Thermal Response of Rolling Components Under Mixed Boundary Conditions: An Analytical Approach

1993 ◽  
Vol 115 (4) ◽  
pp. 857-865 ◽  
Author(s):  
P. Ulysse ◽  
M. M. Khonsari
Keyword(s):  
Temperature Distribution ◽  
Peclet Number ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Order Approximation ◽  
Thermal Response ◽  
Fourier Integral ◽  
Cylinder Surface ◽  
Péclet Number ◽  
Special Cases

An analytical solution for the steady-state temperature distribution in a cylinder undergoing uniform heating and nonuniform cooling is presented. The method of solution is a Fourier integral transform technique. The analysis shows that the Neumann series resulting from an integral equation can be well represented by a first-order approximation when the Peclet number is large. Furthermore, it is shown that the ratio of the Biot number to the square root of the Peclet number of the cooling zones is found to play an important role in governing the thermal response of the cylinder surface. The predicted results for the circumferential temperature distribution are compared to published experimental measurements for hot rolling and also existing analytical solutions for special cases. The agreement is found to be very good. By an appropriate superposition technique, the analysis presented may be easily extended to various heat sources and convective cooling zones at different locations of the cylinder surface.

On the Interaction at Anti-Flat Deformation of Stress Concentrators of the Type of Cracks and Stringers with Regard to the Layer Manufactured from Miscellaneous Materials

2019 ◽  
Vol 828 ◽  
pp. 81-88
Author(s):  
Nune Grigoryan ◽  
Mher Mkrtchyan
Keyword(s):  
Integral Transform ◽  
Composite Layer ◽  
Singular Integral Equations ◽  
Original System ◽  
Fourier Integral ◽  
Quadrature Formulas ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Tangential Forces

In this paper, we consider the problem of determining the basic characteristics of the stress state of a composite in the form of a piecewise homogeneous elastic layer reinforced along its extreme edges by stringers of finite lengths and containing a collinear system of an arbitrary number of cracks at the junction line of heterogeneous materials. It is assumed that stringers along their longitudinal edges are loaded with tangential forces, and along their vertical edges - with horizontal concentrated forces. In addition, the cracks are laden with distributed tangential forces of different intensities. The case is also considered when the lower edge of the composite layer is free from the stringer and rigidly clamped. It is believed that under the action of these loads, the composite layer in the direction of one of the coordinate axes is in conditions of anti-flat deformation (longitudinal shift). Using the Fourier integral transform, the solution of the problem is reduced to solving a system of singular integral equations (SIE) of three equations. The solution of this system is obtained by a well-known numerical-analytical method for solving the SIE using Gauss quadrature formulas by the use of the Chebyshev nodes. As a result, the solution of the original system of SIE is reduced to the solution of the system of systems of linear algebraic equations (SLAE). Various special cases are considered, when the defining SIE and the SLAE of the task are greatly simplified, which will make it possible to carry out a detailed numerical analysis and identify patterns of change in the characteristics of the tasks.

Steady Temperature in a Rotating Cylinder Subject to Surface Heating and Convective Cooling

1984 ◽  
Vol 106 (1) ◽  
pp. 120-126 ◽  
Author(s):  
B. Gecim ◽  
W. O. Winer
Keyword(s):  
Heat Source ◽  
Peclet Number ◽  
High Speed ◽  
Integral Transform ◽  
The Body ◽  
Cooling Zone ◽  
Dimensionless Numbers ◽  
Péclet Number ◽  
Heating And Cooling ◽  
Simultaneous Heating

This study utilizes an integral transform technique in order to solve the heat conduction equation in cylindrical coordinates. The major assumption is the high speed (i.e., large Peclet number) assumption. The boundary value problem is governed by the parabolic form of the heat equation representing the quasi-stationary state. The boundary conditions are a combination of Neumann and mixed type due to simultaneous heating and cooling on the surface of the cylinder. The surface temperature reaches a peak value over the heat source and gradually decreases to a nearly constant level over the cooling zone. Thermal penetration in the radial direction is shown to be only a few percent of the radius, leaving the bulk of the body at a uniform temperature. The width of the heat source and the total heat input are shown to be effective on the level of temperature whereas the input distribution is shown to be unimportant. The dimensionless numbers involved are the Biot and the Peclet numbers where the solution is governed by the ratio of the Biot number to the square root of the Peclet number.

