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Jyoti Ahuja ¹, Urvashi Gupta ², R. K. Wanchoo ²

Affiliations
1 Energy Research Centre, Panjab University, Chandigarh-160014, IN
2 Dr. S.S. Bhatnagar University Institute of Chemical Engineering & Technology, Panjab University, Chandigarh-160014, IN

Abstract

In the present paper, hydromagnetic stability of alumina-water and copper oxide-water nanofluids is investigated for top heavy configuration of nanoparticles. Brownian motion and thermophoretic forces are introduced due to the presence of nanoparticles and Lorentz force term is added in the momentum equation due to the presence of magnetic field. The problem has application in geophysics due to earth’s magnetic field and enhanced heat transfer characteristics of nanofluids. Computations are carried out within the frame work of normal mode technique and single term Galerkin approximation. An eigen value equation representing the relation between various nanofluid parameters, magnetic field, growth rate of disturbance and wave number is obtained. It is observed that the thermal Rayleigh number increases with the increase in Chandrasekhar number and decreases with the increase in volume fraction of nanoparticles. Nanofluids with Al2O3 nanoparticles exhibit higher stability than the nanofluids containing CuO nanoparticles. The mode of instability is found to be through stationary convection. It is expected since for oscillatory motions to exist two of the buoyancy forces must act in the opposite directions.

Keywords

Nanofluids, Brownian Motion, Hydromagnetics, Critical Rayleigh Number.

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Urvashi Gupta ¹

Affiliations
1 University Institute of Chemical Engineering and Technology, Panjab University, Chandigarh-160014, IN

Abstract

A layer of a compressible, electrically conducting Walters' (Model B¢) elastico-viscous fluid permeated with suspended particles heated from below in the presence of a magnetic field and Hall currents is considered. The perturbation equations are analyzed in terms of normal modes after linearizing the relevant hydromagnetic equations. A dispersion relation governing the effects of visco-elasticity, magnetic field, Hall currents and suspended particles has been obtained. For the case of stationary convection, Walters' (Model B¢) fluid behaves like a Newtonian fluid due to the vanishing of the visco-elastic parameter. The compressibility and magnetic field are found to have stabilizing effects on the system, that is, their effect is to postpone the onset of thermal instability whereas Hall currents and suspended particles are found to hasten the onset of thermal instability for permissible range of values of various parameters. The dispersion relation is also analyzed numerically. The critical Rayleigh numbers and the wave numbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behaviour of various parameters on critical thermal Rayleigh numbers has been depicted graphically.

Keywords

Walters’ (Model B') Fluid, Hall Currents, Suspended Particles, Compressibility, Thermal Instability.

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Jyoti Ahuja ¹, Urvashi Gupta ²

Affiliations
1 Energy Research Centre, Panjab University, Chandigarh-160014, IN
2 Dr. S.S. Bhatnagar University Institute of Chemical Engineering and Technology, Panjab University, Chandigarh-160014, IN

Abstract

Rayleigh-Benard convection of a rotating nanofluid layer under local thermal non-equilibrium model in the presence of magnetic field is investigated. The impact of external applied forces rotation and magnetic field are exhibited by introducing Coriolis force term and Lorentz force term in the momentum equations along with the Maxwell's equations. For considering the impact of local thermal non-equilibrium between the fluid and particle phases; a two-temperature model has been considered. The problem is analysed by making use of the normal mode technique and one term approximation of Galerkin type weighted residual method. Due to thermal non-equilibrium three additional parameters Nield number, modified thermal capacity ratio, modified thermal diffusivity ratio and due to the presence of rotation and magnetic field Taylor number and Chandrasekhar number are introduced. The impact of these parameters on thermal Rayleigh number has been found analytically as well as numerically and presented graphically.

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Jyoti Ahuja ¹, Urvashi Gupta ², Veena Sharma ³

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

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.

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Veena Sharma ¹, Abhilasha ², Urvashi Gupta ³

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-5, IN
2 SDWG Govt. College, Beetan, Distt. Una (H.P.), IN
3 Dr. S. S. Bhatnagar University Institute of Chemical Engneering and Technology, Panjab University, Chandigarh 160014, IN

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.

