Shodhganga Collection:
http://hdl.handle.net/10603/190289
2020-09-26T20:42:37ZAlternative proofs of certain fixed point theorems
http://hdl.handle.net/10603/292957
Title: Alternative proofs of certain fixed point theoremsMathematical modelling of an aqueous electrolyte solution by incorporating the variation of dielectric constant
http://hdl.handle.net/10603/291070
Title: Mathematical modelling of an aqueous electrolyte solution by incorporating the variation of dielectric constant
Abstract: The important lapse in the failure of Debye-Huckel theory was established during the last century by detailed theoretical and experimental work of Glueckauff, Pitzer, Buchner, Barthel and the Nobel
newlinePrize winners Eigen and Tamm. The omission of incorporation of dielectric permittivity variation with concentration is attributed to be sole cause for several interesting mechanisms observed in electrolytic solutions. This dissertation developed a model to fill the void. A nonlinear equation for Dielectric constant as a function of three different powers of
newlineconcentration was proposed. Gauss-Newton method was used in curve fitting the Dielectric data. The Poisson-Boltzmann equation provided access to apply the proposed correction to the Debye-Huckel theory. The governing equations for an electro-osmatic flow of an aqueous electrolyte solution were developed by fully coupled Navier Stokes, Maxwell
newlineStefan, Poisson - Boltzmann equations. The Finite difference method and Finite element method were used to solve the governing equations. All through the work advanced computational technique of MATLAB was used. The results of the model used in the governing equations for the potential and other related parameters were presented as one and two dimensional plots drawn with the help of MATLAB. A critical analysis of these plots was presented. An excellent agreement was found between this theory and related results. The possible scope for extension of this model in future work is given.
newlineStudies in problems related to wave propagation in solids with microstructure
http://hdl.handle.net/10603/289442
Title: Studies in problems related to wave propagation in solids with microstructure
Abstract: The theory of elasticity, often called as elasticity, is the branch of solid
newlinemechanics which deals with stresses and deformations in elastic solids produced by external forces or changes in temperature. The theory of micromorphic materials is an extension of the theory of elasticity. The
newlinemicrostructure of the elastic solids is embedded in the theory of micromorphic
newlinematerials. The micropolar elasticity and the theory of micro-isotropic, micro-
newlineelastic materials are special cases of the theory of micromorphic materials. All my investigations related to the wave propagation in micropolar and micro-isotropic, micro-elastic media. The subject has fascinated me because of
newlineits applicability in materials such as polymers, rocks, granular particles, metals and composites, which are typical media with microstructures having
newlineimportance in seismic phenomena.Some investigations on steady and unsteady flow of second order thermo viscous fluids
http://hdl.handle.net/10603/289441
Title: Some investigations on steady and unsteady flow of second order thermo viscous fluids
Abstract: The non-Newtonian behavior of fluid flows has been a subject of serious concern to both experimental and theoretical sciences for over one and half centuries. More particularly there has been much activity in this direction between first and second world wars of the last century. During which the subject Continuum Mechanics has been put on rational mathematical
newlinefoundation to explain the typical behavior of materials of industry and military
newlineimportance. The linear theories based on linear constitutive relations are found to be inadequate to predict the interaction between the mechanical and thermal
newlineresponses individually or severally of materials like liquid polymers, fluid
newlineplastic, the molten metals etc subjected to stresses has been the motivating
newlineforce behind study of the non-linear theories for material description. A non-
newlinelinear generalization of the Voigt type materials was proposed by Rivlin and
newlineErignen. Some of the non-liner theories proposed so far ( listed in references)
newlinehave not taken into account the strong dependence of visco-elastic behavior
newlineupon thermal conduction i.e. interaction /interrelation between mechanical and
newlinenon mechanical (such as thermal, chemical, electromagnetic etc ) effects even
newlinethough the large of amount data of experimental evidence indicate a strong
newlinedependence of visco-elastic nature of the fluid upon thermal behavior (Ferry).For example materials such as solid Propellants exhibit a mechanical
newlinebehavior at moderate temperature variations , where as a little or no correlation between them would be observed with that under the isothermal condition.