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Numerical Investigations of Electro-Thermal Convection in Dielectric Nanofluid Layer


Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-5, India
2 SDWG Govt. College Beetan, Distt. Una (H.P), India
3 Govt. College Beetan, Distt. Una (H.P), India
     

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The numerical investigations of a dielectric nanofluid under the simultaneous action of an Alternating Current electric field and a uniform adverse temperature gradient has been studied using the linear theory and normal mode analysis. The eigen-value problem is solved analytically and numerically using the Galerkin technique. Effect of various non-dimensional parameters on thermal Rayleigh number Ra for the stationary convection has been determined. The boundaries are considered to be stress-free. Thermal Rayleigh number has been computed for various values of electric Rayleigh number for the onset of instability using the software-MATHEMATICA Version 5.2. Numerical results are presented graphically. The thermal Rayleigh number decreases linearly as the concentration Rayleigh number Rn increases. Moreover for stability motion, the value of thermal Rayleigh number Ra occurs only for negative values of Rea and it is positive. The value of critical thermal Rayleigh number Ra decreases with decreasing the value of Rea. It is observed that the role of electric field is not of much sinificance the convection in the fluid layer in case of stability motions. In case of stability, the thermal Rayleigh number is independent of Prandtl number and hence Prandtl number has no role to play.
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  • Numerical Investigations of Electro-Thermal Convection in Dielectric Nanofluid Layer

Abstract Views: 207  |  PDF Views: 3

Authors

Veena Sharma
Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-5, India
Ashwini Kumar
Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-5, India
Abhilasha
SDWG Govt. College Beetan, Distt. Una (H.P), India
Abhishek Sharma
Govt. College Beetan, Distt. Una (H.P), India

Abstract


The numerical investigations of a dielectric nanofluid under the simultaneous action of an Alternating Current electric field and a uniform adverse temperature gradient has been studied using the linear theory and normal mode analysis. The eigen-value problem is solved analytically and numerically using the Galerkin technique. Effect of various non-dimensional parameters on thermal Rayleigh number Ra for the stationary convection has been determined. The boundaries are considered to be stress-free. Thermal Rayleigh number has been computed for various values of electric Rayleigh number for the onset of instability using the software-MATHEMATICA Version 5.2. Numerical results are presented graphically. The thermal Rayleigh number decreases linearly as the concentration Rayleigh number Rn increases. Moreover for stability motion, the value of thermal Rayleigh number Ra occurs only for negative values of Rea and it is positive. The value of critical thermal Rayleigh number Ra decreases with decreasing the value of Rea. It is observed that the role of electric field is not of much sinificance the convection in the fluid layer in case of stability motions. In case of stability, the thermal Rayleigh number is independent of Prandtl number and hence Prandtl number has no role to play.