2008
DOI: 10.1134/s0018151x08030188
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Construction of “on the average exact” asymptotic solution of the problem on radial distribution of temperature field in a well

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Cited by 4 publications
(4 citation statements)
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“…It follows from (45) that the tem perature averaged over the well cross section depends on the Peclet number Pe and, therefore, on the well production, as well as on the thermophysical proper ties of the fluid and the environment. A significant fea ture of the solution obtained is that it describes the temperature averaged over the pipe cross section and coincides with similar expressions for the laminar (R(r) = 1 -r 2 , λ(r) = 1) and averaged (R(r) = 1, λ(r) = 1) velocity profiles [7][8][9].…”
Section: Problem Statement In the Zero Order Appoximationsupporting
confidence: 72%
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“…It follows from (45) that the tem perature averaged over the well cross section depends on the Peclet number Pe and, therefore, on the well production, as well as on the thermophysical proper ties of the fluid and the environment. A significant fea ture of the solution obtained is that it describes the temperature averaged over the pipe cross section and coincides with similar expressions for the laminar (R(r) = 1 -r 2 , λ(r) = 1) and averaged (R(r) = 1, λ(r) = 1) velocity profiles [7][8][9].…”
Section: Problem Statement In the Zero Order Appoximationsupporting
confidence: 72%
“…The existence of such dependencies leads to the appearance of two vari able coefficients in the heat conduction equation for turbulent convective flow, which complicates study of the temperature fields on the basis of analytical solu tions. Difficulties of theoretical study of the tempera ture fields of turbulent flow are connected with the complex dependence of the turbulent heat conduction coefficient and the velocity field on spatial coordi nates, which leads to the necessity of solving conjuga tion problems containing equations for convective heat conduction with variable coefficients, which are difficult to find [7][8][9].…”
Section: Introductionmentioning
confidence: 99%
“…We note that the initial problem can be solved by solution of the parametrized problem upon the reduction of the formal parameter to unity: ε = 1. Thus, problem (1.1)-(1.7) represents the particular case of a more general parametrized problem containing the formal parameter of asymptotic expansion in the equation for the bed and in the conjugation conditions: We will seek the solution of problem (2.1)-(2.7), representing pressures P in the central bed and in the surrounding regions in the form of asymptotic expansion in a parameter ε [2]:…”
Section: Asymptotic-parameter Expansionmentioning
confidence: 99%
“…Problem ( 60)-(65) has only a trivial bounded solution, since the right side of equation ( 61) is equal to zero according to (51). Since the solution of the averaged problem for the remainder term is equal to zero, the first approximation represents the "average exact" asymptotic solution [10].…”
mentioning
confidence: 99%