Trefftz Functions Applied to Direct and Inverse Non-Fourier Heat Conduction Problems

Grysa, Krzysztof; Maciąg, A.; Adamczyk-Krasa, Justyna

doi:10.1115/1.4027770

Cited by 21 publications

(19 citation statements)

References 32 publications

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“…The unknown solutions of Equations (1) Energies 2018, 11, 2057 8 of 13 and (2) were approximated by a linear combination of the Trefftz functions (the harmonic polynomials in this case). The coefficients of a linear combination were to be determined so that the approximate solutions would satisfy the boundary conditions (Equations (3)- (8)) in the least-squares sense as in References [15,19,[21][22][23][24]. Equation (9) was solved with a combination of the Picard and Trefftz method.…”

Section: Hybrid Picard-trefftz Methodsmentioning

confidence: 99%

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Heat Transfer Coefficient Identification in Mini-Channel Flow Boiling with the Hybrid Picard–Trefftz Method

et al. 2018

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This paper summarizes the results of the flow boiling heat transfer study with ethanol in a 1.8 mm deep and 2.0 mm wide horizontal, asymmetrically heated, rectangular mini-channel. The test section with the mini-channel was the main part of the experimental stand. One side of the mini-channel was closed with a transparent sight window allowing for the observation of two-phase flow structures with the use of a fast film camera. The other side of the channel was the foil insulated heater. The infrared camera recorded the 2D temperature distribution of the foil. The 2D temperature distributions in the elements of the test section with two-phase flow boiling were determined using (1) the Trefftz method and (2) the hybrid Picard-Trefftz method. These methods solved the triple inverse heat conduction problem in three consecutive elements of the test section, each with different physical properties. The values of the local heat transfer coefficients calculated on the basis of the Robin boundary condition were compared with the coefficients determined with the simplified approach, where the arrangement of elements in the test section was treated as a system of planar layers.

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Section: Hybrid Picard-trefftz Methodsmentioning

confidence: 99%

“…The coefficients of the linear combinations in Equation (22) were determined based on the adopted boundary conditions, following the method described in References [22,24].…”

Section: Hybrid Picard-trefftz Methodsmentioning

confidence: 99%

Heat Transfer Coefficient Identification in Mini-Channel Flow Boiling with the Hybrid Picard–Trefftz Method

et al. 2018

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“…Trefftz methods as well as the method of fundamental solutions are often used for solving direct and inverse problems for the equation of heat conduction [13,18,23]. Paper [8] presents the solution of direct and inverse non-Fourier heat conduction problems with the use of Trefftz functions and Trefftz method. Paper [9] presents the method of solving nonlinear direct and inverse heat conduction problems with the use of Trefftz functions.…”

Section: Plusmentioning

confidence: 99%

Non-linear unsteady inverse boundary problem for heat conduction equation

Joachimiak¹,

Ciałkowski²

2017

Archives of Thermodynamics

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Direct and inverse problems for unsteady heat conduction equation for a cylinder were solved in this paper. Changes of heat conduction coefficient and specific heat depending on the temperature were taken into consideration. To solve the non-linear problem, the Kirchhoff's substitution was applied. Solution was written as a linear combination of Chebyshev polynomials. Sensitivity of the solution to the inverse problem with respect to the error in temperature measurement and thermocouple installation error was analysed. Temperature distribution on the boundary of the cylinder, being the numerical example presented in the paper, is similar to that obtained during heating in the nitrification process.Keywords: Inverse problem; Sensitivity of the solution to the inverse problem; Application of Chebyshev polynomials

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“…Inverse problems of laminar forced convection in ducts have been studied for estimation of initial temperature profile, wall heat flux and thermophysical properties (Grysa et al 2014;Helcio, 2012). Su et al (2000) used the LevenbergMarquardt method to estimate non-uniform wall heat fluxes in steady-state, thermally-developing, hydro-dynamically-developed turbulent flow in a circular pipe by using the temperature measurements obtained at several different locations in the stream.…”

Section: Introductionmentioning

confidence: 99%

Identification of Drag Force of the Underwater Vehicles

Jahangardy

Madoliat

Nouri

2017

JAFM

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An inverse analysis is conducted for the estimation of drag coefficient and wake's width in incompressible turbulent flows over the moving underwater bodies. The inverse analysis uses the laws of momentum and mass conservation for a control volume to estimate the drag coefficient and the wake's width from the measured velocity in the wake. The drag coefficient and wake's width are determined as unknown parameters by the Levenberg-Marquardt algorithm. The proposed inverse method is applicable for an environment without boundaries (e.g., the sea). Several experiments are conducted to evaluate the developed inverse algorithm. The wake velocity behind a cylinder located in the flow field is measured by a calibrated pitot tube and is used as an input to the algorithm. The cylinder is selected as the test body, because its hydrodynamic information is available in the literature. The effects of the tunnel's wall and the turbulence intensity are considered in the results of the algorithm. The estimated drag coefficient is validated by the values presented in the literature. The estimated wake-velocity profiles are fitted favorably with the measured velocities at the corresponding locations. It is shown that the proposed inverse method can be used to estimate the drag coefficient and wake's width of the underwater vehicles with very good accuracy.

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Trefftz Functions Applied to Direct and Inverse Non-Fourier Heat Conduction Problems

Cited by 21 publications

References 32 publications

Heat Transfer Coefficient Identification in Mini-Channel Flow Boiling with the Hybrid Picard–Trefftz Method

Heat Transfer Coefficient Identification in Mini-Channel Flow Boiling with the Hybrid Picard–Trefftz Method

Non-linear unsteady inverse boundary problem for heat conduction equation

Identification of Drag Force of the Underwater Vehicles

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