Temperature Rise at the Sliding Contact Interface for a Coated Semi-Infinite Body

1993 ◽  
Vol 115 (1) ◽  
pp. 1-9 ◽  
Author(s):  
X. Tian ◽  
F. E. Kennedy
Keyword(s):  
Surface Temperature ◽  
Temperature Rise ◽  
Peclet Number ◽  
Integral Transform ◽  
Sliding Contact ◽  
Contact Interface ◽  
Péclet Number ◽  
Maximum Surface ◽  
Semi Empirical ◽  
Maximum Surface Temperature

In this paper, a three-dimensional model of a semi-infinite layered body is used to predict steady-state maximum surface temperature rise at the sliding contact interface for the entire range of Peclet number. A set of semi-empirical solutions for maximum surface temperature problems of sliding layered bodies is obtained by using integral transform, finite element, heuristic and multivariable regression techniques. Two dimensionless parameters, A and Dp, which relate to coating thickness, contact size, sliding speed and thermal properties of both coating and substrate materials, are found to be the critical factors determining the effect of surface film on the surface temperature rise at a sliding contact interface. A semi-empirical solution for maximum surface temperature problems of homogeneous bodies, which covers the whole range of Peclet number, is also obtained.

Heat transport into a shear flow at high Peclet number

1990 ◽  
Vol 427 (1872) ◽  
pp. 25-30
Keyword(s):  
Thermal Diffusivity ◽  
Temperature Distribution ◽  
Shear Flow ◽  
Heat Transport ◽  
Peclet Number ◽  
Asymptotic Form ◽  
Convex Region ◽  
Heated Region ◽  
Péclet Number ◽  
Special Case

Heat transport from a heated convex region on an otherwise insulating plane, into a fluid in shear flow along the plane, is considered. The asymptotic form of the temperature distribution is determined for large values of the Peclet number sL 2 / k where s is the shear rate of the flow, L is a typical dimension of the heated region and k is the thermal diffusivity of the fluid. From it the asymptotic form of the total heat transport is obtained. Although the shape of the region is arbitrary, the solution is constructed by using previous results for the special case of a heated strip with its edges normal to the flow.

Transfer Matrix Method of Wave Propagation in a Layered Medium With Multiple Interface Cracks: Antiplane Case

2000 ◽  
Vol 68 (3) ◽  
pp. 499-503 ◽  
Author(s):  
Y.-S. Wang ◽  
D. Gross
Keyword(s):  
Wave Propagation ◽  
Transfer Matrix ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Universal Method ◽  
Dynamic Stress Intensity Factors ◽  
Interface Cracks ◽  
Multiple Interface

The paper develops a universal method for SH-wave propagation in a multilayered medium with an arbitrary number of interface cracks. The method makes use of the transfer matrix and Fourier integral transform techniques to cast the mixed boundary value problem to a set of Cauchy singular integral equations of the first type which can be solved numerically. The paper calculates the dynamic stress intensity factors for some simple but typical examples.

scholarly journals Analytical solution of transient temperature in continuous wave end-pumped laser slab: Reduction of temperature distribution and time of thermal response

2017 ◽  
Vol 21 (3) ◽  
pp. 1223-1230 ◽  
Author(s):  
Khalid Shibib ◽  
Mohammad Munshid ◽  
Mohammed Hamza
Keyword(s):  
Temperature Distribution ◽  
Analytical Solution ◽  
Response Time ◽  
Continuous Wave ◽  
Integral Transform ◽  
Convection Heat Transfer ◽  
Thermal Response ◽  
Transient Temperature ◽  
Transform Method ◽  
Thermal Response Time

An analytical solution of transient 3-D heat equation based on integral transform method is derived. The result are compared with numerical solution, and good agreements are obtained. Minimization of response time and temperature distribution through a laser slab are tested. It is found that the increasing in the lateral convection heat transfer coefficient can significantly reduce the response time and the temperature distribution while no effect on response time is observed when changing pumping profile from Gaussian to top hat beam in spite of the latter reduce the temperature distribution, also it is found that dividing the pumping power between two slab ends might reduce the temperature distribution and it has no effect on thermal response time.

scholarly journals Elastic Analysis for Nanocontact Problem with Surface Stress Effects under Shear Load

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
D. X. Lei ◽  
L. Y. Wang ◽  
Z. Y. Ou
Keyword(s):  
Surface Stress ◽  
Solid Mechanics ◽  
Integral Transform ◽  
Surface Elasticity ◽  
Elastic Field ◽  
Fourier Integral ◽  
Shear Load ◽  
Transform Method ◽  
Stress Effects ◽  
Special Cases

Consideration of surface stress effects on the elastic field of nanocontact problem has extensive applications in several modern problems of solid mechanics. In this paper, the effects of surface stress on the contact problem at nanometers are studied in the frame of surface elasticity theory. Fourier integral transform method is adopted to derive the fundamental solution of the nanocontact problem under shear load. As two special cases, the deformations induced by a uniformly distributed shear load and a concentrated shear force are discussed in detail, respectively. The results indicate some interesting characteristics in nanocontact mechanics, which are distinctly different from those in macrocontact problem. At nanoscale, both the contact stresses and the displacements on the deformed surface transit continuously across the uniform distributed shear load boundary as a result of surface stress. In addition, the indent depth and the contact stress depend strongly on the surface stress for nanoindentation.

On the Mechanical Modeling of Functionally Graded Interfacial Zone With a Griffith Crack: Anti-Plane Deformation

2003 ◽  
Vol 70 (5) ◽  
pp. 676-680 ◽  
Author(s):  
Y.-S. Wang ◽  
G.-Y. Huang ◽  
D. Dross
Keyword(s):  
Integral Transform ◽  
Mixed Boundary ◽  
Plane Deformation ◽  
Fourier Integral ◽  
Functionally Graded ◽  
Interfacial Zone ◽  
Griffith Crack ◽  
Elastic Solids ◽  
Fourier Integral Transform ◽  
Graded Interfacial Zone

An analytical model is developed for a functionally graded interfacial zone between two dissimilar elastic solids. Based on the fact that an arbitrary curve can be approached by a continuous broken line, the interfacial zone with material properties varying continuously in an arbitrary manner is modeled as a multilayered medium with the elastic modulus varying linearly in each sublayer and continuous on the interfaces between sublayers. With this new multilayered model, we analyze the problem of a Griffith crack in the interfacial zone. The transfer matrix method and Fourier integral transform technique are used to reduce the mixed boundary-value problem to a Cauchy singular integral equation. The stress intensity factors are calculated. The paper compares the new model to other models and discusses its advantages.

scholarly journals Analytical treatment of transient temperature and thermal stress distribution in CW end pumped laser rod: Thermal response optimization study

2014 ◽  
Vol 18 (2) ◽  
pp. 399-408 ◽  
Author(s):  
Khalid Shibib ◽  
Mayada Tahir ◽  
Mohammad Mahdi
Keyword(s):  
Temperature Distribution ◽  
Analytical Solution ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Beam Quality ◽  
Thermal Response ◽  
Optical Path Difference ◽  
Transient Temperature ◽  
Analytical Treatment ◽  
Transform Method

The analytical solution of transient temperature distribution and Tresca failure stress in CW end- pumped laser rod has been derived using integral transform method. The analytical result is compared with numerical solutions presented by other works and good agreement has been found. Analytical solution with its clear physical meaning and its explicit form permits to predict the influence of various factors on the solution. The optical path difference which gives a valuable means to quantify the optical properties of laser material such as designed beam quality, will converge to a constant value as steady state temperature distribution is reached. One can obtain the dominate factors which affect the laser response to bring the laser rod to the thermal equilibrium; it has been found that fast response can be achieved by reducing pumping power, increasing extracted heat from the rod , choosing a crystal having high thermal diffusivity and decreasing laser rod radius while its volume remains constant. One final advantage of the analytical solution is that a fast result can be obtained where the numerical solution usually is a time consuming technique.

Sign in / Sign up

Export Citation Format

Share Document