Department of Applied Mathematics
http://repository.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/87
Tue, 27 Oct 2020 15:29:47 GMT2020-10-27T15:29:47ZBiomagnetic fluid flows over a stretching sheet
http://repository.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/1623
Biomagnetic fluid flows over a stretching sheet
Talukder, Md. Ghulam Murtaza
Biomagnetic fluid (Blood) is a fluid that exists in a living creature and its flow is influenced
by the presence of a magnetic field. Blood is considered to be a typical biomagnetic fluid due
to the interaction of intercellular proteins, membrane and the hemoglobin. Studies on
biomagnetic fluid flow and heat transfer under the influence of external magnetic fields have
been received much attention of researchers owing to their important applications in
bioengineering and clinical sciences. Design and development of magnetic devices for cell
separation, reduction of blood flow during surgery, targeted transport of drugs through the
use of magnetic particles as drug carriers, magnetic resonance imaging (MRI) of specific
parts of the human body, electromagnetic hyperthermia in cancer treatment are among these
applications.
In this thesis, we emphasized to the theoretical and numerical investigations of both
two-three dimensional, steady-unsteady, Newtonian, viscous, incompressible and laminar
biomagnetic fluid flow and heat transfer over stretching-shrinking sheets under various
boundary geometry with the action of an applied magnetic field.
Throughout this thesis, we first perform the biomagnetic fluid flow (BFD) over an
elastic flat stretching sheet in the presence of a magnetic dipole. For the mathematical
formulation of this problem both magnetization and electrical conductivity of blood are taken
into account and consequently both principles of Magnetohydrodynamics (MHD) and
FerroHydroDynamics (FHD) are adopted. The biomagnetic fluid flow and heat transfer in
three-dimensional unsteady stretching/shrinking sheet in the presence of ferromagnetic
phenomena has also been investigated. The main contribution is the study of three
dimensional time dependent BFD flow which has not been considered yet to our best
knowledge. Then, we investigate the time-dependent two-dimensional biomagnetic fluid
flow (BFD) over a stretching sheet under the action of electrical conductivity and
magnetization. A detailed stability and convergence analysis is performed to determine the
restrictions for the values of the problem parameters like magnetic parameter which are of
crucial importance for the formation of the flow fields. This could be predicted numerically
by the application of the simple efficient finite difference method (EFDM).
Later on, we have analyzed the steady biomagnetic fluid flow which is stretched with a
velocity proportional to dis tan cen i. e. nonlinear stretching sheet considering variable
thickness. In this model, we assume that the fluid is electrically conducting due to an applied
magnetic field and mathematical formulation also incorporates the space and time dependentv
internal heat generation. Internal heat generation accelerates the mechanical strength of fluid
flows throughout the boundary layer. We have also investigated the effects of variable fluid
properties on the flow and heat transfer of three dimensional biomagnetic fluid over a
stretching surface in the presence of a magnetic dipole. In this problem, the dynamic viscosity
and thermal conductivity of biomagnetic fluid is considered to be temperature dependent
whereas the magnetization of the fluid varies as a linear function of temperature and magnetic
field strength. Also the surface temperature distribution across the sheet is non-linear.
To solve the above mathematical problem, the governing boundary layer equations
with associated boundary conditions, are transformed into a system of nonlinear coupled
ordinary differential equations by using suitable similarity transformations. Numerical
solutions for the governing momentum and energy equations are obtained by efficient
numerical techniques based on the common finite difference method with central
differencing, on a tridiagonal matrix manipulation and on an iterative procedure.
Our next intention is to characterize the existence of duality of mathematical problem
solutions and their physical realizable. The dual solutions are obtained by setting different
initial guesses for the missing values of the skin friction coefficient and the local Nusselt
number, where all profiles satisfy the far field boundary conditions asymptotically. For the
first time, we have examined the dual solutions in biomagnetic fluid flow and heat transfer
over a nonlinear stretching or shrinking sheet in the presence of a magnetic dipole
with/without prescribed heat flux. This problem has been treated mathematically by using Lie
group transformation and the resulting equations are solved numerically by using bvp4c
function available in MATLAB and reported the existence of dual solution (stable solution
and unstable solution) in the flow analysis. A stability analysis has also been carried out and
presented here. Results from the stability analysis depict that the first solution (upper branch)
is stable and physically realizable, while the second solution (lower branch) is unstable.
In all these analysis, influence of various physical parameters involved like as
hydrodynamic, magnetohydrodynamic and ferromagnetic interaction parameters,
unsteadiness parameter, suction/injection parameters, stretching ratio and heat generation
parameter, viscosity parameter, thermal conductivity parameter, and velocity/temperature
index parameter on the fluid flow are investigated and the results have been presented
graphically. Missing slope like as the skin friction coefficient, , heat transfer rate and relative
wall pressure is revealed and special case with change in hydrodynamic and ferromagnetic
parameters have also been illustrated. The results of the present study have been compared
with those of an earlier study reported in available literatures in order to ascertain the validityvi
of the computational results. Once we achieved good accuracy we go further for detailed
results. The numerical results of the study reveal that the characteristics of blood flow are
significantly affected by the presence of a magnetic dipole which gives rise to a magnetic
field, sufficiently strong to saturate the biofluid.
