MHD stability of a nanofluid layer using Darcy model: Introduction of oscillatory motions for bottom heavy configuration
Jyoti Ahuja1, Urvashi Gupta2*, Veena Sharma3
1Energy Research Centre, Panjab University, Chandigarh-160014, INDIA
2Dr. S.S. Bhatnagar University Institute of Chemical Engineering and Technology, Panjab University, Chandigarh-160014, INDIA
3Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005.
*Corresponding Author Email: dr_urvashi_gupta@yahoo.com
ABSTRACT
The impact of vertical magnetic field on the thermal instability of a horizontal porous nanofluid layer using Darcy model is considered for free-free boundaries. Brownian motion and thermophoretic forces are introduced due to the presence of nanoparticles and Lorentz’s force term is added in the momentum equation along with the Maxwell’s equations due to magnetic field. Normal mode technique and single term Galerkin approximation is employed to investigate the instability and derive the eigen value problem. It is found that the mode of instability is through oscillatory motions for bottom heavy suspension of nanoparticles. The reason for the existence of oscillatory motions is due to the occurrence of two opposite buoyancy forces i.e. density variation due to heating and density gradient of nanoparticles at the bottom of the layer. The thermal Rayleigh number increases with the increase of Chandrasekhar number and decreases with the increase of porosity. The effect of Lewis number, modified diffusivity ratio, concentration Rayleigh number and heat capacity ratio on the onset of thermal convection has been investigated analytically and presented graphically.
KEYWORDS:
Nanofluid is a highly influential term which is being discussed within the heat transfer community over a wide spectrum. Suspension of nanometer-sized particles (oxides, nitrides, ceramics, metals and semiconductors) in base fluids (water, ethylene glycol, oil) is given the name as nanofluid. Choi (1995) in his study revealed the fact that such suspensions are very useful to enhance the heat transfer mechanism due to their high thermal conductivity. Buongiorno (2006) elaborated the convective transport in nanofluids and suggested a model using the mechanics of nanoparticles and included the effects due to Brownian motion and thermophoretic diffusion. Buongiorno’s model was utilized to study the thermal instability problems by Tzou (2008) and Nield and Kuznetsov (2009).
Gupta et al. (2013, 2014) have studied the impact of applied magnetic field and of Hall currents on a nanofluid layer and have shown that the critical wave number as well as critical Rayleigh number undergo a significant rise with the rise in Chandrasekhar number and decrease with the increase in Hall parameter. The present formulation of the thermal convection problem introduces the impact of permeability and vertical magnetic field using Horton-Rogers-Lapwood model for porous medium for free-free boundaries. The problem has great application in geophysics due to the high magnetic field of earth, its porous structure and due to more realistic boundary conditions. The Rayleigh number at which the instability sets in has been found for free-free boundaries to establish that the thermal Rayleigh number exhibits a significant fall for the case of top heavy configuration of nanoparticles whereas the increment in its value is relatively small for bottom heavy distribution.
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Received on 27.08.2016 Accepted on 16.09.2016 © EnggResearch.net All Right Reserved Int. J. Tech. 2016; 6(2): 233-238. DOI: 10.5958/2231-3915.2016.00036.5 |
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