scholarly journals Solving of Two-Dimensional Unsteady Inverse Heat Conduction Problems Based on Boundary Element Method and Sequential Function Specification Method

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Shoubin Wang ◽  
Yuanzheng Deng ◽  
Xiaogang Sun
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Measuring Error ◽  
Two Dimensional ◽  
Future Time ◽  
Time Step ◽  
Measuring Point ◽  
Specification Method ◽  
Sequential Function Specification ◽  
Function Specification Method

The boundary element method (BEM) and sequential function specification method (SFSM) are used to research the inverse problem of boundary heat flux identification in the two-dimensional heat conduction system. The future time step in the SFSM is optimized by introducing the residual error principles to get the more accurate inversion results. For the forward problems, the BEM is used to calculate the required temperature value of discrete point; for the inverse problems, the impacts of different future time steps, measuring point position, and measuring error on the inversion results are discussed. Furthermore, the comparison is made for the optimal future time step obtained by introducing the residual error principle and the inherent future time step. The example analysis shows that the method proposed still has higher accuracy when the measuring error exists or the measuring point position is far away from the boundary heat flux.

Application of Sequential Function Specification Method in Heat Flux Monitoring of Receding Solid Surfaces

2013 ◽  
Vol 35 (10) ◽  
pp. 933-941 ◽  
Author(s):  
Mohammad Mohammadiun ◽  
Hosein Molavi ◽  
Hamid Reza Talesh Bahrami ◽  
Hamid Mohammadiun
Keyword(s):  
Heat Flux ◽  
Solid Surfaces ◽  
Specification Method ◽  
Flux Monitoring ◽  
Sequential Function Specification ◽  
Function Specification Method

Estimation of the Heat Generation in a Cutting Tool Using a Sequential Inverse Method

2010 ◽  
Author(s):  
Forooza Samadi ◽  
Farshad Kowsary ◽  
Mohsen Hamedi ◽  
Araz Sarchami
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Geometric Modeling ◽  
Cutting Tool ◽  
Parametric Design ◽  
Three Dimensional ◽  
Specification Method ◽  
The Stability ◽  
Sequential Function Specification ◽  
Dimensional Object

In this paper the Sequential Function Specification Method is used to estimate the transient heat flux imposed on the rake face of the cutting tool during the cutting operation. The cutting tool is modeled as a three dimensional object. The capabilities of the geometric modeling, mesh generation as well as solver of the commercial software ANSYS is utilized in order to reduce the time expended for modeling and direct heat conduction solution. This way the inverse heat conduction algorithm employs ANSYS as a subprogram through the ANSYS Parametric Design Language (APDL). The stability as well as accuracy of the heat flux estimation is investigated using familiar triangular as well as step heat flux test cases. The effect of noise level, the number of temperature sensors as well as their locations are investigated in order to arrive at an optimal experimental procedure. Finally, a typical temperature data during the working condition are used to recover the heat flux at the cutting tool surface.

Real-Time Evaluation of Severe Heat Load Over Moving Interface of Decomposing Composites

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
Hamid Mohammadiun ◽  
Hosein Molavi ◽  
Hamid Reza Talesh Bahrami ◽  
Mohammad Mohammadiun
Keyword(s):  
Heat Flux ◽  
Gas Phase ◽  
Moving Boundary ◽  
Chemical Species ◽  
Front Surface ◽  
Moving Interface ◽  
Specification Method ◽  
Sequential Function Specification ◽  
Time Evaluation ◽  
Function Specification Method

Decomposing composites undergo both surface removal and in-depth decomposition, when they are subjected to severe heating environments. As a result, the gas phase and the chemical species are injected into the boundary layer, resulting in a reduction of the heat flux entering into the solid structure. Under such conditions that geometry changes, the reconstruction of heat flux at the ablating front is quite complicated. Utilizing a procedure based on the sequential function specification method, an inverse problem is solved to anticipate the front-surface heating condition. Temperature measurements as well as measurement of the position of the ablating surface accompanied with additive noises are used for the implementation of the current procedure. Taking into account a complex set of phenomena, a numerical experiment is employed to examine the accuracy and appropriateness of the proposed technique for such problems. The results obtained demonstrate the usefulness and efficiency of the proposed method for the estimation of heat flux at the moving boundary of decomposing materials.

