Solution of the inverse heat conduction problem with Neumann boundary condition by using the homotopy perturbation method

Hetmaniok, Edyta�; Nowak, Iwona; Słota, Damian; Wituła, Roman; Zielonka, Adam�

doi:10.2298/tsci120826051h

Cited by 12 publications

(8 citation statements)

References 40 publications

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“…Due to Theorem 2.1, we have that the phase-change process (2)-( 8) has the solution given in ( 9)- (10) if and only if ǫ and γ satisfy equation (11) and the remainder physical parameters satisfy condition (12). Then, we have from equation (11) that γ must be given by (17) for any ǫ ∈ (0, 1). To finish the proof, only remains to observe that this coefficient γ is positive if and only if inequality (R1) holds.…”

Section: Explicit Solution To the Phase-change Processmentioning

confidence: 98%

Simultaneous Determination of Two Unknown Thermal Coefficients Through a Mushy Zone Model With an Overspecified Convective Boundary Condition

Ceretani¹,

Tarzia²

2016

JPHMT

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The simultaneous determination of two unknown thermal coefficients for a semi-infinite material under a phase-change process with a mushy zone according to the SolomonWilson-Alexiades model is considered. The material is assumed to be initially liquid at its melting temperature and it is considered that the solidification process begins due to a heat flux imposed at the fixed face. The associated free boundary value problem is overspecified with a convective boundary condition with the aim of the simultaneous determination of the temperature of the solid region, one of the two free boundaries of the mushy zone and two thermal coefficients among the latent heat by unit mass, the thermal conductivity, the mass density, the specific heat and the two coefficients that characterize the mushy zone. The another free boundary of the mushy zone, the bulk temperature and the heat flux and heat transfer coefficients at the fixed face are assumed to be known. According to the choice of the unknown thermal coefficients, fifteen phasechange problems arise. The study of all of them is presented and explicit formulae for * aceretani@austral.edu.ar † dtarzia@austral.edu.ar 1 the unknowns are given, beside necessary and sufficient conditions on data in order to obtain them. Formulae for the unknown thermal coefficients, with their corresponding restrictions on data, are summarized in a table.

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Section: Explicit Solution To the Phase-change Processmentioning

confidence: 98%

Simultaneous Determination of Two Unknown Thermal Coefficients Through a Mushy Zone Model With an Overspecified Convective Boundary Condition

Ceretani¹,

Tarzia²

2016

JPHMT

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“…In orden to have the solution to problem (1)- (7), we impose conditions (2)-(4), (6) and (7) on (13)- (15) and obtain that coefficients A, B and µ must be given by:…”

Section: Explicit Solution To the Phase-change Processmentioning

confidence: 99%

Determination of One Unknown Thermal Coefficient through a Mushy Zone Model with a Convective Overspecified Boundary Condition

Ceretani

Tarzia

2015

Mathematical Problems in Engineering

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A semi-infinite material under a solidification process with the Solomon-Wilson-Alexiades's mushy zone model with a heat flux condition at the fixed boundary is considered. The associated free boundary problem is overspecified through a convective boundary condition with the aim of the simultaneous determination of the temperature, the two free boundaries of the mushy zone and one thermal coefficient among the latent heat by unit mass, the thermal conductivity, the mass density, the specific heat and the two coefficients that characterize the mushy zone. Bulk temperature and coefficients which characterize the heat flux and the heat transfer at the boundary are assumed to be determined experimentally. Explicit formulae for the unknowns are given for the resulting six phase-change problems, beside necessary and sufficient conditions on data in order to obtain them. In addition, relationship between the phase-change process solved in this paper with an analogous process overspecified by a temperature boundary condition is presented, and this second problem is solved by considering a large heat transfer coefficient at the boundary in the problem with the convective boundary condition. Formulae for the unknown thermal coefficients corresponding to both problems are summarized in two tables.

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“…Obviously, there exist many other methods, less known and less often applied, dedicated for solving ODEs tasks. Among them, we can specify the Adomian decomposition method [2,3], the homotopy perturbation method [4] and many others.…”

Section: Introductionmentioning

confidence: 99%

Comparison of the Selected Methods Used for Solving the Ordinary Differential Equations and Their Systems

Hetmaniok

Pleszczyński

2022

Mathematics

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Ordinary differential equations (ODEs), and the systems of such equations, are used for describing many essential physical phenomena. Therefore, the ability to efficiently solve such tasks is important and desired. The goal of this paper is to compare three methods devoted to solving ODEs and their systems, with respect to the quality of obtained solutions, as well as the speed and reliability of working. These approaches are the classical and often applied Runge–Kutta method of order 4 (RK4), the method developed on the ground of the Taylor series, the differential transformation method (DTM), and the routine available in the Mathematica software (Mat).

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Solution of the inverse heat conduction problem with Neumann boundary condition by using the homotopy perturbation method

Cited by 12 publications

References 40 publications

Simultaneous Determination of Two Unknown Thermal Coefficients Through a Mushy Zone Model With an Overspecified Convective Boundary Condition

Simultaneous Determination of Two Unknown Thermal Coefficients Through a Mushy Zone Model With an Overspecified Convective Boundary Condition

Determination of One Unknown Thermal Coefficient through a Mushy Zone Model with a Convective Overspecified Boundary Condition

Comparison of the Selected Methods Used for Solving the Ordinary Differential Equations and Their Systems

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