Library Subscription: Guest
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections
Heat Transfer Research
IF: 0.404 5-Year IF: 0.8 SJR: 0.264 SNIP: 0.504 CiteScore™: 0.88

ISSN Print: 1064-2285
ISSN Online: 2162-6561

Volumes:
Volume 50, 2019 Volume 49, 2018 Volume 48, 2017 Volume 47, 2016 Volume 46, 2015 Volume 45, 2014 Volume 44, 2013 Volume 43, 2012 Volume 42, 2011 Volume 41, 2010 Volume 40, 2009 Volume 39, 2008 Volume 38, 2007 Volume 37, 2006 Volume 36, 2005 Volume 35, 2004 Volume 34, 2003 Volume 33, 2002 Volume 32, 2001 Volume 31, 2000 Volume 30, 1999 Volume 29, 1998 Volume 28, 1997

Heat Transfer Research

DOI: 10.1615/HeatTransRes.v36.i8.30
pages 641-653

Application of the "Geometrical-Optical" Asymptotic Method for Accounting the Impacts of a Complex-Shape Boundary of the Random Region on Multidimensional Nonlinear Irregular Thermal Fields

G. A. Nesenenko
N. E. Bauman Moscow State Technical University, Moscow, Russia

ABSTRACT

A method for obtaining approximate analytical solutions of nonlinear boundary-value problems, formulated for multidimensional parabolic equations with a small parameter ε > 0 and the Laplace operator has been proposed and substantiated. Such problems are called singularly perturbed boundary-value problems or irregular boundary-value problems. Regions, in which solutions of the above irregular heat-conduction problems are sought by the proposed method, can have a random shape, and nonlinear boundary conditions can be specified at the boundaries. The approximate solutions are represented by the Poincare asymptotics, containing both powers of a small parameter ε > 0 and powers of respective boundary layer variables. The Poincare asymptotic coefficients depend on the geometrical characteristics of the surface, bounding the region in which the solution is analyzed; in so doing, they do not depend on the small parameter ε > 0. To calculate explicitly the coefficients of asymptotic expansion, a mathematically correct analysis of integral solution representations, written by means of respective Green functions, is used.


Articles with similar content:

Study of the Thermal Resonance in Multidimensional Irregular Thermal Fields that is Initiated by the Nonlinear Boundary Conditions
Heat Transfer Research, Vol.37, 2006, issue 2
A. V. Kotovich, G. A. Nesenenko
On Homogenization of Problems of Optimal Control. Part I. Analysis of Existing Approaches
Journal of Automation and Information Sciences, Vol.38, 2006, issue 5
Peter I. Kogut, Victor N. Mizernyi, Tatyana N. Rudyanova
ELLIPSOIDAL DROPLET DETECTION USING RANDOMIZED HOUGH TRANSFORM
Atomization and Sprays, Vol.16, 2006, issue 4
Bo-Seon Kang, Y. J. Choo
About the Optimal Dual Control Algorithm of Observation of Two Normal Markov Sequences in Infinite Interval
Journal of Automation and Information Sciences, Vol.33, 2001, issue 1
Shamil M. Ihsanov
Synthesis of Discrete Adaptive Control Systems for Linear and Certain Classes of Nonlinear Objects
Journal of Automation and Information Sciences, Vol.41, 2009, issue 6
Vsevolod M. Kuntsevich