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Article

Mousa Huntul, Daniel Lesnic and Tomas Johansson

The purpose of this study is to provide an insight and to solve numerically the identification of an unknown coefficient of radiation/absorption/perfusion appearing in the…

Abstract

Purpose

The purpose of this study is to provide an insight and to solve numerically the identification of an unknown coefficient of radiation/absorption/perfusion appearing in the heat equation from additional temperature measurements.

Design/methodology/approach

First, the uniqueness of solution of the inverse coefficient problem is briefly discussed in a particular case. However, the problem is still ill-posed as small errors in the input data cause large errors in the output solution. For numerical discretization, the finite difference method combined with a regularized nonlinear minimization is performed using the MATLAB toolbox routine lsqnonlin.

Findings

Numerical results presented for three examples show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data.

Research limitations/implications

The mathematical formulation is restricted to identify coefficients which separate additively in unknown components dependent individually on time and space, and this may be considered as a research limitation. However, there is no research implication to overcome this, as the known input data are also limited to single measurements of temperature at a particular time and space location.

Practical implications

As noisy data are inverted, the study models real situations in which practical measurements are inherently contaminated with noise.

Social implications

The identification of the additive time- and space-dependent perfusion coefficient will be of great interest to the bio-heat transfer community and applications.

Originality/value

The current investigation advances previous studies which assumed that the coefficient multiplying the lower-order temperature term depends on time or space separately. The knowledge of this physical property coefficient is very important in biomedical engineering for understanding the heat transfer in biological tissues. The originality lies in the insight gained by performing for the first time numerical simulations of inversion to find the coefficient additively dependent on time and space in the heat equation from noisy measurements.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Mohammed Shuker Mahmood and D. Lesnic

The purpose of this paper is to solve numerically the identification of the thermal conductivity of an inhomogeneous and possibly anisotropic medium from interior/internal…

Abstract

Purpose

The purpose of this paper is to solve numerically the identification of the thermal conductivity of an inhomogeneous and possibly anisotropic medium from interior/internal temperature measurements.

Design/methodology/approach

The formulated coefficient identification problem is inverse and ill-posed, and therefore, to obtain a stable solution, a non-linear regularized least-squares approach is used. For the numerical discretization of the orthotropic heat equation, the finite-difference method is applied, while the non-linear minimization is performed using the MATLAB toolbox routine lsqnonlin.

Findings

Numerical results show the accuracy and stability of solution even in the presence of noise (modelling inexact measurements) in the input temperature data.

Research limitations/implications

The mathematical formulation uses temporal temperature measurements taken at many points inside the sample, and this may be too much information that is provided to identify a space-wise dependent only conductivity tensor.

Practical implications

As noisy data are inverted, the paper models real situations in which practical temperature measurements recorded using thermocouples are inherently contaminated with random noise.

Social implications

The identification of the conductivity of inhomogeneous and orthotropic media will be of great interest to the inverse problems community with applications in geophysics, groundwater flow and heat transfer.

Originality/value

The current investigation advances the field of coefficient identification problems by generalizing the conductivity to be anisotropic in addition of being heterogeneous. The originality lies in performing, for the first time, numerical simulations of inversion to find the orthotropic and inhomogeneous thermal conductivity from noisy temperature measurements. Further value and physical significance are brought in by determining the degree of cure in a resin transfer molding process, in addition to obtaining the inhomogeneous thermal conductivity of the tested material.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Moataz Alosaimi, Daniel Lesnic and Jitse Niesen

This study aims to at numerically retrieve five constant dimensional thermo-physical properties of a biological tissue from dimensionless boundary temperature measurements.

Abstract

Purpose

This study aims to at numerically retrieve five constant dimensional thermo-physical properties of a biological tissue from dimensionless boundary temperature measurements.

Design/methodology/approach

The thermal-wave model of bio-heat transfer is used as an appropriate model because of its realism in situations in which the heat flux is extremely high or low and imposed over a short duration of time. For the numerical discretization, an unconditionally stable finite difference scheme used as a direct solver is developed. The sensitivity coefficients of the dimensionless boundary temperature measurements with respect to five constant dimensionless parameters appearing in a non-dimensionalised version of the governing hyperbolic model are computed. The retrieval of those dimensionless parameters, from both exact and noisy measurements, is successfully achieved by using a minimization procedure based on the MATLAB optimization toolbox routine lsqnonlin. The values of the five-dimensional parameters are recovered by inverting a nonlinear system of algebraic equations connecting those parameters to the dimensionless parameters whose values have already been recovered.

