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International Journal of Scientific and Engineering Research
ISSN Online 2229-5518
ISSN Print: 2229-5518 6    
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scirp IJSER >> Volume 3,Issue 6,June 2012
Positive Operator Method to Establish Principle of Exchange of Stabilities in Thermal Convection of a Viscoelastic Fluid
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Joginder S. Dhiman and Pushap Lata
The theoretical treatments of convective stability problems usually invoked the so-called principle of exchange of stabilities (PES), which is demonstrated physically as convection occurring initially as a stationary convection. Weinberger [1969] used a method of a positive operator, a generalization of a positive matrix operator, to establish the PES, wherein, the resolvent of the linearized stability operator is analyzed, which is a composition of certain integral operators. Motivated by method of positive operator of Weinberger, we aim to extend this analysis of Herron[2000] to establish the PES to more general convective problems from the domain of non-Newtonian fluid. In the present paper, the problem of heated from below with variable gravity is analyzed by the method of positive and it is established that PES is valid for this general problem, when the gravity is a nonnegative throughout the fluid layer and the elastic number of the medium is less than the ratio of permeability to porosity
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