• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.18 no.3
• /
• pp.245-256
• /
• 2014

This work is focused on the boundary layer and heat transfer characteristics of hydromagnetic flow over a stretching sheet with variable thickness. Steady, two dimensional, nonlinear, laminar flow of an incompressible, viscous and electrically conducting fluid over a stretching sheet with variable thickness and power law velocity in the presence of variable magnetic field and variable temperature is considered. Governing equations of the problem are converted into ordinary differential equations utilizing similarity transformations. The resulting non-linear differential equations are solved numerically by utilizing Nachtsheim-Swigert shooting iterative scheme for satisfaction of asymptotic boundary conditions along with fourth order Runge-Kutta integration method. Numerical computations are carried out for various values of the physical parameters and the effects over the velocity and temperature are analyzed. Numerical values of dimensionless skin friction coefficient and non-dimensional rate of heat transfer are also obtained.

• Journal of the Korean Physical Society
• /
• v.73 no.9
• /
• pp.1303-1309
• /
• 2018

In the present paper, we study the entropy analysis of boundary layer flow over a slender stretching sheet under the action of a non uniform magnetic field that is acting perpendicular to the flow direction. The effects of viscous dissipation and Joule heating are included in the energy equation. Using similarity transformation technique the momentum and thermal boundary layer equations to a system of nonlinear differential equations. Numerical solutions are obtained using the shooting and fourth-order Runge-Kutta method. The expressions for the entropy generation number and Bejan number are also obtained using a suggested similarity transformation. The main objective of this article is to investigate the effects of different governing parameters such as the magnetic parameter ($M^2$), Prandtl number (Pr), Eckert number (Ec), velocity index parameter (m), wall thickness parameter (${\alpha}$), temperature difference parameter (${\Omega}$), entropy generation number (Ns) and Bejan number (Be). All these effects are portrayed graphically and discussed in detail. The analysis reveals that entropy generation reduces with decreasing wall thickness parameter and increasing temperature difference between the stretching sheet and the fluid outside the boundary layer. The viscous and magnetic irreversibilities are dominant in the vicinity of the stretching surface.

• Transactions of Materials Processing
• /
• v.19 no.4
• /
• pp.236-241
• /
• 2010

The frictional behavior of bare steel sheet highly depends on surface roughness. It was investigated that the change of surface roughness of bare steel sheet due to deformation for each forming mode. The flat type friction test was done to check the effect of surface roughness change on frictional characteristics of bare steel sheet. As increasing the deformation, the Ra value was increased at stretching forming mode and drawing forming mode, however the change of Pc showed different trends. The Pc was decreased as increasing stretch deformation but increased at compression deformation. At drawing forming mode, the friction coefficient was increased as deformation was increased after initial big drop with drawing oil. As deformation was increased, the friction coefficient was decreased with drawing oil at stretching forming mode. The results show that the deformation changes the surface roughness and frictional characteristics of steel sheet but the effect depends on the forming mode.

• Transactions of Materials Processing
• /
• v.7 no.5
• /
• pp.459-464
• /
• 1998

Effect of the several initial textures such as random texture, rolling texture and cube texture, on the plane strain stretching was studied by interpretation of the finite element method. The calculation of yield locus indicated that the sheet oriented in the cube texture exhibits easy yielding on uniaxial stress state whereas the sheet having either a random or the rolling texture exhibits easy yielding on shear deformation. Upon stretching tests, the thickness strain at the center region contacting the punch was identical regardless of the initial textures while the dependence of the thickness strain on the initial texture was found in the other regions. In general punch loads required or the sheet with an initial cube texture was as expected from calculated yield locus, lower than those for the others.

• Transactions of Materials Processing
• /
• v.7 no.4
• /
• pp.354-363
• /
• 1998

In order to analyze the stretch forming characteristics of tailored blanks, laser welded blanks of different thickness and strength combinations were prepared and stretching tests were done. The stretching formability of laser welded blanks was reduced as increasing the deformation restraining force ($strength{\times}thickness$) ratio between two welded sheets. Weld line movement was attributed to strain concentration at weaker sheets and resulted in fracture at weaker sid, so that fracture could be predicted by the forming limit of the weak sheet. In the case of a welded blank with the similar deformation restraining force rations between two welded sheets, crack occurred at weld and its forming limit was about 15% less than the base sheet. The effects of lubrication and weld line position on stretch-ing formability were also investigated by experiments. Lower friction did not always give better formability for tailored blanks. Stretching formability was observed to be improved as increasing the area of weak sheet.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 2003.10a
• /
• pp.125-131
• /
• 2003

The U-draw bending operation is known as a representative test method for springback evaluation of sheet metals since the sheet in U-draw bending operation undergoes stretching, bending and unbending deformations occurred at read stamping process. In this study, a simplified approach was proposed for predicting springback and side-wall curls in U-draw bending operations, using moment-curvature relationships derived for sheets undergoing stretching, bending and unbending deformation.

• Journal of applied mathematics & informatics
• /
• v.35 no.5_6
• /
• pp.505-512
• /
• 2017

In this paper, we explain how the exact closed-form solutions of the classical problems of viscous fluid flow over a heated stretching plate and shrinking sheet can be obtained by a reliable method.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 1998.03a
• /
• pp.242-245
• /
• 1998

Effects of the anisotrpy due to the initial textures in the plane sheet on plane strain punch stretching has been investigated. In this study, the anisotropy from textures in the sheet is incoporated into the finite element process model by combining the theory of crstal plasticity. Three different textures such as random texture, plane strain compression texture and cube texture are considered. Variations of puch loads as well as thickness distributions of the sheets with three different initial textures are investigated.

• Transactions of Materials Processing
• /
• v.7 no.1
• /
• pp.81-93
• /
• 1998

Identification of forming limits of sheet metals is an important task to be done before the sheet metal forming processes. The information of the forming limit is indispensable for design of deformed shapes and related forming processes. This procedure becomes more important than ever as the auto-body becomes complicated and the number of auto-body parts is reduced for lower production cost. To identify the forming limit of sheet metals stretching with a hemispherical punch has gained popularity because of the convenient experimental procedure. The stretching experiment however has localized deformation or the shear band is originated from the non-unifrom deformation in the critical circum-stance instead of the absolute criterion. More accurate information of the forming limit therefore could be obtained by a more appropriate experiment to the real process. In this papaer an experiment program is devised to practivally identify the forming limits of sheet metals for auto-body parts. The experiment program contains not only stretching but deep-drawing Both forming experiments use the same hemispherical punch while they use different specimens. Deep-drawing experiments use speci-mens cut out in circular arc on both sides of circular blank to make it torn during the deep-drawing They also use speciments cut out straight in one side of a circular blank to make it deformed unevenly which causes local deformation during the deep-drawing. The experimental result demonstrates that the forming limit diagrams in the two cases show difference in their effective magnitude. The forming limit curve from deep-drawing is located lower than that from stretching. It is noted from the result that the deep-drawing process causes acceleration of localized deformation in comparison with the stretching process. From the experimental result the maximum value of forming limit could be pre-dicted for safe design.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 2003.10b
• /
• pp.193-197
• /
• 2003

In order to restrain the local necking during stretching of sheet metals, the combined stretching processes with simultaneous compression are proposed. The combined stretching tests with two types of compression to top of the cup were carried out using the pure aluminum sheets; (1) stroke control loading process and (2) pinpoint loading process. It was clarified that the metal flow in the cross-section of the cup is affected significantly both by the magnitude of load and the stroke in the compression process. It was also found that the local necking can be restrained effectively by the metal flow from center of the cup and therefore the forming limit is improved.