Findings

Accurate and stable numerical solutions for the unknown thermo-physical properties of a biological tissue from dimensionless boundary temperature measurements are obtained using the proposed numerical procedure.

Research limitations/implications

The current investigation is limited to the retrieval of constant physical properties, but future work will investigate the reconstruction of the space-dependent blood perfusion coefficient.

Practical implications

As noise inherently present in practical measurements is inverted, the paper is of practical significance and models a real-world situation.

Social implications

The findings of the present paper are of considerable significance and interest to practitioners in the biomedical engineering and medical physics sectors.

Originality/value

In comparison to Alkhwaji et al. (2012), the novelty and contribution of this work are as follows: considering the more general and realistic thermal-wave model of bio-heat transfer, accounting for a relaxation time; allowing for the tissue to have a finite size; and reconstructing five thermally significant dimensional parameters.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

N.S. Mera, L. Elliott, D.B. Ingham and D. Lesnic

In this paper, various regularization methods are numerically implemented using the boundary element method (BEM) in order to solve the Cauchy steady‐state heat conduction…

Abstract

In this paper, various regularization methods are numerically implemented using the boundary element method (BEM) in order to solve the Cauchy steady‐state heat conduction problem in an anisotropic medium. The convergence and the stability of the numerical methods are investigated and compared. The numerical results obtained confirm that stable numerical results can be obtained by various regularization methods, but if high accuracy is required for the temperature, or if the heat flux is also required, then care must be taken when choosing the regularization method since the numerical results are substantially improved by choosing the appropriate method.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

D. Lesnic

Initial value problems for the one‐dimensional third‐order dispersion equations are investigated using the reliable Adomian decomposition method (ADM).

Abstract

Purpose

Initial value problems for the one‐dimensional third‐order dispersion equations are investigated using the reliable Adomian decomposition method (ADM).

Design/methodology/approach

The solutions are obtained in the form of rapidly convergent power series with elegantly computable terms.

Findings

It was found that the technique is reliable, powerful and promising. It is easier to implement than the separation of variables method. Modifications of the ADM and the noise terms phenomenon are successfully applied for speeding up the convergence of non‐homogeneous equations.

Research limitations/implications

The method is restricted to initial value problems in which the space variable fills the whole real axis. Modifications are required to deal with initial boundary value problems. Further, the input initial condition is required to be an infinitely differentiable function and obviously, the convergence radius of the decomposition series depends on the input data.

Practical implications

The method was mainly illustrated for linear partial differential equations occuring in water resources research, but the natural extension of the ADM to solving nonlinear problems is extremely useful in nonlinear studies and soliton theory.

Originality/value

The study undertaken in this paper provides a reliable approach for solving both linear and nonlinear dispersion equations and new explicit or recursively‐based exact solutions are found.

Details

Kybernetes, vol. 36 no. 5/6
Type: Research Article
ISSN: 0368-492X

Keywords

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Article

A. Rap, L. Elliott, D.B. Ingham, D. Lesnic and X. Wen

To develop a numerical technique for solving the inverse source problem associated with the constant coefficients convection‐diffusion equation.

Abstract

Purpose

To develop a numerical technique for solving the inverse source problem associated with the constant coefficients convection‐diffusion equation.

Design/methodology/approach

The proposed numerical technique is based on the boundary element method (BEM) combined with an iterative sequential quadratic programming (SQP) procedure. The governing convection‐diffusion equation is transformed into a Helmholtz equation and the ill‐conditioned system of equations that arises after the application of the BEM is solved using an iterative technique.

Findings

The iterative BEM presented in this paper is well‐suited for solving inverse source problems for convection‐diffusion equations with constant coefficients. Accurate and stable numerical solutions were obtained for cases when the number of sources is correctly estimated, overestimated, or underestimated, and with both exact and noisy input data.

Research limitations/implications

The proposed numerical method is limited to cases when the Péclet number is smaller than 100. Future approaches should include the application of the BEM directly to the convection‐diffusion equation.

Practical implications

Applications of the results presented in this paper can be of value in practical applications in both heat and fluid flow as they show that locations and strengths for an unknown number of point sources can be accurately found by using boundary measurements only.

Originality/value

The BEM has not as yet been employed for solving inverse source problems related with the convection‐diffusion equation. This study is intended to approach this problem by combining the BEM formulation with an iterative technique based on the SQP method. In this way, the many advantages of the BEM can be applied to inverse source convection‐diffusion problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 16 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

B. Tomas Johansson

To propose and investigate a stable numerical procedure for the reconstruction of the velocity of a viscous incompressible fluid flow in linear hydrodynamics from…

Abstract

Purpose

To propose and investigate a stable numerical procedure for the reconstruction of the velocity of a viscous incompressible fluid flow in linear hydrodynamics from knowledge of the velocity and fluid stress force given on a part of the boundary of a bounded domain.

