (a) nanoparticle concentration Rayleigh number Rn, (b) Lewis number Ln, (c) viscosity ratio ν, (d) conductivity ratio η, (e) Vadász number Va, (f) relaxation parameter λ1, and (g) retardation parameter λ2

Grahic Jump Location
Fig. 3

Variation of Nusselt number Nu with critical Rayleigh number for different values of (a) nanoparticle concentration Rayleigh number Rn, (b) Lewis number Ln, (c) viscosity ratio ν, and (d) conductivity ratio η

Grahic Jump Location
Fig. 4

Variation of Sherwood number Sh with critical Rayleigh number for different values of (a) nanoparticle concentration Rayleigh number Rn, (b) Lewis number Ln, (c) modified diffusivity ratio NA, (d) viscosity ratio ν, and (e) conductivity ratio η

Grahic Jump Location
Fig. 5

Transient Nusselt number Nu with time for different values of (a) nanoparticle concentration Rayleigh number Rn, (b) Lewis number Ln, (c) modified diffusivity ratio NA, (d) viscosity ratio ν, (e) conductivity ratio η, (f) Vadász number Va, (g) relaxation parameter λ1, and (h) retardation parameter λ2

Grahic Jump Location
Fig. 6

Transient Sherwood number Sh with time for different values of (a) nanoparticle concentration Rayleigh number Rn, (b) Lewis number Ln, (c) modified diffusivity ratio NA, (d) viscosity ratio ν, (e) conductivity ratio η, (f) Vadász number Va, (g) relaxation parameter λ1, and (h) retardation parameter λ2

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