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Rayleigh-Benard convection in a nanofluid layer using a thermal non-equilibrium model.

[+] Author and Article Information
shilpi agarwal

greater noida greater noida, 201306 Indiadrshilpimath@gmail.com

Puneet Rana

Department of Mathematics, JIIT Noida, A-10, Sector 62 Noida, 201307 Indiapuneetranaiitr@gmail.com

B. S. Bhadauria

Department of Applied Mathematics and Statistics School for Physical Sciences, Lucknow-226025, Uttar Pradesh 226025 Indiamathsbsb@yahoo.com

Corresponding author.

ASME doi:10.1115/1.4028491 History: Received December 10, 2013; Revised August 13, 2014

Abstract

In this paper, we study the effect of local thermal non-equilibrium on the linear thermal instability in a horizontal layer of a Newtonian nanofluid. The nanofluid layer incorporates the effect of Brownian motion along with thermophoresis. A two-temperature model has been used for the effect of local thermal non-equilibrium among the particle and fluid phases. The linear stability is based on normal mode technique and for nonlinear analysis, a minimal representation of the truncated Fourier series analysis involving only two terms has been used. We observe that for linear instability, the value of Rayleigh number can be increased by a substantial amount on considering a bottom heavy suspension of nano particles. The effect of various parameters on Rayleigh number has been presented graphically. A weak nonlinear theory based on the truncated representation of Fourier series method has been used to find the concentration and the thermal Nusselt numbers. The behavior of the concentration and thermal Nusselt numbers is also investigated by solving the finite amplitude equations using a numerical method.

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