This paper is concerned with the investigation of steady, two-dimensional, and laminar boundary layer flow of a biomagnetic fluid over a continuously moving sheet in the presence of a magnetic dipole. The magnetic field resulting from the dipole is contemplated to be strong enough to saturate the biofluid. The magnetization of the fluid is regarded to be a linear function of temperature. The solution procedure involves the reduction of a nonlinear system of coupled PDEs into ODEs that comprise five parameters. The transformed ODEs along with the boundary conditions are then solved numerically by introducing an efficient numerical technique based on the finite difference algorithm. The velocity, as well as temperature profiles within the boundary layer, are illustrated at specified values of free stream velocity (U-infinity), wall velocity (U-w) and ferrohydrodynamic interaction parameter(beta) .The demonstration of the Nusselt number and friction factor are achieved for various governing parameters. Considering a specified Prandtl number (Pr = 7) and normalized velocity difference|U-w-U-infinity|, higher values of the friction factor are obtained for increasing beta and U-w > U-infinity than that of U-infinity > U-w. Whereas for the Nusselt number, we attain higher values for decreasing beta and U-w > U-infinity . Moreover, an increase in the velocity ratio U-infinity /U-w results in a decrease in both heat transfer rate as well as friction factor. Further-more, as beta increases, the heat transfer rate decreases yet we get higher values for higher Pr ,U-infinity and U-w. In the case of friction factor, it increases with increasing beta and gives higher values for lower Pr, U-infinity and higher U-w . We have also depicted the stream lines for the 2-D boundary layer flow of the biomagnetic fluid for different beta. The graphical results manifest that the flow field is greatly impacted by the ferrohydrodynamic field, which could be of interest in medical as well as bioengineering implementations, like, magnetic drug delivery in blood cells, separating RBCs as well as controlling the flow of blood during surgical procedures.

This research concentrates on the 2-D, steady, laminar, viscous, incompressible boundary layer flow of a biomagnetic fluid containing two different magnetic particles (CoFe2O4andFe3O4) over a continuously moving horizontal plate in the presence of a magnetic field generated by a magnetic dipole. For the mathematical formulation the comprehensive concept of Biomagnetic Fluid Dynamics (BFD) is adopted incorporating the principles of FerroHydroDynamics (FHD) and MagnetoHydroDynamics (MHD). The physical problem which is constituted by a coupled system of Partial Differential Equations (PDEs) along with corresponding boundary conditions, is transformed into a coupled system of nonlinear Ordinary Differential Equations (ODEs) subject to analogous boundary conditions by establishing newly simplified similarity transformations. The transformed ODEs along with the boundary conditions are then solved numerically by introducing an efficient numerical technique based on a finite difference algorithm. Verification of this work has been also done by comparing the obtained results with previously published results and found in quite good agreement. The significant effects caused by the variation of the governing parameters such as the skin friction, heat transfer rate and wall pressure are presented more intricately. It has been contemplated that including magnetic particles with pure blood enhances the impact of the magnetic field on the flow, temperature and pressure profiles which could be of interest engineering implementations, like, magnetic drug delivering in blood cells, separating RBCs (Red Blood Cells), controlling the flow of blood during surgeries, treating cancer by producing magnetic hyperthermia etc.

The present study used a simplified axisymmetric biomagnetic fluid dynamics and porous mediamodel which includes FHD (Ferrohydrodynamics), porosity and inertia effects saturated by magnetic dipole to study the influences of the leading parameters on various flow variables along a flat plate.The governing equations are simplified and solved by finite difference approach. We clarify how the ferromagnetic interaction parameter, B and porosity,ε assumptions contribute in the bio-background of the problem of interest. Moreover, from the results of the flow profiles, accelerating and decelerating phenomena are noticed for B, and ε interaction.

A two-dimensional (2D) steady boundary layer flow along with heat transfer of a self-similar biomagnetic fluid over a permeable moving flat plate has been taken into consideration in this work. The flow is contemplated to be embedded by a magnetic dipole of sufficient magnetic strength. Transpiration as well as movement along the wall is also regarded. By imposing the appropriate similarity technique, the governing equations are converted into a system of coupled nondimensional equations. An efficient numerical technique has been incorporated to solve these dimensionless coupled nonlinear ordinary differential equations. The existence of dual solutions along with their stability has been established with the consideration of stability analysis. We discovered from our analysis that two solutions exist (one stable and another unstable) for the arbitrary values of transpiration, movement velocity and biomagnetic interaction parameters on flow and physical parameters. The attained results are demonstrated graphically and in tabular form. For the validity of our numerical scheme, we compared our findings with others previously published and found significant agreement.

This work aims at the investigation of 2D, steady, laminar, viscous, incompressible boundary layer and heat transfer flow of a biomagnetic fluid over a convectively heated moving horizontal plate in the presence of a magnetic dipole. It is assumed that the fluid viscosity is the inverse linear function of temperature and the temperature at the wall varies as power law function. The governing equations involve a system of coupled PDEs (momentum and energy equations) which are converted into a system of nonlinear ODEs by utilizing similarity transformations. The transformed ODEs along with the boundary conditions are then solved numerically by adopting a finite difference algorithm. The physical effects of the governing parameters (i.e., ferrohydrodynamic interaction parameter, buoyancy force parameter, viscosity-temperature parameter, wall parameter) on the flow fields along with the skin friction and heat transfer rate are presented. Verification of this work has been done by comparing former published results and acceptable agreement is found. It has been analyzed theoretically by using suitable transformations, that the ferrohydrodynamic interaction parameter, has a great enhancement effect on biomagnetic fluid rather than that on a regular fluid. It has been discovered that the inclusion of certain intensity of magnetic field along with the consideration of the variable viscosity and temperature, has significant effects on the flow and heat transfer mechanism. These outcomes could be of interest in medical as well as bioengineering implementations, like magnetic drug delivering in blood cells, separating RBCs (Red Blood Cells), controlling the flow of blood during surgeries and treating cancer by producing magnetic hyperthermia.

In this work, we discuss some very simple and extremely efficient lattice models, namely, Binomial tree model (BTM) and Trinomial tree model (TTM) for valuing some types of exotic barrier options in details. For both these models, we consider the concept of random walks in the simulation of the path which is followed by the underlying stock price. Our main objective is to estimate the value of barrier options by using BTM and TTM for different time steps and compare these with the exact values obtained by the benchmark Black-Scholes model (BSM). Moreover, we analyze the convergence of these lattice models for these exotic options. All the results have been shown numerically as well as graphically.GANITJ. Bangladesh Math. Soc.41.1 (2021) 26-40

The 2-D MHD nanofluid with mixed convection above a stretching/shrinking plate has been investigated. Melting heat transfer near surface is contemplated. Consider the saline water as base fluid with containing single SWCNTs as well as MWCNTs. Suitable similarity variables are employed to transform the governing PDEs into ODEs. These transformed equations which are coupled, and of high nonlinearity, have been solved through applying the bvp4c solver. The consequences of the relevant parameters like, the MHD parameter, mixed convection parameter, melting parameter, volume fraction on the flow field along with the skin friction and heat transfer rate are displayed in graphical form. Results show that the thin layer thickness diminishes as magnetic parameter enhances and at the same time temperature increases with magnetic parameter. It is also demonstrated that the melting parameter leads to a reduction in the thin layer thickness as well as dimensionless temperature. Obtain dual solutions for flow fields which delineates to identify the stable solution.