http://hdl.handle.net/20.500.12228/50 2026-04-07T02:40:31Z 2026-04-07T02:40:31Z Kundu, Dipa http://hdl.handle.net/20.500.12228/543 2019-10-02T21:00:13Z 2019-08-01T00:00:00Z

Analytical Technique for Solving Second Order Generalized Strongly Nonlinear Duffing Equation with Varying Coefficients in Presence of Small Damping Kundu, Dipa In this thesis, we have extended He’s homotopy perturbation method for obtaining the approximate analytical solution of second order generalized strongly nonlinear Duffing equation with varying coefficients in presence of significant small damping based on the extended form of the Krylov-Bogoliubov-Mitropolskii (KBM) method. Accuracy and validity of the solutions obtained by the present method are compared with the corresponding numerical solutions obtained by the well-known fourth order Runge- Kutta method in graphically. The method has been illustrated by examples. In this study, the present technique gives acceptable results avoiding any numerical complexity. The results presented through figures show that the approximations are of extreme accuracy with significant damping. The proposed method is simple and suitable for solving the above mentioned nonlinear damped systems. This thesis is submitted to the Department of Mathematics, Khulna University of Engineering & Technology in partial fulfillment of the requirements for the degree of Master of Science in Mathematics, August 2019.; Cataloged from PDF Version of Thesis.; Includes bibliographical references (pages 28-31).

2019-08-01T00:00:00Z Hossen, Md Imran http://hdl.handle.net/20.500.12228/520 2019-07-07T21:00:15Z 2019-04-01T00:00:00Z

A study on standard n-ideal of a lattice Hossen, Md Imran Lattice theory is an important part of mathematics . Ideal lattice and n-ideal of a lattice have played many roles in development of lattice theory. Historically, lattice theory started with Boolean distributive lattices: as a result, the theory of ideal lattice and n-ideal of a lattice is the most extensive and most satisfying chapter in the history of lattice theory. Ideal lattice have provided the motivation for many results, in general lattice theory. Many conditions on lattices and on element and ideals of lattices are weakened forms of distributivity is imposed on lattices arising in various areas of mathematics, especially algebra. In lattice theory there are different classes of lattices known as variety of lattices. Class of Boolean lattice is of course most powerful variety. Throughout this thesis we will be concerned with another large variety known as the class of ideal lattice and n-ideal of a lattice have been studied by several authors. The realization of special role of ideal lattices moved to break with the traditional approach to lattice theory, which proceeds from partially ordered sets to general lattices, semi modular lattices, modular lattices and finally ideal lattices. In this thesis we give several result on ideal and n-ideal which will certainly extend and generalize many results in lattice theory. In order to review, we include definations, examples, solved problems and proof of some theorems. The thesis contains four chapter. Chapter 1 we have discussed the basic defination of relation, poset, lattice, complete lattice, convex sub lattice, complemented and relatively complemented lattice. We also proved that, Dual of a complete lattice is complete . Chapter 2 have discussed basic concept of ideal and n-ideal of lattice. Here we study the defination and examples of ideal and n-ideal. Some imprtant theorem like “If n is a neutral element of a lattice, then I (L) n is modular if and only if L is modular”. Chapter 3 we have discussed Standard element and n-ideals. We also discussed in this chapter Congruence relation. Chapter 4 deals with standard n-ideal and Principal n-ideal. This is the main part of this thesis work. In this chapter we have discussed some defination and some important theorems like “For a neutral element n and a standard n-ideal S and an n-ideal I, S I is also a standard n-ideal” . This thesis is submitted to the Department of Mathematics, Khulna University of Engineering & Technology in partial fulfillment of the requirements for the degree of Master of Science in Mathematics, April 2019.; Cataloged from PDF Version of Thesis.; Includes bibliographical references (pages 49-50).

