Numerical Solution of Axisymmetric Inverse Heat Conduction Problem by the Trefftz Method

Hożejowska, Sylwia; Piasecka, Magdalena

doi:10.3390/en13030705

Cited by 11 publications

(5 citation statements)

References 32 publications

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“…The ratio test is sufficient but not necessary. We next proceed to show that u(r, θ) in Equation ( 7) is indeed the solution to the elliptic problem posed in Equation (1). The Dirichlet problem for Equation (1) with specified boundary conditions at r = 1 and r = w is well-posed and has a unique solution [27].…”

Section: A Direct Methods Based On Homotopy-perturbationmentioning

confidence: 99%

“…In this note, we introduce two direct (Non-iterative) methods for the solution of a particular ill-posed elliptic inverse problem. Specific applications of this problem in annulus domains appear in various fields including thermal systems [1], corrosion detection in pipes [2,3], interior boundary evaluation in Tokamak [4,5], reconstruction of interior voltage distribution [6], and continuation of magnetic field [7]. This problem falls within the general area of inverse problems (IHCP) that have numerous applications in various fields of engineering [8,9].…”

Section: Introductionmentioning

confidence: 99%

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Non-Iterative Solution Methods for Cauchy Problems for Laplace and Helmholtz Equation in Annulus Domain

Tadi

Radenković

2021

Mathematics

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This note is concerned with two new methods for the solution of a Cauchy problem. The first method is based on homotopy-perturbation approach which leads to solving a series of well-posed boundary value problems. No regularization is needed in this method. Laplace and Helmholtz equations are considered in an annular region. It is also proved that the homotopy solution for the Laplace operator converges to the actual exact solution. The second method is also non-iterative. It is based on the application of the Green’s second identity which leads to a moment problem for the unknown boundary condition. Tikhonov regularization is used to obtain a stable and close approximation of the missing boundary condition. A number of examples are used to study the applicability of the methods with the presence of noise.

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Section: A Direct Methods Based On Homotopy-perturbationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-Iterative Solution Methods for Cauchy Problems for Laplace and Helmholtz Equation in Annulus Domain

Tadi

Radenković

2021

Mathematics

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“…As for minigaps, such a single wide minichannel is a progressive option for dealing with high heat fluxes, mainly in electronic systems. Investigations into minigaps of different geometries (e.g., rectangular [21] or annular [22]) usually focus on the thermal performance (e.g., local heat transfer coefficients [23], Nusselt number [24], or temperature distribution [25]). Flow distribution in minigaps is discussed rarely, and if so, then usually as a side experimental observation [26] or in the form of numerical analyses using computational fluid dynamics (CFD) [27].…”

Section: Introductionmentioning

confidence: 99%

Experimentally Verified Flow Distribution Model for a Composite Modelling System

Fialová

Jegla

2021

Energies

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Requirements of modern process and power technologies for compact and highly efficient equipment for transferring large heat fluxes lead to designing these apparatuses as dense parallel flow systems, ranging from conventional to minichannel dimensions according to the specific industrial application. To avoid operating issues in such complex equipment, it is vital to identify not only the local distribution of heat flux in individual parts of the heat transfer surface but also the uniformity of fluid flow distribution inside individual parallel channels of the flow system. A composite modelling system is currently being developed for accurate design of such complex heat transfer equipment. The modeling approach requires a flow distribution model enabling to yield accurate-enough predictions in reasonable time frames. The paper presents the results of complex experimental and modeling investigation of fluid flow distribution in dividing headers of tubular-type equipment. Different modeling approaches were examined on a set of header geometries. Predictions obtained via analytical and numerical models were validated using data from the experiments conducted on additively manufactured header samples. Two case studies employing parallel flow systems (mini-scale systems and a conventional-size heat exchanger) demonstrated the applicability of the distribution model and the accuracy of the composite modelling system.

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“…The main aim of Ref. [7] was computation of the boiling heat transfer coefficient at the working fluid-heated wall contact surface, during HFE-649 flow in an annular minigap. The mathematical model was proposed assuming the laminar fluid flow and axisymmetric steady-state heat transfer process.…”

Section: Introductionmentioning

confidence: 99%

“…To date, the authors of the present work have studied heat transfer enhancement during flow boiling in one [38,39], two [40,41], or three minichannels [42] of rectangular cross-section and in an annular gap [7]. Most of the previous research focused on experiments conducted in the stationary state, although some of the latest works concerned time-dependent studies [41,43].…”

Section: Introductionmentioning

confidence: 99%

Heat Transfer Coefficient Determination during FC-72 Flow in a Minichannel Heat Sink Using the Trefftz Functions and ADINA Software

2020

Self Cite

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This work focuses on subcooled boiling heat transfer during flow in a minichannel heat sink with three or five minichannels of 1 mm depth. The heated element for FC-72 flowing along the minichannels was a thin foil of which temperature on the outer surface was measured due to the infrared thermography. The test section was oriented vertically or horizontally. A steady state heat transfer process and a laminar, incompressible flow of the fluid in a central minichannel were assumed. The heat transfer problem was described by the energy equations with an appropriate system of boundary conditions. Several mathematical methods were applied to solve the heat transfer problem with the Robin condition to determine the local heat transfer coefficients at the fluid/heated foil interface. Besides the 1D approach as a simple analytical method, a more sophisticated 2D approach was proposed with solutions by the Trefftz functions and ADINA software. Finite element method (FEM) calculations were conducted to find the temperature field in the flowing fluid and in the heated wall. The results were illustrated by graphs of local heated foil temperature and transfer coefficients as a function of the distance from the minichannel inlet. Temperature distributions in the heater and the fluid obtained from the FEM computations carried out by ADINA software were also shown. Similar values of the heat transfer coefficient were obtained in both the FEM calculations and the 1D approach. Example boiling curves indicating nucleation hysteresis are shown and discussed.

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Numerical Solution of Axisymmetric Inverse Heat Conduction Problem by the Trefftz Method

Cited by 11 publications

References 32 publications

Non-Iterative Solution Methods for Cauchy Problems for Laplace and Helmholtz Equation in Annulus Domain

Non-Iterative Solution Methods for Cauchy Problems for Laplace and Helmholtz Equation in Annulus Domain

Experimentally Verified Flow Distribution Model for a Composite Modelling System

Heat Transfer Coefficient Determination during FC-72 Flow in a Minichannel Heat Sink Using the Trefftz Functions and ADINA Software

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