Magneto-Thermosolutal Instability in Viscoelastic Nanofluid Layer
Veena Sharma1, Abhilasha2, Urvashi Gupta3
1Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-5 India
2SDWG Govt. College Beetan, Distt. Una (H.P.) India
3Dr. S. S. Bhatnagar University Institute of Chemical Engneering and Technology, Panjab University, Chandigarh 160014, India
*Corresponding Author Email: veena_math_hpu@yahoo.com, abhilashadutta@gmail.com, dr_urvashi_gupta@yahoo.com
ABSTRACT:
Thermosolutal convection in an infinitely, extending layer of viscoelastic nanofluids in the presence of uniform vertical magnetic field with Soret and Dufour effect is investigated. The rheology of nanofluids is described by Maxwell’s model. The coupled partial differential equations with the stress free boundaries are solved using the normal mode technique and linear theory. The first approximation of Galerkin procedure is used to obtain the numerical solution of the set of ordinary differential equation by using the software MATHEMATICA. The effects of the various parameters are shown graphically on both the stationary and oscillatory motions.
KEYWORDS:
INTRODUCTION:
In recent years, considerable interest has been evinced in the study of nanofluids and it has become an innovative idea for thermal engineering, because it has various applications in automotives industries, nuclear reactors, energy savings, etc. Further suspensions of nanoparticles are being developed medical applications including cancer therapy. The term nanofluids denotes a mixture of solid nanoparticles and a common base fluid. Nanoparticles used in nanofluids preparation usually have diameters below 100 nm. Colloidal suspensions have been used since ancient times. Choi [1] was among the first to suggest that such colloidal suspensions could be used as heat transfer medium. Due to their small size, nanoparticles fluidize easily inside the base fluid, and as the consequences, blockage of channels and erosion in channel walls do not occur.
The characteristics feature of nanofluids is thermal conductivity enhancement, a phenomenon observed by Masuda et al [2]. There is variety of potential engineering applications of nanofluids, including advanced nuclear systems (Buongiorno and Hu ).The general topic of heat transfer in nanofluids has been surveyed in a review article by Das and Choi[3] and a book by Das et al.[4]
Eastman et al.[5] revealed that if 0.3% of copper nanoparticles were added in ethylene glycol, the thermal conductivity of ethylene glycol would increase 40%.
A comprehensive survey of convective transport in nanofluids was made by Buogiorno who proposed a model incorporating the effects of Brownian motion and thermophoresis. This model was applied to the Hortan-Rogers-Lapwood problem by Nield and Kuznetsov [6] and Kuznetsov and Nield to study . Both Brownian diffusion and thermophoresis give rise to cross diffusion terms that are in some ways analogous to familiar Soret and Dufourcross diffusion terms that arise with a binary fluid resulting thereby triple diffusion. This aspect of transport in nanofluids has been discussed by Kim et al. The thermal instability of nanofluis in natural convection was studied by Tzou [7].
The effect of magnetic field on double-diffusive convection finds importance in geophysics, particularly in the study of Earth’s mantle, which consists of conducting fluid. Magnetic field plays an important role in engineering and industrial applications. These applications include design of chemical processing equipment, formation and dispersion of fog, distributions of temperature and moisture over agricultural fields and groves of fruit trees and damage of crops due to freezing and pollution of the environment etc .Chandersekhar [8] studied in detail the thermal convection in a hydromagnetics. Rana and Sharma [9] considered the problem of thermosolutal convection in the presence of magnetic field for different boundary conditions. Chand and Rana [10] have studied magnet- convection in a layer of nanofluid with Sorret effect and have found that Sorret effect, Lewis number, modified diffusivity ratio and nanoparticle Rayleigh number destabilize the fluid layer. Urvashi et al. [11] have studied instability of binary nanofluids with magnetic field and found that the critical wave number and the critical Rayleigh number increases whereas the frequency of oscillation(for bottom heavy configuration) decreases when the Chandrasekhar number increases.
The onset of thermal convection in a viscoelastic fluid was studied by many authors[12-18]. Since elastic behavior is inherent in non- Newtonian fluids, oscillatory instabilities can set in before stationary modes. It is commonly believed that oscillatory convection is not possible in viscoelastic fluids under realistic experiments conditions. However experiments with a DNA suspensions showed that convection pattern take the form of spatially localized standing and travelling waves which exhibit small amplitudes and extremely long oscillations periods. Those experiments triggered a new interest in convection by applying such type of triple aspects to viscoelastic nanofluids. Sheu [19] has investigated the Linear stability of convection in a viscoelastic nanofluid layer and found that the effect of the Deborah number is to advance the onset of convection in a viscoelastic nanofluid layer.
Keeping in mind the various applications mentioned in the above literature A fresh approach to cross-diffusion with regular cross-diffusion effects and the cross-diffusion effects peculiar to the viscoelatic nanofluids in the presence of magnetic field,in this research paper. The analysis is an extension of the work presented by Gupta et al.[11] to include viscoelastic parameter.
Formulation of the problem and perturbation equations
An infinitely
extending horizontal layer of an incompressible Maxwellian viscoelastic
nanofluid for bottom-heavy distribution of nanoparticles is considered which is
heated from below, and is confined between two parallel planes 
and 
, where temperature and
volumetric fraction of nanoparticles are kept constant: 
and 
at and 
and 
at . Both the bounding surfaces are
assumed to be stress free. The thermophysical properties of nanofluids
(viscosity, density, thermal conductivity and specific heat) are taken as
constants for the analytical formulation, but these quantities are not constant
and strongly depend on the volume fraction of nanoparticles. The fluid layer is
acted on by a uniform vertical magnetic field
and the acceleration due to
gravity 
pervade the system, 
-axis being taken as vertical.
The basic equations describing the physical model are based upon the following assumptions:
1. Thermophysical properties except for density in the buoyancy force (Boussinesq hypothesis) are constant;
2. The fluid phase and nanoparticles are in thermal equilibrium state;
3. Nanoparticles are of spherical shape;
4. Nanofluid is incompressible and laminar;
5. Radiation heat transfer between the sides of wall is negligible, when compared with other.
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Received on 15.09.2016 Accepted on 21.09.2016 © EnggResearch.net All Right Reserved Int. J. Tech. 2016; 6(2): 258-264. DOI: 10.5958/2231-3915.2016.00040.7 |
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