2019-04-01T00:00:00Z Rana, Md. Sohel http://hdl.handle.net/20.500.12228/478 2018-12-31T21:00:10Z 2018-08-01T00:00:00Z

Steady MHD Natural Convection Heat and Mass Transfer Flow above a Vertical Porous Surface with Thermal Diffusion and Inclined Magnetic Field Rana, Md. Sohel In this study the effect thermal diffusion and inclined magnetic field on the steady laminar natural convection heat and mass transfer flow of viscous incompressible MHD electrically conducting fluid past a vertical porous surface is considered under the influence of induced magnetic field. The governing non-dimensional equations relevant to the problem, containing the partial differential equations, are transformed by usual similarity transformations into a system of coupled non-linear ordinary differential equations and have been solved by using the perturbation technique. On introducing the non-dimensional concept and applying usual Boussinesq’s approximation, the solutions for velocity fields, temperature distribution, induced magnetic fields and mass concentration are obtained up to the second order approximations for different selected values of the established dimensionless parameters and numbers. The influences of these various establish parameters and numbers on the velocity and temperature fields, induced magnetic field and mass concentration are exhibited under certain assumptions and are studied graphically. Further, the effects of these dimensionless parameters on the coefficients of skin friction and rate of heat and mass transfers are also studied in tabular form in the present analysis. The effect of different angle of inclinations of the externally applied uniform magnetic field on the field variables have been investigated for the present problem. It is observed that with other useful associated parameters, the thermal diffusion and the angle of inclination of the applied magnetic field have a retarding influence on the fluid velocity, induced magnetic field and mass concentration as well. It is also found that the dimensionless Prandtl number, Grashof number, Modified Grashof number, magnetic parameter and suction parameter have their own dependency on the concerned independent field variables like the velocity, temperature, concentration and induced magnetic fields as well as on other physical parameters of interests like local skin-friction coefficient (Cf), Nusselt number (Nu) and Sherwood number (Sh). This thesis is submitted to the Department of Mathematics, Khulna University of Engineering & Technology in partial fulfillment of the requirements for the degree of Master of Science in Mathematics, August 2018.; Cataloged from PDF Version of Thesis.; Includes bibliographical references (pages 65-69).

2018-08-01T00:00:00Z Ghosh, Tumpa Rani http://hdl.handle.net/20.500.12228/466 2018-12-23T21:00:13Z 2018-07-01T00:00:00Z

Similarity Solution of Unsteady Convective Heat and Mass Transfer Flow along an Isothermal Vertical Plate with Suction Ghosh, Tumpa Rani In this study the similarity solutions of unsteady convective boundary layer heat and mass transfer flow of viscous incompressible fluid along an isothermal plate with suction is investigated. The similarity equations of the specified problem are obtained first by employing the usual similarity technique and Bousinesq approximation. Then the set of transformed ordinary differential equations has been solved numerically adopting the 6th order Range-Kutta method and to enumerate the unspecified initial conditions shooting method has been adopted. The non-dimensional solutions regarding the velocity, temperature and mass concentration have been found for different selected values of the established dimensionless numbers and parameters entering into the problem. The effect of suction on fluid flow and temperature fields as well as concentration distributions and other topics of interest like skin friction and heat transfer coefficients are extensively investigated. It is observed that the velocity at any point within the boundary layer increases with the increase of suction parameter (Fw). But both temperature and mass concentration decrease rapidly with the increasing values of Fw. The effects of some other involved dimensionless numbers and parameters like Prandtl number (Pr), local concentration Grashof number (Gc) and unsteadiness parameters (A1, A2, A3) on the velocity and temperature fields and on the concentration distributions have been investigated. The results show that fluid velocity decreases slowly but temperature decreases significantly with the increase of Pr whereas no appreciable change is found on concentration for increasing values of Pr. It is also found that velocity increases highly with the increase of Gc while the impact of Gc on the temperature and concentration are very diminutive. All the unsteadiness parameters also apparently affect the velocity, temperature and concentration distributions. The obtained numerical results involving the effects of these non-dimensional numbers and parameters on the velocity, temperature and concentration profiles are displayed with the help of various graphs. Finally, the dependency of wall shear stress (in terms of local Skin-friction coefficients) and wall heat flux (in terms of Nusselt number), which are of physical interests, on the concerned non-dimensional parameters and numbers are also illustrated and discussed through the tables. The obtained results might be of great interest for the creative learners regarding aerodynamics and hydrodynamics including industrial applications. This thesis is submitted to the Department of Mathematics, Khulna University of Engineering & Technology in partial fulfillment of the requirements for the degree of Master of Science in Mathematics, July 2018.; Cataloged from PDF Version of Thesis.; Includes bibliographical references (pages 38-41).

2018-07-01T00:00:00Z