On the convergence of the heat balance integral method

Mosally, F.; Wood, Alastair S.; Al-Fhaid, A. S.

doi:10.1016/j.apm.2004.12.001

Cited by 12 publications

(4 citation statements)

References 6 publications

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“…In a separate paper they detail the necessary starting solution for their scheme. In [24,25] linear proles are employed in the subdivision. This requires an increase in the number of subregions to improve accuracy.…”

Section: Introductionmentioning

confidence: 99%

Optimising the heat balance integral method in spherical and cylindrical Stefan problems

Ribera

Myers

MacDevette

2019

Applied Mathematics and Computation

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The Heat Balance Integral Method (HBIM) is generally applied to one-dimensional Cartesian heat ow and Stefan problems. The main reason for this being that solutions in spherical and cylindrical coordinates are less accurate than in Cartesian. Consequently, in this paper we examine the application of the HBIM to Stefan problems in spherical and cylindrical coordinates, with the aim of improving accuracy. The standard version as well as one designed to minimise errors will be applied on the original and transformed systems. Results are compared against numerical and perturbation solutions. It is shown that for the spherical case it is possible to obtain highly accurate approximate solutions (more accurate than the rst order perturbation for realistic values of the Stefan number). For the cylindrical problem the results are signicantly less accurate.Keywords Heat balance integral method • Stefan problem • spherical coordinates • cylindrical coordinates • phase change

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Section: Introductionmentioning

confidence: 99%

Optimising the heat balance integral method in spherical and cylindrical Stefan problems

Ribera

Myers

MacDevette

2019

Applied Mathematics and Computation

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“…The fourth con di tion (1d) is know as "smooth ing con di tion" and works well when a poly no mial ap prox i ma tion of 4 th or der is used. Gen er ally, the ac cu racy of the HBIM de pends on the ad e quate choice of the ap prox i mat ing func tions and the lit er a ture provided many ex am ples of suc cess ful so lu tions [3][4][5][6][7][8][9][10]. The pres ent work fo cus the at ten tion on HBIM so lu tion of heat-con duc tion prob lems (iso ther mal con di tion and pre scribed flux problems):…”

Section: Introductionmentioning

confidence: 99%

Research note on a parabolic heat-balance integral method with unspecified exponent: An entropy generation approach in optimal profile determination

Hristov¹

2009

Therm. sci.

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An En tropy Gen er a tion Ap proach in Op ti mal Pro file De ter mi na tion by Jor dan HRISTOV Orig i nal sci en tific pa per UDC: 536.75:517.95The heat-bal ance in te gral method of Good man is stud ied with two sim ple 1-D heat con duc tion prob lems with pre scribed tem per a ture and flux bound ary con di tions. These clas si cal prob lems with well known ex act so lu tions en able to dem on strate the heat-bal ance in te gral method performance by a par a bolic pro file and the en tropy gen er a tion minimization con cept in def i ni tion of the ap pro pri ate pro file ex po nent. The ba sic as sump tion gen er at ing the ad di tional con straints needed to per form the so lu tion is based on the re quire ment to min i mize the dif fer ence in the lo cal ther mal en tropy gen er a tion rates cal cu lated by the ap prox i mate and the ex act pro file, respec tively. This con cept is eas ily ap pli ca ble since the gen eral con cept has sim ple im ple men ta tion of the con di tion re quir ing the ther mal en tropy generations cal culated through both pro files to be the same at the bound ary. The en tropy minimization gen er a tion ap proach au to mat i cally gen er ates the ad di tional re quirement which is de fi cient in the set of con di tions de fined by the heat-bal ance in te gral method con cept.

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“…O método refinado com subdivisões espaciais é revisto para problemas de Stefan através de duas exposições. A primeira é uma técnica similar ao estudo inicial da técnica de aproximações em subdivisões espaciais do problema termal, desenvolvida por Bell e Abbas (1985) e estudada por Mosally et al (2005). A segunda é a continuação do estudo para problemas termais com imobili-…”

Section: Organização Do Trabalhounclassified

O problema de Stefan unidimensional

Santo¹,

Miranda²

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The current work aims to study moving boundary problems, known as Stefan problems, and approximate their solutions. Applications of Stefan problems are found in situations where there is change of physical state, present in several natural and industrial physical and chemical phenomena. Due to their inherent nonlinearity, most of these problems have no known analytic solution and a common technique to approximate solutions is the heat balance integral method, originally studied by Goodman (1958). This method and its variations propose an approximating profile and solve an integral version of the differential equation. The problem is reduced to solving an ordinary differential equation in time involving the depth of heat penetration and the proposed profile. This work studies such classic methods to thermal problems first, in a way that the extension to Stefan problems is natural. Refinements are presented, as well as a technique of subdividing the space domain which results in a numerical scheme. The technique of boundary immobilization is developed and applied at different times in order to simplify the use of these methods.

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On the convergence of the heat balance integral method

Cited by 12 publications

References 6 publications

Optimising the heat balance integral method in spherical and cylindrical Stefan problems

Optimising the heat balance integral method in spherical and cylindrical Stefan problems

Research note on a parabolic heat-balance integral method with unspecified exponent: An entropy generation approach in optimal profile determination

O problema de Stefan unidimensional

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