This thesis submitted for the degree of Doctor of Philosophy in The University of Dhaka.
Mon, 16 Mar 2020 00:00:00 GMThttp://repository.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/16232020-03-16T00:00:00ZStudies on Eigenvalue Analysis for a Class of Differential Equations by the Methods of Weighted Residuals
http://repository.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/1545
Studies on Eigenvalue Analysis for a Class of Differential Equations by the Methods of Weighted Residuals
Farzana, Humaira
This thesis submitted for the degree of Doctor of Philosophy in The University of Dhaka.
Tue, 10 Dec 2019 00:00:00 GMThttp://repository.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/15452019-12-10T00:00:00ZMHD free-forced convection and mass transfer flow through temperature stratified high-porosity medium from a vertical plate with power-law variation wall temperature in the presence of hall and ion-slip currents
http://repository.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/964
MHD free-forced convection and mass transfer flow through temperature stratified high-porosity medium from a vertical plate with power-law variation wall temperature in the presence of hall and ion-slip currents
Hossain, Md. Delowar
Considerable research efforts have been devoted to the study of MHD free-force convection and mass transfer flow through temperature stratified high porosity medium from a vertical plate with power-law variation wall temperature in the presence of Hall and ion-slip currents under various flow conditions. A magnetic field is applied perpendicular to the plates. Various configurations have been considered for the plates. The whole system is rotated with a constant angular velocity Ω. The Hall and ion-slip currents effect has also been put into consideration. The effects of changing various parameters on the velocity, temperature and concentration distributions have been discussed. However, finding exact solutions of nonlinear problems is very difficult. In particular, obtaining an exact analytic solution of a given nonlinear problem is often more complicated as compared to that of a numerical solution, despite the availability of high performance supercomputers and software which provide efficient ways to perform high quality symbolic computations. In our analysis, the primary focus has been shown on the study of the physical and mathematical structure of fluid models. Method of explicit and implicit finite difference method, Nachtsheim-Swigert iteration technique are used as main tools for numerical approach while the perturbation technique is used for the analytical approach. The studies of the flow feature mentioned above are made in different sections taking different aspects of the flow that are of practical importance. The non-dimensional coupled partial differential equations of the momentum, energy and concentration equations are derived by considering suitable usual transformation and similarity variables. Also stability analysis has been derived for conversed solutions. In section 4.1 of chapter 4, the similarity solutions have been obtained for one dimensional unsteady MHD free convection and mass transfer flow through a vertical oscillatory porous plate in a rotating porous medium with Hall, ion-slip currents and heat source. Two cases are considered, (a) analytical solution with perturbation technique, (b) numerical solution by implicit finite difference method. In section 4.2 of chapter 4 and section 5.1, 5.2 of chapter 5, similarity solutions have been obtained by finite difference method (implicit and explicit). The numerical solutions for the velocity profiles, temperature distributions as well as concentration distributions are obtained using implicit finite difference method for the effects of the various important parameters entering into the problem in case of the one dimensional problem. Also the shear stress, Nusselt number as well as Sherwood number have been computed by implicit finite difference method in case of one dimensional flow. Further the above mentioned flow problem has been considered for two dimensional case, unsteady MHD free convective flow. The local and average shear stresses as well as Nusselt number and Sherwood number have been computed by explicit finite difference technique in case of two dimensional flows. In both cases the stability conditions and convergence criteria of the explicit finite difference scheme have been analyzed for finding the restriction of the values of various parameters to get more accuracy. In chapter 6, similarity equations of the corresponding momentum and energy equations are derived by introducing a time dependent length scale which in fact plays the role of a similarity parameter. The suction velocity is taken to be inversely proportional to this parameter. In Chapter 7, the flow structures of stratification fluid models are investigated in detail and some new exact solutions have been obtained. The ambient temperature has been assumed to be an increasing function with the distance along the plate. The heat transfer changes significantly with the stratification and magnetic parameters. In Chapter 8, power-law variation wall temperature along vertical plate, in the presence of Hall and ion-slip currents are discussed. The plate surface has a power-law variation wall temperature and is permeable to allow for possible fluid with wall suction or blowing, velocity varied according to a power-law. The Nachtsheim-Swigert iteration technique has been used Chapter6, Chapter 7 and Chapter 8. The effects on the velocities, temperature, concentration, local and average shear stresses, Nusselt and Sherwood numbers of the various important parameters entering into the problems separately are discussed for each problem with the help of graphs and tables. Finally, in Chapter 9, a general discussion on the overall results of the problems considered in the dissertation is sorted out.
This thesis Submitted in Fulfillment of the Requirements for the Award of the Degree of Doctor of Philosophy in Applied Mathematics.
Sun, 16 Jun 2019 00:00:00 GMThttp://repository.library.du.ac.bd:8080/xmlui/xmlui/handle/123456789/9642019-06-16T00:00:00Z