Design/methodology/approach

Earlier works have involved the similar problem but for stationary case (time‐independent fluid flow). Extending these ideas a procedure is proposed and investigated also for the time‐dependent case.

Findings

The paper finds a novel variation method for the Cauchy problem. It proves convergence and also proposes a new boundary element method.

Research limitations/implications

The fluid flow domain is limited to annular domains; this restriction can be removed undertaking analyses in appropriate weighted spaces to incorporate singularities that can occur on general bounded domains. Future work involves numerical investigations and also to consider Oseen type flow. A challenging problem is to consider non‐linear Navier‐Stokes equation.

Practical implications

Fluid flow problems where data are known only on a part of the boundary occur in a range of engineering situations such as colloidal suspension and swimming of microorganisms. For example, the solution domain can be the region between to spheres where only the outer sphere is accessible for measurements.

Originality/value

A novel variational method for the Cauchy problem is proposed which preserves the unsteady Stokes operator, convergence is proved and using recent for the fundamental solution for unsteady Stokes system, a new boundary element method for this system is also proposed.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Haolong Chen, Zhibo Du, Xiang Li, Huanlin Zhou and Zhanli Liu

The purpose of this paper is to develop a transform method and a deep learning model to identify the inner surface shape based on the measurement temperature at the outer…

Abstract

Purpose

The purpose of this paper is to develop a transform method and a deep learning model to identify the inner surface shape based on the measurement temperature at the outer boundary of the pipe.

Design/methodology/approach

The training process is assisted by the finite element method (FEM) simulation which solves the direct problem for the data preparation. To avoid re-meshing the domain when the inner surface shape varies, a new transform method is proposed to transform the shape identification problem into the effective thermal conductivity identification problem. The deep learning model is established to set up the relationship between the measurement temperature and the effective thermal conductivity. Then the unknown geometry shape is acquired by the mapping between the inner shape and the effective thermal conductivity through the inverse transform method.

Findings

The new method is successfully applied to identify the internal boundary of a pipe with eccentric circle, ellipse and nephroid inner geometries. The results show that as the measurement points increased and the measurement error decreased, the results became more accurate. The position of the measurement point and mesh density of the FEM model have less effect on the results.

Originality/value

The deep learning model and the transform method are developed to identify the pipe inner surface shape. There is no need to re-mesh the domain during the computation progress. The results show that the proposed method is a fast and an accurate tool for identifying the pipe inner surface.

Details

Engineering Computations, vol. 37 no. 9
Type: Research Article
ISSN: 0264-4401

Keywords

Abstract

Details

Kybernetes, vol. 41 no. 7/8
Type: Research Article
ISSN: 0368-492X

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Article

Mousa Huntul and Mohammad Tamsir

The purpose of this paper is to provide an insight and to solve numerically the identification of timewise terms and free boundaries coefficient appearing in the heat…

Abstract

Purpose

The purpose of this paper is to provide an insight and to solve numerically the identification of timewise terms and free boundaries coefficient appearing in the heat equation from over-determination conditions.

Design/methodology/approach

The formulated coefficient identification problem is inverse and ill-posed, and therefore, to obtain a stable solution, a nonlinear Tikhonov regularization least-squares approach is used. For the numerical discretization, the finite difference method combined with a regularized nonlinear minimization is performed using the MATLAB subroutine lsqnonlin.

Findings

The numerical results presented for two examples show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data.

Research limitations/implications

The mathematical formulation is restricted to identify coefficients in unknown components dependent on time, and this may be considered as a research limitation. However, there is no research implication to overcome this, as the known input data is also limited to single temperature in heat equation with Stefan conditions, and the first- and second-order heat moments measurements at a particular time location.

Practical implications

As noisy data are inverted, the study models real situations in which practical measurements are inherently contaminated with noise.

Social implications

The identification of the timewise terms and free boundaries will be of great interest in the heat transfer community and related fluid flow applications.

Originality/value

The current investigation advances previous studies, which assumed that the coefficient multiplying the lower order temperature term depends on time. The knowledge of this physical property coefficient is very important in heat transfer and fluid flow. The originality lies in the insight gained by performing for the numerical simulations of inversion to find the timewise terms and free boundaries coefficient dependent on time in the heat equation from noisy measurements.

Details

Engineering Computations, vol. 38 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

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