Biomagnetic fluid flows over a stretching sheet

Abstract

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 cen 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.