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Papers by renu bala
International Journal of Psychiatric Nursing, 2015
Zeitschrift für angewandte Mathematik und Physik, 2015
The present paper mathematically establishes that rotatory hydrodynamic triply diffusive convecti... more The present paper mathematically establishes that rotatory hydrodynamic triply diffusive convection with one of the components as heat with diffusivity κ cannot manifest as oscillatory motions of growing amplitude in an initially bottom heavy configuration if the two concentration Rayleigh numbers R 1 and R 2 , the Lewis numbers τ 1 and τ 2 for the two concentrations with diffusivities κ 1 and κ 2 , respectively (with no loss of generality κ > κ 1 > κ 2) and the Prandtl number σ satisfy the inequality R 1 + R 2 ≤ 27π 4 4 1+ τ 1 +τ 2 σ 1+ τ 1 τ 2 2. It is further established that this result is uniformly valid for the quite general nature of the bounding surfaces.
Research Journal of Engineering and Technology, 2015
In the present paper it is mathematically established that the linear growth rate of an arbitrary... more In the present paper it is mathematically established that the linear growth rate of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude in a triply diffusive fluid layer (with one of the component as heat with diffusivity κ) must lie inside a semicircle in the right half of the (pr,pi) -plane whose centre is at the origin and radius equals where R and R1 are the thermal Rayleigh number and concentration Rayleigh number with diffusivities κ and κ_1. Further, it is proved that this result is uniformly valid for quite general nature of the bounding surfaces.
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2014
Upper bounds for the complex growth rate of an arbitrary oscillatory perturbation, which may be n... more Upper bounds for the complex growth rate of an arbitrary oscillatory perturbation, which may be neutral or unstable for triply diffusive convection under the simultaneous presence of a uniform vertical magnetic field and a vertical uniform rotation, are obtained. It is further proved that the results obtained herein are uniformly valid for all combinations of rigid perfectly conducting or rigid insulating boundaries.
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2014
The present paper mathematically establishes that the principle of the exchange of stabilities in... more The present paper mathematically establishes that the principle of the exchange of stabilities in a rotatory triply diffusive convection is valid in the regime R 1 r 2s 2 1 p 4 þ R 2 r 2s 2 2 p 4 þ T a p 4 1; where R 1 and R 2 are the Rayleigh numbers for the two concentration components, s 1 and s 2 are the Lewis numbers for the two concentration components, T a is the Taylor number and r is the Prandtl number. Keywords Triply diffusive convection Á The principle of the exchange of stabilities Á Concentration Rayleigh number Á Rotation j À Á Lewis number for concentration S 2 j Thermal diffusivity j 1 Mass diffusivity of S 1 j 2 Mass diffusivity of S 2
International Journal of Psychiatric Nursing, 2015
Zeitschrift für angewandte Mathematik und Physik, 2015
The present paper mathematically establishes that rotatory hydrodynamic triply diffusive convecti... more The present paper mathematically establishes that rotatory hydrodynamic triply diffusive convection with one of the components as heat with diffusivity κ cannot manifest as oscillatory motions of growing amplitude in an initially bottom heavy configuration if the two concentration Rayleigh numbers R 1 and R 2 , the Lewis numbers τ 1 and τ 2 for the two concentrations with diffusivities κ 1 and κ 2 , respectively (with no loss of generality κ > κ 1 > κ 2) and the Prandtl number σ satisfy the inequality R 1 + R 2 ≤ 27π 4 4 1+ τ 1 +τ 2 σ 1+ τ 1 τ 2 2. It is further established that this result is uniformly valid for the quite general nature of the bounding surfaces.
Research Journal of Engineering and Technology, 2015
In the present paper it is mathematically established that the linear growth rate of an arbitrary... more In the present paper it is mathematically established that the linear growth rate of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude in a triply diffusive fluid layer (with one of the component as heat with diffusivity κ) must lie inside a semicircle in the right half of the (pr,pi) -plane whose centre is at the origin and radius equals where R and R1 are the thermal Rayleigh number and concentration Rayleigh number with diffusivities κ and κ_1. Further, it is proved that this result is uniformly valid for quite general nature of the bounding surfaces.
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2014
Upper bounds for the complex growth rate of an arbitrary oscillatory perturbation, which may be n... more Upper bounds for the complex growth rate of an arbitrary oscillatory perturbation, which may be neutral or unstable for triply diffusive convection under the simultaneous presence of a uniform vertical magnetic field and a vertical uniform rotation, are obtained. It is further proved that the results obtained herein are uniformly valid for all combinations of rigid perfectly conducting or rigid insulating boundaries.
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2014
The present paper mathematically establishes that the principle of the exchange of stabilities in... more The present paper mathematically establishes that the principle of the exchange of stabilities in a rotatory triply diffusive convection is valid in the regime R 1 r 2s 2 1 p 4 þ R 2 r 2s 2 2 p 4 þ T a p 4 1; where R 1 and R 2 are the Rayleigh numbers for the two concentration components, s 1 and s 2 are the Lewis numbers for the two concentration components, T a is the Taylor number and r is the Prandtl number. Keywords Triply diffusive convection Á The principle of the exchange of stabilities Á Concentration Rayleigh number Á Rotation j À Á Lewis number for concentration S 2 j Thermal diffusivity j 1 Mass diffusivity of S 1 j 2 Mass diffusivity of S 2