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Urvashi Gupta ¹, Jyoti Ahuja ²

Affiliations
1 University Institute of Chemical Engineering and Technology, Panjab University, Chandigarh-160014, IN
2 Energy Research Centre, Panjab University, Chandigarh-160014, IN

Abstract

The present paper investigates the stability analysis of an electrically conducting horizontal layer of nanofluid in the presence of Hall currents saturating a porous medium for bottom heavy distribution of nanoparticles. Hall currents are the effects whereby a conductor carrying an electric current perpendicular to an applied magnetic field develops a voltage gradient which is transverse to both the current and the magnetic field. The nanofluid layer incorporates the effect of Brownian motion and the rmophoresis while Darcy's law is used for the porous medium. The analysis is carried out in the framework of linear stability theory, normal mode technique and Galerkin type weighted residuals method. The present formulation of the problem leads to oscillatory mode of instability whereas for top heavy arrangement of nanoparticles the instability is invariably through stationary convection. The reason for the oscillatory mode of convection is the competition between the density gradient caused by bottom heavy nanoparticle distribution with the density variation caused by heating from the bottom. Further, it is found that the effect of magnetic field is to postpone the onset of instability while that of Hall currents and porosity is to hasten the onset of thermal convection.

Keywords

Thermal Convection, Nanofluid Layer, Brownian Motion, Darcy Law, Hall Currents, Thermophoresis.

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Jyoti Sharma ¹, Urvashi Gupta ²

Affiliations
1 U.I.E.T., Panjab University, Chandigarh-160014, IN
2 Dr. S. S. Bhatnagar University Institute of Chemical Engineering and Technology, Panjab University, Chandigarh-160014, IN

Abstract

The effect of an externally impressed magnetic field on the onset of convection in a binary nanofluid layer saturating a Darcy-Brinkman model for porous medium is considered in this work. Magnetic field imparts to the fluid rigidity as well as some properties of elasticity which results in the disturbances by new mode of wave propagation. The effects of Brownian motion and thermophoresis due to the presence of nanoparticles and the effects of Dufour and Soret parameters due to the presence of solute have been included in the model under investigation. For analytical study, valid approximations are made in the complex expression for Rayleigh number to get interesting results. The mode of instability is invariably through stationary convection for top heavy distribution of nanoparticles in the fluid. Oscillatory mode of convection is possible for bottom heavy configuration and the frequency of oscillation shows a decrease with an increase in Chandrasekhar number and porosity. It is found that alumina nanoparticles stabilize the water based fluid more than copper nanoparticles which in turn have more stabilizing influence than silver nanoparticles. Fluids do not have much influence of physical properties of nanoparticles on the stability when the particles concentrate more on the bottom of the layer. The stability of the fluid rises appreciably due to the inclusion of magnetic field. Effects of various parameters on the stability of the fluid are studied numerically using Mathematical software and results are shown graphically.

Keywords

Darcy-Brinkman Model, Binary Nanofluid Convection, Chandrasekhar Number, Porosity, Thermophoresis, Brownian Motion.

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Jyoti Ahuja ¹, Urvashi Gupta ²

Affiliations
1 Energy Research Centre, Panjab University, Chandigarh-160014, IN
2 Dr. S.S. Bhatnagar University Institute of Chemical Engineering & Technology, Panjab University, Chandigarh-160014, IN

Abstract

Present paper investigates the onset of thermal convection of a porous nanofluid layer under the combined influence of rotation and magnetic field using Darcy-Brinkman model which is the modification of the Darcy model where in viscous shear effects and change in viscosity are accounted in momentum equation.In the present model, due to the presence of rotation Coriolis force term and due to the presence of magnetic field Lorentz's force term get introduced in the conservation equations of momentum coupled with the Maxwell's equations. To investigate the combined effect of these forces on the thermal convection of nanofluid layer normal mode technique and Galerkin type weighted residual method is applied. A comparative analysis of the thermal instability of metallic (Cu, Ag) and semiconducting (TiO₂, SiO₂) nanofluids is examined. It is observed that metals are more stable as compared to semiconductors. Further, it is found that silver nanoparticles stabilize the water based fluid more as compared to copper nanoparticles and in semiconductors TiO₂ nanoparticles enhance the stability of the system more as compared to SiO₂ nanoparticles. Stability of the system enhances with the rise in Chandrasekhar number and Taylor number whereas it falls with the rise in porosity. An additional parameter i.e. Darcy number is introduced due to the consideration of Darcy Brinkman model which has a stabilizing effect on the nanofluid layer system.

Keywords

Nanofluid, Brownian Motion, Thermophoresis, Darcy Number, Chandrasekhar Number, Taylor Number.

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