M.Sc.http://hdl.handle.net/20.500.12228/502022-10-02T16:09:43Z2022-10-02T16:09:43ZAnalytical Technique for Solving Second Order Generalized Strongly Nonlinear Duffing Equation with Varying Coefficients in Presence of Small DampingKundu, Dipahttp://hdl.handle.net/20.500.12228/5432019-10-02T21:00:13Z2019-08-01T00:00:00ZAnalytical 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).
2019-08-01T00:00:00ZA study on standard n-ideal of a latticeHossen, Md Imranhttp://hdl.handle.net/20.500.12228/5202019-07-07T21:00:15Z2019-04-01T00:00:00ZA 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).
2019-04-01T00:00:00ZSteady MHD Natural Convection Heat and Mass Transfer Flow above a Vertical Porous Surface with Thermal Diffusion and Inclined Magnetic FieldRana, Md. Sohelhttp://hdl.handle.net/20.500.12228/4782018-12-31T21:00:10Z2018-08-01T00:00:00ZSteady 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).
2018-08-01T00:00:00ZSimilarity Solution of Unsteady Convective Heat and Mass Transfer Flow along an Isothermal Vertical Plate with SuctionGhosh, Tumpa Ranihttp://hdl.handle.net/20.500.12228/4662018-12-23T21:00:13Z2018-07-01T00:00:00ZSimilarity 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