Enhanced Explicit Scheme to Solve Transient Heat Conduction Problem

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
Ganesh Hegde ◽  
Madhu Gattumane
Keyword(s):  
Heat Conduction ◽  
Correction Factor ◽  
Truncation Error ◽  
Transient Heat Conduction ◽  
Explicit Scheme ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Time Step ◽  
One Dimensional ◽  
Partial Derivatives

Improvement in accuracy without sacrificing stability and convergence of the solution to unsteady diffusion heat transfer problems by computational method of enhanced explicit scheme (EES), has been achieved and demonstrated, through transient one dimensional and two dimensional heat conduction. The truncation error induced in the explicit scheme using finite difference technique is eliminated by optimization of partial derivatives in the Taylor series expansion, by application of interface theory developed by the authors. This theory, in its simple terms gives the optimum values to the decision vectors in a redundant linear equation. The time derivatives and the spatial partial derivatives in the transient heat conduction, take the values depending on the time step chosen and grid size assumed. The time correction factor and the space correction factor defined by step sizes govern the accuracy, stability and convergence of EES. The comparison of the results of EES with analytical results, show decreased error as compared to the result of explicit scheme. The paper has an objective of reducing error in the explicit scheme by elimination of truncation error introduced by neglecting the higher order terms in the expansion of the governing function. As the pilot examples of the exercise, the implementation is aimed at solving one-dimensional and two-dimensional problems of transient heat conduction and compared with the results cited in the referred literature.

Finite Element Formulation for Two-Dimensional Inverse Heat Conduction Analysis

1992 ◽  
Vol 114 (3) ◽  
pp. 553-557 ◽  
Author(s):  
T. R. Hsu ◽  
N. S. Sun ◽  
G. G. Chen ◽  
Z. L. Gong
Keyword(s):  
Heat Flux ◽  
Finite Element ◽  
Heat Conduction ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Element Formulation ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
Discrete Point ◽  
Element Algorithm

This paper presents a finite element algorithm for two-dimensional nonlinear inverse heat conduction analysis. The proposed method is capable of handling both unknown surface heat flux and unknown surface temperature of solids using temperature histories measured at a few discrete point. The proposed algorithms were used in the study of the thermofracture behavior of leaking pipelines with experimental verifications.

Two-dimensional hybrid analytical approach for the investigation of thermal aspects in human tissue undergoing regional hyperthermia therapy

2020 ◽  
Vol 234 (20) ◽  
pp. 3951-3966
Author(s):  
Jaideep Dutta ◽  
Balaram Kundu
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Cancer Treatment ◽  
Thermal Response ◽  
Skin Tissue ◽  
Hyperbolic Heat Conduction ◽  
Two Dimensional ◽  
Regional Hyperthermia ◽  
Hyperthermia Therapy ◽  
The Impact

The formation of the present work is based on the development of the exact analytical solution of two-dimensional temperature response by employing the hyperbolic heat conduction bioheat model in a single-layered human skin tissue subjected to the regional hyperthermia therapy (RHT) for cancer treatment. The mathematical approach has been utilized as a hybrid form of ‘separation of variables’ and ‘finite integral transform’ method. Three kinds of surface heat fluxes (constant, sinusoidal and cosine) have been employed as an external heat source on the therapeutic surface of the square-shaped skin tissue of 100 mm × 100 mm. An innovative form of initial condition (spatially dependent) has been implemented in the present mathematical formulation as skin tissues are highly non-homogeneous and non-uniform in structure. The present research outcome indicates that cosine heat flux would be a suitable alternative for the sinusoidal heat flux. The impact of the relaxation time lag has been clearly noted in the thermal response with the waveform-like behaviour and it justifies the postulate of hyperbolic heat conduction. The two-dimensional temperature of the skin tissue has been observed in the range of 48.1 ℃–40 ℃ (in decreasing order). Estimated peak temperatures are in the proposed spectrum of hyperthermia therapy for an exposure time of 100 s, and this fact is true in an agreement with the medical protocol of the cancer treatment. The accuracy of the mathematical modelling and in-house computer codes are justified with the published numerical models and the maximum deviation of the thermal response has been noticed in order of 1.5–3%. The two-dimensional surface thermal contours have provided a glimpse of heat flow in the physical domain of skin tissue under different heating conditions and this research output may be beneficial to establish the theoretical standard of the regional hyperthermia treatment for cancer eradication.

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