Journal :   International Journal of Technology

Volume No. :   4

Issue No. :  1

Year :  2014

Pages :   100-105

ISSN Print :  2231-3907

ISSN Online :  2231-3915


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On the Effect of Non-Uniform Temperature Gradients on the Stability of Modified Thermal Convection Problem



Address:   Joginder Singh Dhiman1, Vijay Kumar2, Som Krishan Sharma3
1Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla (H.P.)-171005
2Govt. Degree College, Sunni, Distt. Shimla (H.P.)-171301
3Govt. Degree College, Kullu (H.P.)-175101
DOI No:

ABSTRACT:
The aim of the present paper is to study the effect of non-uniform basic temperature gradients on the onset of modified thermal convection in a layer of fluid heated from below for different combinations of rigid and dynamically free boundary conditions. It is shown that the principle of exchange of stabilities (PES) is valid when the temperature gradient is monotonically decreasing upward, which means that the instability sets in as stationary mode. The expressions for the Rayleigh numbers for each combination of rigid and dynamically free boundary conditions for the stationary case of instability are derived using Galerkin method. The effects of non-uniform temperature gradients and the modification factor which arises due to modified theory of Banerjee et al on the instability are studied from the values of the critical Rayleigh numbers calculated numerically for various temperature profiles and the coefficient of specific heat variation due to temperature variation for the given values of other parameters. It is observed from these values that the Cubic temperature profile is more stabilizing than the inverted parabolic temperature distribution profile. Further, it is also found that the critical Rayleigh numbers for thermally insulating boundaries are lower than those for the corresponding isothermal cases.
KEYWORDS:
thermal convection; modified theory; temperature gradient; stationary convection; Galerkin Method; Rayleigh numbers; boundary conditions.
Cite:
Joginder Singh Dhiman1, Vijay Kumar2, Som Krishan Sharma3. On the Effect of Non-Uniform Temperature Gradients on the Stability of Modified Thermal Convection Problem. Int. J. Tech. 4(1): Jan.-June. 2014; Page 100-105
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