Triple-diffusive convection in a layer of viscoelastic nanofluid

 

G. C. Rana¹*, Ramesh Chand², S. K. Kango³

¹Department of Mathematics, NSCBM Govt. College, Hamirpur-177005, Himachal Pradesh, INDIA

²Department of Mathematics, Govt. College, Nurpur-177 103, District Kangra, Himachal Pradesh, INDIA

 

ABSTRACT

Triple-diffusive convection in a horizontal layer of nanofluid heated from below and salted from above and below is considered. The Rivlin-Ericksen type fluid model is used to describe the rheological behavior of viscoelastic nanofluid. The effects of thermophoresis and Brownian diffusion parameters are also introduced through Buongiorno model in the governing equations. By using linear stability analysis and normal modes analysis method, the dispersion relation accounting for the effect of various parameters is derived. The influences of solute-Rayleigh number, analogous solute-Rayleigh number, thermo-nanofluid Lewis number, modified diffusivity ratio and nanoparticle Rayleigh number on the stability of stationary convection are presented analytically and graphically.

 

 

1.      Introduction:

Double-diffusive convection is a mixing process of two fluid components which diffuse at different rates. It has various applications in different areas such as geophysics, soil sciences, food processing, oil reservoir modeling, oceanography, limnology and engineering, among others. Double-diffusive convection problems related to different types of fluids have been extensively studied [1-8]. 

 

There are many physical situations in which more than two fluid components involved. Examples of such multiple diffusive convection fluid systems include the solidification of molten alloys, geothermally heated lakes and sea water etc. The problems of triple-diffusive convection fluid (where the density depends on three independently diffusing agencies with different diffusivities) have been studied [9-12]. These researchers found that small concentrations of a third component with a smaller diffusivity can have a significant effect upon the nature of diffusive instabilities and ‘oscillatory’ and direct ‘salt finger’ modes are simultaneously unstable under a wide range of conditions, when the density gradients due to components with the greatest and smallest diffusivity are of same signs. Triple-diffusive convection in Walters’ (model B') fluid with varying gravity field saturating a porous medium studied by Kango et al. [13].

 

In recent years, much research has been evinced on the study of nanofluids with a view to applications in several industries such as the automotive, pharmaceutical and energy supply industries. A nanofluid is a colloidal suspension of nano sized particles. Common fluids such as water, ethanol or engine oils are typically used as base fluids in nanofluids. Choi [14] was first who coined the term nanofluid. Nanofluids are being looked upon as great coolants due to their enhanced thermal conductivities and suspensions of nanoparticles are being developed medical applications including cancer therapy. Buongiorno [15] proposed that the absolute nanoparticle velocity can be viewed as the sum of the base fluid velocity and a relative slip velocity. Thus convection of nanofluids based on Buongiorno’s model has attracted great interest.

 

A considerable number of double-diffusive convection problems in a horizontal layer saturated by a nanofluid have also been numerically and analytically investigated [16-21]. In this paper, triple-diffusive convection in a layer of nanofluid heated from below and salted from above and below by salt S' and S''  respectively is studied. To the best of my knowledge, this paper has not been published as yet.

 

2.      formulation of the problem and governing equations:

We consider an infinite horizontal layer of nanofluid of thickness d, bounded by the planes z = 0 and z = d heated from below and salted from above and below by salt S' and S''  respectively as shown in figure 1. Each boundary wall is assumed to be impermeable and perfectly thermal conducting. The layer is acted upon by a gravity force g = (0, 0, -g) aligned in the z direction. The temperature T, concentrations C', C'' and the volumetric fraction of nanoparticles φ at the lower (upper) boundary is assumed to take constant values T₀, ,  and φ₀ (T₁, ,  and φ₁), respectively.

 

6. Conclusions:

Triple-diffusive convection in a layer of viscoelastic Nanofluid heated from below and soluted from below and above has been investigated. For the case of stationary convection, the viscoelastic nanofluid behaves like an ordinary nanofluid. The solute Rayleigh number () and analogous solute Rayleigh number () have stabilizing effects on the onset of stationary convection for both top-heavy and bottom-heavy arrangements. The thermo-nanofluid Lewis number () and diffusivity ratio () have stabilizing effects on the onset of stationary convection for bottom-heavy arrangements. Nanoparticle Rayleigh number () has destabilizing effect on the onset of stationary convection.

 

7. REFERENCES:

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Received on 17.08.2016            Accepted on 02.09.2016            © EnggResearch.net All Right Reserved Int. J. Tech. 2016; 6(2): 71-80. DOI: 10.5958/2231-3915.2016.00011.0