Abstract: 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.
Abstract: The magnetohydrodynamic (MHD) Falkner-Skan
equations appear in study of laminar boundary layers flow over
a wedge in presence of a transverse magnetic field. The partial
differential equations of boundary layer problems in presence of
a transverse magnetic field are reduced to MHD Falkner-Skan
equation by similarity solution methods. This is a nonlinear ordinary
differential equation. In this paper, we solve this equation via
spectral collocation method based on Bessel functions of the first
kind. In this approach, we reduce the solution of the nonlinear
MHD Falkner-Skan equation to a solution of a nonlinear algebraic
equations system. Then, the resulting system is solved by Newton
method. We discuss obtained solution by studying the behavior
of boundary layer flow in terms of skin friction, velocity, various
amounts of magnetic field and angle of wedge. Finally, the results
are compared with other methods mentioned in literature. We can
conclude that the presented method has better accuracy than others.
Abstract: A cold, thin film of liquid impinging on an isothermal
hot, horizontal surface has been investigated. An approximate
solution for the velocity and temperature distributions in the flow
along the horizontal surface is developed, which exploits the
hydrodynamic similarity solution for thin film flow. The approximate
solution may provide a valuable basis for assessing flow and heat
transfer in more complex settings.
Abstract: This analysis is performed to study the momentum, heat and mass transfer characteristics of MHD mixed convective flow past inclined porous plate in porous medium, including the effect of fluid suction. The fluid is assumed to be steady, incompressible and dense. Similarity solution is used to transform the problem under consideration into coupled nonlinear boundary layer equations which are then solved numerically by using the Runge-Kutta sixth-order integration scheme together with Nachtsheim-Swigert shooting iteration technique. Numerical results for the various types of parameters entering into the problem for velocity, temperature and concentration distributions are presented graphically and analyzed thereafter. Moreover, expressions for the skin-friction, heat transfer co-efficient and mass transfer co-efficient are discussed with graphs against streamwise distance for various governing parameters.
Abstract: Non-isothermal stagnation-point flow with consideration of thermal radiation is studied numerically. A set of partial differential equations that governing the fluid flow and energy is converted into a set of ordinary differential equations which is solved by Runge-Kutta method with shooting algorithm. Dimensionless wall temperature gradient and temperature boundary layer thickness for different combinaton of values of Prandtl number Pr and radiation parameter NR are presented graphically. Analyses of results show that the presence of thermal radiation in the stagnation-point flow is to increase the temperature boundary layer thickness and decrease the dimensionless wall temperature gradient.
Abstract: The group invariant solution for Prandtl-s boundary layer equations for an incompressible fluid governing the flow in radial free, wall and liquid jets having finite fluid velocity at the orifice are investigated. For each jet a symmetry is associated with the conserved vector that was used to derive the conserved quantity for the jet elsewhere. This symmetry is then used to construct the group invariant solution for the third-order partial differential equation for the stream function. The general form of the group invariant solution for radial jet flows is derived. The general form of group invariant solution and the general form of the similarity solution which was obtained elsewhere are the same.
Abstract: In this paper, the two-dimensional reversed stagnationpoint
flow is solved by means of an anlytic approach. There are
similarity solutions in case the similarity equation and the boundary
condition are modified. Finite analytic method are applied to obtain
the similarity velocity function.
Abstract: The boundary layer flow and heat transfer on a
stretched surface moving with prescribed skin friction is studied for
permeable surface. The surface temperature is assumed to vary
inversely with the vertical direction x for n = -1. The skin friction at
the surface scales as (x-1/2) at m = 0. The constants m and n are the
indices of the power law velocity and temperature exponent
respectively. Similarity solutions are obtained for the boundary layer
equations subject to power law temperature and velocity variation.
The effect of various governing parameters, such as the buoyancy
parameter λ and the suction/injection parameter fw for air (Pr = 0.72)
are studied. The choice of n and m ensures that the used similarity
solutions are x independent. The results show that, assisting flow (λ >
0) enhancing the heat transfer coefficient along the surface for any
constant value of fw. Furthermore, injection increases the heat
transfer coefficient but suction reduces it at constant λ.
Abstract: This paper investigates the nature of the development
of two-dimensional laminar flow of an incompressible fluid at the
reversed stagnation-point. ". In this study, we revisit the problem
of reversed stagnation-point flow over a flat plate. Proudman and
Johnson (1962) first studied the flow and obtained an asymptotic
solution by neglecting the viscous terms. This is no true in neglecting
the viscous terms within the total flow field. In particular it is pointed
out that for a plate impulsively accelerated from rest to a constant
velocity V0 that a similarity solution to the self-similar ODE is
obtained which is noteworthy completely analytical.
Abstract: The data measurement of mean velocity has been
taken for the wake of single circular cylinder with three different diameters for two different velocities. The effects of change in
diameter and in velocity are studied in self-similar coordinate system.
The spatial variations of velocity defect and that of the half-width
have been investigated. The results are compared with those
published by H.Schlichting. In the normalized coordinates, it is also observed that all cases except for the first station are self-similar. By attention to self-similarity profiles of mean velocity, it is observed for all the cases at the each station curves tend to zero at a same point.
Abstract: Fluid flow and heat transfer of vertical full cone
embedded in porous media is studied in this paper. Nonlinear
differential equation arising from similarity solution of inverted cone
(subjected to wall temperature boundary conditions) embedded in
porous medium is solved using a hybrid neural network- particle
swarm optimization method.
To aim this purpose, a trial solution of the differential equation is
defined as sum of two parts. The first part satisfies the initial/
boundary conditions and does contain an adjustable parameter and
the second part which is constructed so as not to affect the
initial/boundary conditions and involves adjustable parameters (the
weights and biases) for a multi-layer perceptron neural network.
Particle swarm optimization (PSO) is applied to find adjustable
parameters of trial solution (in first and second part). The obtained
solution in comparison with the numerical ones represents a
remarkable accuracy.
Abstract: The problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers based on the boundary layer approximation and the Darcy-s law have been studied before. Similarity solutions for a full cone with the prescribed wall temperature or surface heat flux boundary conditions which is the power function of distance from the vertex of the inverted cone give us a third-order nonlinear differential equation. In this paper, an approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev Tau (RCT) method. The operational matrices of the derivative and product of rational Chebyshev (RC) functions are presented. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. We also present the comparison of this work with others and show that the present method is applicable.
Abstract: The problem of laminar fluid flow which results from
the shrinking of a permeable surface in a nanofluid has been
investigated numerically. The model used for the nanofluid
incorporates the effects of Brownian motion and thermophoresis. A
similarity solution is presented which depends on the mass suction
parameter S, Prandtl number Pr, Lewis number Le, Brownian motion
number Nb and thermophoresis number Nt. It was found that the
reduced Nusselt number is decreasing function of each dimensionless
number.