**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**13

# Search results for: Similarity solution

##### 13 Similarity Solutions of Nonlinear Stretched Biomagnetic Flow and Heat Transfer with Signum Function and Temperature Power Law Geometries

**Authors:**
M. G. Murtaza,
E. E. Tzirtzilakis,
M. Ferdows

**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.

**Keywords:**
slip parameter,
biomagnetic fluid,
FHD,
nonlinear stretching sheet

##### 12 Spectral Investigation for Boundary Layer Flow over a Permeable Wall in the Presence of Transverse Magnetic Field

**Authors:**
Saeed Sarabadan,
Mehran Nikarya,
Kouroah Parand

**Abstract:**

**Keywords:**
velocity,
skin friction,
Bessel functions,
nonlinear ODE,
MHD Falkner-Skan,
spectral
collocation method

##### 11 Heat Transfer of an Impinging Jet on a Plane Surface

**Authors:**
Jian-Jun Shu

**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.

**Keywords:**
flux,
free impinging jet,
solid-surface,
uniform wall
temperature

##### 10 Flow and Heat Transfer of a Nanofluid over a Shrinking Sheet

**Authors:**
N. Bachok,
N. L. Aleng,
N. M. Arifin,
A. Ishak,
N. Senu

**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.

**Keywords:**
Nanofluid,
boundary layer,
shrinking sheet,
thermophoresis,
similarity solution,
Brownian motion

##### 9 Effect of Conjugate Heat and Mass Transfer on MHD Mixed Convective Flow past Inclined Porous Plate in Porous Medium

**Authors:**
Md. Nasir Uddin,
M. A. Alim,
M. M. K. Chowdhury

**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.

**Keywords:**
Heat and Mass Transfer,
MHD,
porous medium,
mixed convection,
Fluid suction,
inclined porous plate

##### 8 Mixed Convection Boundary Layer Flows Induced by a Permeable Continuous Surface Stretched with Prescribed Skin Friction

**Authors:**
Mohamed Ali

**Abstract:**

**Keywords:**
Boundary layers,
suction or injection,
similarity solutions,
Stretching surface,
Prescribed skin friction,
buoyancy effects

##### 7 Unsteady Reversed Stagnation-Point Flow over a Flat Plate

**Authors:**
Vai Kuong Sin,
Chon Kit Chio

**Abstract:**

**Keywords:**
Numerical Solution,
analytical solution,
reversed stagnation-point flow,
similarity solutions

##### 6 Another Approach of Similarity Solution in Reversed Stagnation-point Flow

**Authors:**
Vai Kuong Sin,
Chon Kit Chio

**Abstract:**

**Keywords:**
Asymptotic solution,
reversed stagnation-point flow,
similarity solutions

##### 5 Rational Chebyshev Tau Method for Solving Natural Convection of Darcian Fluid About a Vertical Full Cone Embedded in Porous Media Whit a Prescribed Wall Temperature

**Authors:**
Kourosh Parand,
Zahra Delafkar,
Fatemeh Baharifard

**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.

**Keywords:**
Porous Media,
tau method,
semi-infinite,
nonlinear ODE,
rational Chebyshev

##### 4 A New Solution for Natural Convection of Darcian Fluid about a Vertical Full Cone Embedded in Porous Media Prescribed Wall Temperature by using a Hybrid Neural Network-Particle Swarm Optimization Method

**Authors:**
M.A.Behrang,
M. Ghalambaz,
E. Assareh,
A.R. Noghrehabadi

**Abstract:**

**Keywords:**
Porous Media,
Particle Swarm Optimization (PSO),
Ordinary Differential Equations
(ODE),
Neural Network (NN)

##### 3 Effect of Thermal Radiation on Temperature Variation in 2-D Stagnation-Point flow

**Authors:**
Vai Kuong Sin

**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.

**Keywords:**
Thermal radiation,
similarity solution,
stagnation-point flow

##### 2 Investigation of Self-Similarity Solution for Wake Flow of a Cylinder

**Authors:**
A. B. Khoshnevis,
F. Zeydabadi,
F. Sokhanvar

**Abstract:**

**Keywords:**
Self-similarity,
wake of single circular cylinder

##### 1 Group Invariant Solutions for Radial Jet Having Finite Fluid Velocity at Orifice

**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.

**Keywords:**
Two-dimensional jets,
radial jets,
group invariant solution