Identification of the heat transfer coefficient during cooling process by means of Trefftz method

In this article, a novel spacetime collocation Trefftz method for solving the inverse heat conduction problem is presented. This pioneering work is based on the spacetime collocation Trefftz method; the method operates by collocating the boundary points in the spacetime coordinate system. In the spacetime domain, the initial and boundary conditions are both regarded as boundary conditions on the spacetime domain boundary. We may therefore rewrite an initial value problem (such as a heat conduction problem) as a boundary value problem. Hence, the spacetime collocation Trefftz method is adopted to solve the inverse heat conduction problem by approximating numerical solutions using Trefftz base functions satisfying the governing equation. The validity of the proposed method is established for a number of test problems. We compared the accuracy of the proposed method with that of the Trefftz method based on exponential basis functions. Results demonstrate that the proposed method obtains highly accurate numerical solutions and that the boundary data on the inaccessible boundary can be recovered even if the accessible data are specified at only one-fourth of the overall spacetime boundary.

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“…The exact solution is given as equation (24). In this example, we attempt to recover the absent initial condition.…”

Section: Example 3-one-dimensional Bhcpmentioning

confidence: 99%

“…The advantage is that it can identify the heat transfer coefficient during the cooling process. 24 However, solving the IHCP still presents a great challenge because the IHCP is a highly ill-posed system, which is one of the difficult issues of many inverse problems.…”

Section: Introductionmentioning

confidence: 99%

A spacetime collocation Trefftz method for solving the inverse heat conduction problem

Liu

Xiao

et al. 2019

Advances in Mechanical Engineering

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“…Many studies on methods for solving inverse problems and on their stability were conducted [8][9][10][11], with particular focus on cylindrical geometries, what was discussed in papers [12][13][14]. Determination of the heat transfer coefficient for the cooling process by solving the inverse problem with the use of the Trefftz method was presented in the paper [15]. Today, inverse problems are widely used to determine the temperature, the heat flux and the heat transfer coefficient in elements of machines and thermal devices during heating and cooling processes [16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Modelling of the cylindrical geometry cooling process based on the solution of the inverse problem

Joachimiak

2021

E3S Web Conf.

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Processes of thermo-chemical treatment, such as nitriding, are used to create a surface layer of high mechanical values. When the nitriding process, often consisting of a multi-stage heating and soaking, is ended, elements being under treatment are cooled. The cooling rate depends on the massiveness and geometry of the given element. Too fast cooling can result in the formation of high temperature gradients, which leads to the element damage. This paper presents numerical analysis of a cylinder cooling. The non-linear, unsteady inverse problem for the heat equation was solved. Test examples were chosen based on experimental research conducted in the furnace for thermo-chemical treatment.

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“…The proposed system of two energy equations in the heater and flowing fluid together with an adequate set of boundary conditions leads to the solution of the conjugated inverse and direct heat conduction problems [20]. Inverse heat conduction problems (IHCPs) like those presented, e.g., in [21][22][23][24][25][26][27], belong to ill-posed problems [28] and require effective and stable solution methods. The Trefftz method [29] complies with this requirement, even when not all boundary conditions are fully known [30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

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

Hożejowska

Piasecka

2020

Energies

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In this paper, the issue of flow boiling heat transfer in an annular minigap was discussed. The main aim of the paper was determining the boiling heat transfer coefficient at the HFE-649 fluid–heater contact during flow along an annular minigap. The essential element of the experimental stand was a test section vertically oriented with the minigap 2 mm wide. Thermocouples were used to measure the temperature of the heater and fluid at the inlet and the outlet to the minigap. The mathematical model assumed that the fluid flow was laminar and the steady–state heat transfer process was axisymmetric. The temperatures of the heated surface and of the flowing fluid were assumed to fulfill energy equations with adequate boundary conditions. The problem was solved by the Trefftz method. The local heat transfer coefficients at the fluid–test surface interface were calculated due to the third kind boundary condition at the saturated boiling. Graphs were used to illustrate: the measurement of the heater surface temperature, 2D temperature distributions in the pipe and fluid, and the heat transfer coefficient as a function of the distance from the minigap inlet. The measurement uncertainties and accuracy of the heat transfer coefficient determination were estimated.

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Identification of the heat transfer coefficient during cooling process by means of Trefftz method

Cited by 10 publications

References 38 publications

A spacetime collocation Trefftz method for solving the inverse heat conduction problem

A spacetime collocation Trefftz method for solving the inverse heat conduction problem

Modelling of the cylindrical geometry cooling process based on the solution of the inverse problem

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

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