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Effects of Viscous Dissipation and Heat Generation on Magneto Hydrodynamics Natural Convection Flow along a Vertical Wavy Surface
Sujon Nath,
Nazma Parveen
Issue:
Volume 2, Issue 6, December 2014
Pages:
197-203
Received:
13 November 2014
Accepted:
24 November 2014
Published:
27 November 2014
Abstract: In this paper we consider the combined effects of viscous dissipation and heat generation on MHD natural convection flow along a vertical wavy surface are studied. The governing Navier-Stokes equations with associated boundary conditions are transformed into non-dimensional boundary layer equations using appropriate variables. Implicit finite difference method based on Keller-box scheme is used to solve these governing equations. The numerical results in terms of the skin friction coefficient, the rate of heat transfer in terms of local Nusselt number, the streamlines as well as the isotherms are discussed and shown graphically for different values of viscous dissipation parameter N, heat generation parameter Q and magnetic parameter M.
Abstract: In this paper we consider the combined effects of viscous dissipation and heat generation on MHD natural convection flow along a vertical wavy surface are studied. The governing Navier-Stokes equations with associated boundary conditions are transformed into non-dimensional boundary layer equations using appropriate variables. Implicit finite diffe...
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Cyclical Surfaces Created by Helix on Torus
Issue:
Volume 2, Issue 6, December 2014
Pages:
204-208
Received:
25 November 2014
Accepted:
6 December 2014
Published:
17 December 2014
Abstract: This paper describes method of modelling of cyclical surfaces created by helix on the torus . The axis of the cyclical surface ´ is the helix s as a trajectory of movement of a point composed of two motions of rotation. The circle moves together with Frenet-Serret moving trihedron along the helix s and creates the cyclical surface ´. The paper describes modelling of cyclical surfaces created by moving circles about tangent, principal normal or binormal of the helix s. Paper describes also modelling of triangular grids on the torus. The grids are created by right-handed and left-handed cyclical helical surfaces and by cyclical surfaces with axis on meridians and circles on the torus.
Abstract: This paper describes method of modelling of cyclical surfaces created by helix on the torus . The axis of the cyclical surface ´ is the helix s as a trajectory of movement of a point composed of two motions of rotation. The circle moves together with Frenet-Serret moving trihedron along the helix s and creates the cyclical surface ´. The paper d...
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A Grey Relational Analysis Based Study on Green Degree Evaluation of Urban Logistics
Lijuan Qian,
Jinlin Ma,
Zongbo Zhang,
Daming Zhang,
Kaiping Ma
Issue:
Volume 2, Issue 6, December 2014
Pages:
209-213
Received:
13 November 2014
Accepted:
26 November 2014
Published:
18 December 2014
Abstract: According to the urban logistics green degree’s evaluation, a weighted grey correlation analysis method based on the analytic hierarchy process is proposed to determine the weight of each index in the urban logistics green degree evaluation system, and then figure out the optimal relative degree, realizing the green degree of each urban logistics. Finally, an example was given for proving the evaluation methods’ intuitive and high efficient.
Abstract: According to the urban logistics green degree’s evaluation, a weighted grey correlation analysis method based on the analytic hierarchy process is proposed to determine the weight of each index in the urban logistics green degree evaluation system, and then figure out the optimal relative degree, realizing the green degree of each urban logistics. ...
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Radiative MHD Flow over a Vertical Plate with Convective Boundary Condition
Christian John Etwire,
Yakubu Ibrahim Seini
Issue:
Volume 2, Issue 6, December 2014
Pages:
214-220
Received:
10 December 2014
Accepted:
24 December 2014
Published:
4 January 2015
Abstract: This paper investigates the effect of thermal radiation on magneto hydrodynamic (MHD) flow over a vertical plate with convective boundary conditions. The governing partial differential equations were transformed into coupled nonlinear differential equations which were solved numerically using the fourth order Runge-Kutta algorithm with a shooting method. Numerical results for the skin friction coefficient, the rate of heat transfer represented by the local Nusselt number and the plate surface temperature were presented whilst the velocity and temperature profiles illustrated graphically and analyzed. The effects of the Biot number, Grashof number, magnetic field parameter, Eckert number, Prandtl number and radiation parameter on the flow field were discussed.
Abstract: This paper investigates the effect of thermal radiation on magneto hydrodynamic (MHD) flow over a vertical plate with convective boundary conditions. The governing partial differential equations were transformed into coupled nonlinear differential equations which were solved numerically using the fourth order Runge-Kutta algorithm with a shooting m...
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Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM)
Samson Adebayo Olorunsola,
Temitayo Emmanuel Olaosebikan,
Kayode James Adebayo
Issue:
Volume 2, Issue 6, December 2014
Pages:
221-226
Received:
21 December 2014
Accepted:
25 December 2014
Published:
6 January 2015
Abstract: In this paper, we imbed Langrage Multiplier Method (LMM) in Conjugate Gradient Method (CGM), which enables Conjugate Gradient Method (CGM) to be employed for solving constrained optimization problems of either equality, inequality constraint or both. In the past, Langrage Multiplier Method has been used extensively to solve constrained optimization problems. However, with some special features in CGM which makes it unique in solving unconstrained optimization problems, we see that this features we be advantageous to solve constrained optimization problems if we can add or subtract one or two things into the CGM. This, then call for the Numerical Experiments with the Lagrange Multiplier Conjugate Gradient Method (ILMCGM) that is aimed at taking care of any constrained optimization problems, either with equality or inequality constraint The authors of this paper desire that, with the construction of the Algorithm, one will circumvent the difficulties undergone using only LMM to solve constrained optimization problems and its application will further improve the result of the Conjugate Gradient Method in solving this class of optimization problem. We applied the new algorithm to some constrained optimization problems of two, three and four variables in which some of the problems are pertain to quadratic functions. Some of these functions are subject to linear, nonlinear, equality and inequality constraints.
Abstract: In this paper, we imbed Langrage Multiplier Method (LMM) in Conjugate Gradient Method (CGM), which enables Conjugate Gradient Method (CGM) to be employed for solving constrained optimization problems of either equality, inequality constraint or both. In the past, Langrage Multiplier Method has been used extensively to solve constrained optimization...
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