The thermal convection in a horizontal layer of a porous medium saturated with a viscoelastic nanofluid was studied analytically. A Kuvshiniski-type constitutive equation is used to describe the behavior of viscoelastic nanofluids. The model used for the viscoelastic nanofluid incorporates the effects of Brownian motion and thermophoresis. A physically more realistic boundary condition than the previous ones on the nanoparticle volume fraction is considered i.e. the nanoparticle flux is assumed to be zero rather than prescribing the nanoparticle volume fraction on the boundaries. Using linear stability theory, the exact analytical expression for the Darcy–Rayleigh number is obtained in terms of various non-dimensional parameters. Results indicate that the coefficient of viscosity, porous medium and nanoparticles significantly influences the stability characteristics of the system. The effect of various parameters on the thermal instability is also presented graphically.
Bibliographical noteFunding Information:
This work was supported by the Yonsei University Research Fund of 2015 and the Human Resources Development program (No. 20144030200560 ) of Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by Korea Government Ministry of Trade . We would like to thank Prof. M.A. Kamel and Prof. M.F. Elsayed (Ain Shams University, Egypt) for their critical reading of the manuscript and for their valuable comments and discussion.
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