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MHD Stability of a Nanofluid Layer Using Darcy Model:Introduction of Oscillatory Motions for Bottom Heavy Configuration


Affiliations
1 Energy Research Centre, Panjab University, Chandigarh-160014, India
2 Dr. S.S. Bhatnagar University Institute of Chemical Engineering and Technology, Panjab University, Chandigarh-160014, India
3 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India
     

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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.
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  • MHD Stability of a Nanofluid Layer Using Darcy Model:Introduction of Oscillatory Motions for Bottom Heavy Configuration

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Authors

Jyoti Ahuja
Energy Research Centre, Panjab University, Chandigarh-160014, India
Urvashi Gupta
Dr. S.S. Bhatnagar University Institute of Chemical Engineering and Technology, Panjab University, Chandigarh-160014, India
Veena Sharma
Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India

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.