Biomagnetic fluid dynamics is an interdisciplinary field comprising engineering, medicine, and biology. Bio fluid dynamics is directed towards finding and developing the solutions to some of the human body related diseases and disorders. This article describes the flow and heat transfer of two dimensional, steady, laminar, viscous and incompressible biomagnetic fluid over a non-linear stretching sheet in the presence of magnetic dipole. Our model is consistent with blood fluid namely biomagnetic fluid dynamics (BFD). This model based on the principles of ferrohydrodynamic (FHD). The temperature at the stretching surface is assumed to follow a power law variation, and stretching velocity is assumed to have a nonlinear form with signum function or sign function. The governing boundary layer equations with boundary conditions are simplified to couple higher order equations using usual 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. Computations are performed for a wide range of the governing parameters such as magnetic field parameter, power law exponent temperature parameter, and other involved parameters and the effect of these parameters on the velocity and temperature field is presented. It is observed that for different values of the magnetic parameter, the velocity distribution decreases while temperature distribution increases. Besides, the finite difference solutions results for skin-friction coefficient and rate of heat transfer are discussed. This study will have an important bearing on a high targeting efficiency, a high magnetic field is required in the targeted body compartment.
The objective of this theoretical study is to develop simple design formulas for the prediction of minimum film thickness and maximum mean film temperature rise in lightly loaded high-speed rolling/sliding lubricated elliptical contacts incorporating starvation effect. Herein, the reported numerical analysis focuses on thermoelastohydrodynamically lubricated rolling/sliding elliptical contacts, considering the Newtonian rheology of lubricant for wide range of operating parameters, namely load characterized by Hertzian pressure (PH = 0.01 GPa to 0.10 GPa), rolling speed (>10 m/s), slip parameter (S varies up to 1.0), and ellipticity ratio (k = 1 to 5). Starvation is simulated by systematically reducing the inlet supply. This analysis reveals that influences of load, rolling speed, and level of starvation are significant on the minimum film thickness. However, the maximum mean film temperature rise is strongly influenced by slip in addition to load, rolling speed, and level of starvation. In the presence of starvation, reduction in minimum film thickness and increase in maximum mean film temperature are observed. Based on the results of this study, empirical relations are developed for the prediction of dimensionless minimum film thickness and dimensionless maximum mean film temperature rise at the contacts in terms of various operating parameters.
In this paper, the problem of steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is considered. The similarity transformations are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual solutions are found for a certain range of the suction and stretching/shrinking parameters. The effects of the suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed.