Ablation by Frictional Heating

1983 ◽  
Vol 50 (4a) ◽  
pp. 712-716 ◽  
Author(s):  
L. N. Tao
Keyword(s):  
Exact Solution ◽  
Physical Interpretation ◽  
Frictional Heating ◽  
Constant Speed ◽  
Numerical Example ◽  
Similarity Transformations ◽  
Reduced Problem ◽  
As If

The ablation problem of a semi-infinite solid, moving at a constant speed parallel to its surface, is investigated. The study includes all induced motions caused by the density differences of various phases of the materials. Some appropriate transformations are introduced to reduce the problem to one where all phases behave as if they had the same density. The reduced problem is then solved by similarity transformations. It is found that the exact solution exists if and only if an inequality is satisfied. The physical interpretation of the inequality is examined. A numerical example is given to illustrate the result.

The Exact Solution to an Ablation Problem With Arbitrary Initial and Boundary Conditions

1984 ◽  
Vol 51 (4) ◽  
pp. 821-826 ◽  
Author(s):  
L. N. Tao
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Surface Temperature ◽  
Exact Solutions ◽  
Melting Temperature ◽  
Physical Interpretation ◽  
Existence And Uniqueness ◽  
Frictional Heating ◽  
Convective Motions ◽  
Initial And Boundary Conditions

The problem of ablation by frictional heating in a semi-infinite solid with arbitrarily prescribed initial and boundary conditions is investigated. The study includes all convective motions caused by the density differences of various phases of the materials. It is found that there are two cases: (i) ablation appears immediately and (ii) there is a waiting period of redistribution prior to ablation. The exact solutions of velocities and temperatures of both cases are derived. The solutions of the interfacial positions are also established. Existence and uniqueness of the solutions are examined and proved. The conditions for the occurrence of these two cases are expressed by an inequality. Physical interpretation of the inequality is explored. Its implication coincides with one’s expectation. Ablation appears only when the surface temperature is at or above the melting temperature.

scholarly journals FRICTIONAL HEATING OF SLIDING SEMI-SPACES WITH SIMPLE THERMAL NONLINEARITIES

2013 ◽  
Vol 7 (4) ◽  
pp. 236-240 ◽  
Author(s):  
Ewa Och
Keyword(s):  
Numerical Analysis ◽  
Analytical Solution ◽  
Integral Transform ◽  
Frictional Heating ◽  
Thermal Contact ◽  
Constant Speed ◽  
Thermal Problem ◽  
Laplace Integral ◽  
Kirchhoff Transformation

Abstract In the article the nonstationary thermal problem of friction for two semi-spaces with taking into account their imperfect thermal contact and thermosensitivity of materials (simple nonlinearity), has been considered. The linearization of this problem has been carried out using Kirchhoff transformation, and next using the Laplace integral transform. The analytical solution to the problem in the case of constant speed sliding, has been obtained. On the basis of the obtained solutions and using Duhamel's formula, the analytical solution to the problem for sliding with constant deceleration, has been obtained, too. The results of numerical analysis are presented for two friction pairs

A Theory of Lubrication With Turbulent Flow and Its Application to Slider Bearings

1960 ◽  
Vol 27 (1) ◽  
pp. 1-4 ◽  
Author(s):  
L. N. Tao
Keyword(s):  
Exact Solution ◽  
Reynolds Number ◽  
Turbulent Flow ◽  
Closed Form ◽  
Governing Equation ◽  
Reynolds Equation ◽  
Three Dimensions ◽  
Slider Bearing ◽  
Numerical Example ◽  
Special Case

The governing equation of turbulent lubrication in three dimensions, equivalent to the Reynolds equation of laminar lubrication, is derived. The problem of a slider bearing with no side leakage is then analyzed. An exact solution is found in closed form. Bearing characteristics are also established. It is found that the Reynolds number is an important parameter in the problem of turbulent lubrication. Furthermore, it is shown that the laminar lubrication may be considered as the special case of the present study. A numerical example is also included.

scholarly journals Almost complete convergence for the sequence of approximate solutions in linear calibration problem with α-mixing random data

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3251-3264
Author(s):  
Samia Khalfoune ◽  
Halima Zerouati
Keyword(s):  
Exact Solution ◽  
Complete Convergence ◽  
Approximate Solutions ◽  
Stochastic Method ◽  
Linear Calibration ◽  
Random Data ◽  
Exponential Inequalities ◽  
Numerical Example ◽  
Calibration Problem ◽  
Confidence Domain

In this work, we propose a stochastic method which gives an estimated solution for a linear calibration problem with ?-mixing random data. We establish exponential inequalities of Fuk Nagaev type, for the probability of the distance between the approximate solutions and the exact one. Furthermore, we build a confidence domain for the so mentioned exact solution. To check the validity of our results, a numerical example is proposed.

Seismic refraction interferometry with a semblance analysis on the crosscorrelation gather

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. SA77-SA82 ◽  
Author(s):  
Dylan Mikesell ◽  
Kasper van Wijk
Keyword(s):  
Field Data ◽  
Seismic Refraction ◽  
Seismic Interferometry ◽  
Virtual Source ◽  
Numerical Example ◽  
Source Method ◽  
Reflection And Refraction ◽  
Research Site ◽  
Refracted Waves ◽  
As If

Crosscorrelating wavefields recorded at two receivers to produce data as if one receiver was a source is commonly referred to as seismic interferometry, or the virtual source method. An artifact in seismic interferometry related to critically refracted waves allowed us to estimate the velocity in the refracting layer. In addition, we devised a new semblance analysis on the crosscorrelation of reflection and refraction energy to robustly estimate the depth and velocity of the slow layer, tested with a numerical example and field data from the Boise Hydrogeophysical Research Site.

scholarly journals Optimal control for stochastic singular integro-differential Takagi-Sugeno fuzzy system using ant colony programming

Filomat ◽  
2012 ◽  
Vol 26 (3) ◽  
pp. 415-426 ◽  
Author(s):  
N. Kumaresan
Keyword(s):  
Optimal Control ◽  
Exact Solution ◽  
Algebraic Equation ◽  
Fuzzy System ◽  
Ant Colony ◽  
Differential Algebraic Equation ◽  
Numerical Example ◽  
Quadratic Performance ◽  
Takagi Sugeno

In this paper, optimal control for stochastic singular integro-differential Takagi-Sugeno (T-S) fuzzy system with quadratic performance is obtained using ant colony programming (ACP). To obtain the optimal control, the solution of MRDE is computed by solving differential algebraic equation (DAE) using a novel and nontraditional ACP approach. The obtained solution in this method is equivalent or very close to the exact solution of the problem. An illustrative numerical example is presented for the proposed method.

Impact of Frictional Heating on MHD Radiative Ferrofluid Past a Convective Shrinking Surface

2017 ◽  
Vol 378 ◽  
pp. 157-174 ◽  
Author(s):  
Anantha Kumar Kempannagari ◽  
Venkata Ramana Reddy Janke ◽  
Sugunamma Vangala ◽  
Sandeep Naramgari
Keyword(s):  
Heat Transfer ◽  
Volume Fraction ◽  
Frictional Heating ◽  
Fluid Velocity ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Governing Equations ◽  
Similarity Transformations ◽  
Shrinking Surface

The intention of this analysis is to analyse the heat transfer impact on MHD ferrofluid flow over a shrinking sheet. This study is carried out under the knowledge of frictional heating, Biot number and thermal radiation. With the assist of suitable similarity transformations, the governing equations are transmuted into coupled nonlinear ODE’s and then numerically solved by R.K. Fehlberg Technique. For this study, we considered the ferrofluid. The behavior of sundry physical parameters on fluid velocity, temperature, skin friction coefficient and local Nusselt number are discussed and presented through plots and tables. Through this investigation, we found that the magnitude of fluid velocity enhances with rising values of volume fraction of nanoparticles. Also, it is found that the Eckert number has tendency to reduce the rate of heat transport.

scholarly journals "Approximate solution for the two-dimensional Volterra-Integro differential equation of fractional order by using Generalized Deferential Transform method "

2018 ◽  
Vol 5 (2) ◽  
pp. 1-9
Author(s):  
Mohammed G. S. AL-Safi ◽  
Wurood R. Abd AL- Hussein
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Fractional Order ◽  
Two Dimensional ◽  
Transform Method ◽  
Integro Differential Equation ◽  
Numerical Example ◽  
Differential Transform ◽  
Generalized Differential

"In this work, an efficient generalized differential transform method (GDTM) is proposed for solving the twodimensional Volterra-Integro differential equation (2-DVIDE) of fractional order. The results of the proposed method are compared with exact solution, a numerical example is considered for testing the accuracy and validity of this method."

scholarly journals Preventing Internal Congestion in an Integrated European Balancing Activation Optimization

Energies ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 490 ◽  
Author(s):  
Martin Håberg ◽  
Hanna Bood ◽  
Gerard Doorman
Keyword(s):  
Market Structure ◽  
Transmission System ◽  
New Method ◽  
Numerical Example ◽  
Cross Border ◽  
Balancing Energy ◽  
System Operator ◽  
Transmission Constraints ◽  
Energy Activation ◽  
As If

New common platforms for optimization of balancing energy activation will facilitate cross-border exchange and integrate the fragmented European balancing markets. Having a zonal market structure, these platforms will optimize balancing actions as if intra-zonal transmission constraints did not exists, leaving it to each Transmission System Operator (TSO) to manage internal congestion caused by balancing energy activations. This paper describes a new method to pre-filter balancing bids likely to cause internal congestion due to their location. Furthermore, the complementary concept of exchange domains has been developed to prevent congested and infeasible balancing situations. A numerical example illustrates both the effectiveness and limitations of each method.

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