Shodhganga Collection:
http://hdl.handle.net/10603/204286
2019-10-17T06:26:33ZRayleigh benard convection in couple stress fluid with maxwell cattaneo law
http://hdl.handle.net/10603/245234
Title: Rayleigh benard convection in couple stress fluid with maxwell cattaneo law
Abstract: The onset of thermal instability in horizontal layers of fluid heated from below illustrates many physical and mathematical features of the general theory of hydrodynamic stability. The effect of non-Fourier heat transfer in couple stress in a Rayleigh Benard configuration is analyzed theoretically in this thesis. Broad range of applications of couple stress fluid and the need for its characterization at a relatively small scale of time and length act as a motivation for the study of buoyancy driven convection in such fluids under the influence of magnetic field and under various modulations such as temperature, gravity, rotation and magnetic field by employing Maxwell Cattaneo law.
newlineLinear and non linear magneto convection in couple stress fluid with Maxwell Cattaneo law
newlineThe interesting facets brought about by the interactions between convection and magnetic fields in a Rayleigh Benard configuration for free free boundaries are analyzed in this chapter. Linear and weakly non linear stability analysis are carried out to study the system. It is proved that the oscillatory mode is not the preferred mode of instability. The couple stresses in the fluid and magnetic field are found to enhance the stability of the system whereas non-Fourier effects destabilized the system.
newlineEffect of temperature modulation on the onset of Rayleigh Benard convection in a couple stress fluid with Maxwell Cattaneo law
newlineThe effect of externally imposed time-periodic boundary temperature on the setting in of convection is examined using linear stability analysis. The Venezian approach is applied to deduce the critical Rayleigh number and critical wave number. The stability of the system is characterized by a correction Rayleigh number and is obtained as a function of the Cattaneo number couple stress parameter Prandtl number and the frequency of modulation. The study analyzes three types of temperature modulations viz. in phase, out of phase and only lower wall modulation.Study of different types of modulations on double diffusive convection in oldroyd b liquids
http://hdl.handle.net/10603/244973
Title: Study of different types of modulations on double diffusive convection in oldroyd b liquids
Abstract: THE STUDY OF EFFECTS OF TEMPERATURE MODULATION ON DOUBLE DIFFUSIVE CONVECTION IN OLDROYD B LIQUIDS
newlineThe problem aims to find the effects of temperature modulation in viscoelastic
newlinefluids namely Oldroyd B liquids subjected to double diffusive convection. Both linear as well as a non-linear study has been carried out. A regular perturbation technique has been employed to determine the correction Rayleigh number. The results show that the Lewis number and strain retardation parameter induces stability to the system whereas stress relaxation parameter destabilizes the system for synchronous modulation. Truncated Fourier series represents the non-linear
newlineanalysis. Mean Nusselt number and mean Sherwood number are used to quantify the
newlineheat and mass transfer respectively. Strain retardation parameter and the Lewis number decrease the heat and mass transfer for synchronous modulation while stress relaxation parameter increases them. The opposite results are obtained for
newlineasynchronous and lower wall modulations. Modulation is shown mostly to give rise
newlineto super critical motion.
newlineTHE STUDY OF EFFECTS OF GRAVITY MODULATION ON DOUBLE DIFFUSIVE CONVECTION IN OLDROYD B LIQUIDS
newlineThe effect of gravity modulation is analysed in Oldroyd-B liquids subjected to double diffusive convection. Both linear and non-linear analysis has been done. A regular perturbation technique has been employed to arrive at the thermal Rayleigh number. The results show that stress relaxation destabilises the system whereas strain retardation parameter and Lewis number stabilises the system. Truncated Fourier series expansion gives a system of Lorentz equations that represent the nonlinear analysis. Mean Nusselt and mean Sherwood numbers are used to quantify the heat and mass transfer respectively. It is observed that Lewis number and strain retardation parameter decreases heat and mass transfer and stress relaxation parameter increases them. It is seen that modulation gives rise to sub critical motion.
newline
newlinePaired curves on riemannian manifolds
http://hdl.handle.net/10603/244156
Title: Paired curves on riemannian manifolds
Abstract: The thesis examines certain curves in Riemannian manifolds, which exist in one-one correspondence with other curves. This correspondence is described by means of a rigid link between the frame vectors allied
newlineto these quotpairedquot curves. The Combescure transformation is made use of to exhibit that one of the paired curves can be obtained as an infinitesimal deformation of the other. The correspondence between the paired curves is exploited to formulate expressions relating the curvature and torsion functions of one with the other.
newlineThe primary setting for this study is the Euclidean space R3, with brief considerations of 3-dimensional Riemannian space forms(i.e. Riemannian manifolds of constant sectional curvature). The exponential map is the desired tool of analysis in the latter case. The major classes of curves treated are the Mannheim class of curves in R3 and their partner curves. Further, with the help of the
newlinenotion of the osculating helix, a new class of curves called constantpitch curves are defined, which are seen to naturally arise in motion analysis studies in theoretical kinematics. Constant-pitch curves are
newlinealso shown to be inherent counterparts of Mannheim curves by means of a deformation.
newlinePivotal properties of Mannheim and constant-pitch curves are established and a few examples are put forth. Integral characterizations of both curves are derived in terms of their spherical indicatrices. A
newlineconsequence of this to geometric modeling problems involving energy functionals and also to the study of elastic curves is discussed.
newlineCertain ruled surfaces generated by Mannheim and constant-pitch curves which occur as axodes associated to a rigid body motion are
newlinedetailed and their applications to kinematics are studied. Further, the nature of paired curves in connection with tubular neighbourhoods/surfaces are investigated.
newlineA Study on certain chromatic parameters and polynomials of graphs
http://hdl.handle.net/10603/220079
Title: A Study on certain chromatic parameters and polynomials of graphs
Abstract: In graph theory, graph colouring pertains to the assignment of colours to the elements of a graph such as vertices, edges and faces. Because of the theoretical and practical implications of graph colourings in real-life situations, it is an adequate mathematical model for a wide range of applications such as network analysis, genomic, routing,
newlineoptimisation techniques, digital networks and so forth.Motivated by various problems in chemical graph theory and information networks, chromatic topological indices were introduced in recent literature [81], opening ample and vibrant research area in graph theory.In the research reported in this thesis,the vertices of a graph are assigned with colours subject to certain conditions and manipulating their colour codes, a rich research area on chromatic topological indices and different chromatic polynomials are established.
newlineAfter mentioning some fundamental terminologies, the study handles the notions of chromatic topological indices and chromatic irregularity indices. A detailed discussion of their upper and lower bounds concerning certain colouring conditions is carried out in this thesis. Chromatic topological indices of a wide variety of graph classes such as wheels, double wheels, helm graphs, closed helm graphs, flower graphs, sunflower graphs and blossom graphs are considered and investigated. The chromatic topological indices of certain derived graphs such as Mycielskian of paths and cycles are also included. Equitable chromatic topological and irregularity indices and injective chromatic topological and irregularity indices are defined and their values are determined for a handful of graph classes. As an indirect analogue to chromatic polynomials in the literature, the notion of chromatic Zagreb polynomials and chromatic irregularity polynomials are being introduced and the same is determined and discussed for paths, cycles and certain cycle related graph classes.