Inverse Heat Conduction Problems

Grysa, Krzysztof

doi:10.5772/26575

Cited by 15 publications

(6 citation statements)

References 34 publications

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“…Therefore an exact value cannot be obtained theoretically and semi-empirical indirect methods are needed. An inverse method, namely the Inverse Heat Conduction Problem (IHCP) [36,37], was used to obtain values for this parameter. This method is used to find, by solving the equations iteratively, a convergence value of this unknown parameter.…”

Section: Heat Transfer Modelingmentioning

confidence: 99%

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Applicability of Solid Solution Heat Treatments to Aluminum Foams

Lázaro

Solórzano

Escudero

et al. 2012

Metals

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Present research work evaluates the influence of both density and size on the treatability of Aluminum-based (6000 series) foam-parts subjected to a typical solid solution heat treatment (water quenching). The results are compared with those obtained for the bulk alloy, evaluating the fulfilment of cooling requirements. Density of the foams was modeled by tomography analysis and the thermal properties calculated, based on validated density-scaled models. With this basis, cooling velocity maps during water quenching were predicted by finite element modeling (FEM) in which boundary conditions were obtained by solving the inverse heat conduction problem. Simulations under such conditions have been validated experimentally. Obtained results address incomplete matrix hardening for foam-parts bigger than 70 mm in diameter with a density below 650 kg/m 3 . An excellent agreement has been found in between the predicted cooling maps and final measured microhardness profiles.

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Section: Heat Transfer Modelingmentioning

confidence: 99%

“…The overall heat transfer coefficient (h) of each process/material was obtained after applying the Inverse Heat Conduction Problem (IHCP) method [36,37] (see experimental section) over the registered experimental data at the central point of the samples. The calculated convergence values are displayed in Figure 10.…”

Section: Heat Transfer Coefficientsmentioning

confidence: 99%

Applicability of Solid Solution Heat Treatments to Aluminum Foams

Lázaro

Solórzano

Escudero

et al. 2012

Metals

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“…In present study, the quenched target was taken as homogeneous, isotropic, and flat. A mathematical illustration of the inverse heat conduction problem is given as [ 15 , 24 – 26 ]

…”

Section: Spray Parameters and Mathematical Model Of Ihcpmentioning

confidence: 99%

“…At this point, let us introduce a new sensitivity coefficient, defined as

The temperature T i , M = T ( x i , t m ) can be expanded in a Taylor series about an arbitrary but known values of heat flux q M *. Considering the first-order derivatives, we get

Solving ( 12 ) by using ( 10 ) and ( 11a ), ( 11b ), ( 11c ), and ( 11d ) for heat flux component q M for temperature history only in one location x 1 , we get the formula

In case when future temperature measurements are used to estimate q M , we arrived to another formula [ 24 – 26 ]

For only one point temperature ( 14 ) can be written as

where

.…”

Section: Spray Parameters and Mathematical Model Of Ihcpmentioning

confidence: 99%

Estimation of Surface Heat Flux and Surface Temperature during Inverse Heat Conduction under Varying Spray Parameters and Sample Initial Temperature

Aamir

Liu

Zhu

et al. 2014

The Scientific World Journal

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An experimental study was carried out to investigate the effects of inlet pressure, sample thickness, initial sample temperature, and temperature sensor location on the surface heat flux, surface temperature, and surface ultrafast cooling rate using stainless steel samples of diameter 27 mm and thickness (mm) 8.5, 13, 17.5, and 22, respectively. Inlet pressure was varied from 0.2 MPa to 1.8 MPa, while sample initial temperature varied from 600°C to 900°C. Beck's sequential function specification method was utilized to estimate surface heat flux and surface temperature. Inlet pressure has a positive effect on surface heat flux (SHF) within a critical value of pressure. Thickness of the sample affects the maximum achieved SHF negatively. Surface heat flux as high as 0.4024 MW/m2 was estimated for a thickness of 8.5 mm. Insulation effects of vapor film become apparent in the sample initial temperature range of 900°C causing reduction in surface heat flux and cooling rate of the sample. A sensor location near to quenched surface is found to be a better choice to visualize the effects of spray parameters on surface heat flux and surface temperature. Cooling rate showed a profound increase for an inlet pressure of 0.8 MPa.

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“…Beck et al [2] developed a whole theory, and other researchers have used it to adapt it to particular objectives [3][4][5]. Therefore, the characteristic of the inverse problems of not meeting the criteria of existence and uniqueness of the solution has promoted the implementation of more robust mathematical methods in each classification of the IHCP to optimize its stability since minor errors in the measured data can induce significant inaccuracies in the estimated variable [6][7][8][9][10][11][12]. The analyses have oriented the study with an analytical mathematical approach [13][14][15] and to applying numerical solutions in various physical phenomena, particularly thermal phenomena [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Fundamental Procedure for Solving the Inverse Heat Conduction Problem Applied to Simple Systems

Sergio Téllez-Martínez,

Zulma Sánchez-Hernández,

Janeth Vega-Flores

et al. 2024

Heat Transfer - Advances in Fundamentals and Applications

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Heat transfer phenomena develop in various natural and artificially created processes. Fundamental laws of physics allow the transfer mechanisms to be classified; however, describing the phenomena is relatively complex, even if the analysis is limited to conduction. In particular, to determine the temperature distribution in a solid body, the definition of the boundary conditions that perturb it is required. Such conditions mathematically model a fluid’s hydrodynamic and thermodynamic behavior, and when the temperature differences are significantly high, the flow by radiation. It is then complex to define the functions of the thermal boundary conditions and solve the well-posed problem. Naturally, nonlinear system results and applying numerical methods are constant in the analysis. However, a unique solution for the thermal field in a solid does ensure. Alternatively, the scheme of the discretization of the system allows us to propose that through the knowledge of a fraction of the thermal field, the boundary condition is quantified independently of its nature. Such a procedure is called inverse analysis and has the characteristic of not satisfying the single solution criterion. However, some cases of interest can treat, and the estimate is guaranteed to be highly accurate.

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Inverse Heat Conduction Problems

Cited by 15 publications

References 34 publications

Applicability of Solid Solution Heat Treatments to Aluminum Foams

Applicability of Solid Solution Heat Treatments to Aluminum Foams

Estimation of Surface Heat Flux and Surface Temperature during Inverse Heat Conduction under Varying Spray Parameters and Sample Initial Temperature

Analysis of a Fundamental Procedure for Solving the Inverse Heat Conduction Problem Applied to Simple Systems

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