1988
DOI: 10.1007/bf01103256
|View full text |Cite
|
Sign up to set email alerts
|

Generalization of the method of integral relations and its application to some heat flow problems

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
2

Citation Types

0
12
0

Year Published

2003
2003
2010
2010

Publication Types

Select...
6
1

Relationship

0
7

Authors

Journals

citations
Cited by 8 publications
(12 citation statements)
references
References 2 publications
0
12
0
Order By: Relevance
“…Since the integral balance method converges for n → ∞ (Volkov et al, 1988), the accuracy of the approximate solutions found for n = 1 (first approximation) or n = 2 (second approximation) can be improved by adding the subsequent terms in formulae (15) and (16), i.e. by obtaining the solutions of higher-order of accuracy.…”
Section: Analytical Solutionsmentioning
confidence: 99%
See 1 more Smart Citation
“…Since the integral balance method converges for n → ∞ (Volkov et al, 1988), the accuracy of the approximate solutions found for n = 1 (first approximation) or n = 2 (second approximation) can be improved by adding the subsequent terms in formulae (15) and (16), i.e. by obtaining the solutions of higher-order of accuracy.…”
Section: Analytical Solutionsmentioning
confidence: 99%
“…Prior to applying this method for the practically important case when r w = 1, it would be reasonable to assess the accuracy of this method by comparison with exact solutions (11)-(14) obtained for r w = 0. In further analysis, modification of this method, suggested by Volkov et al (1988), is employed. The advantages of the modified integral balance method were demonstrated in (Fomin et al, 2003a) and (Chugunov et al, 2003), where this method was successfully applied to analyzing different engineering problems.…”
Section: Analytical Solutionsmentioning
confidence: 99%
“…The difficulties arising in solving these problems are well known, especially, in the cases in which it is necessary to take into account the nonstationarity of the employed mode of thermal stimulation [4][5][6][7][8], the mobility of the cylindrical channel boundary [4,9,10], or the anisotropy of properties of the solid [11]. These difficulties are aggravated in the presence of a coating on the cylindrical channel surface [12][13][14].…”
Section: Introductionmentioning
confidence: 99%
“…A logical conclusion of the HBI method is to look for a series solution. The generalized integral balance method involves a solution of the form (2) u = a 0 + Σ n k=1 a k (t)f k (x) , where f k form a linearly independent system and satisfy recurrence relations, see [41] (the method is described in [12]). Fomin et al [12] carry out calculations only up to n = 2 and describe the calculations as "tedious but straightforward".…”
Section: Introductionmentioning
confidence: 99%