Determine the special term of a two-dimensional heat source

Trong, Dang Duc; Alain, Pham Ngoc Dinh; Nam, Phan Thành

doi:10.1080/00036810902889534

Cited by 9 publications

(3 citation statements)

References 14 publications

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“…A more mathematical background dealing with uniqueness and establishing the problem as an inverse problem is given by J. R. Cannon in [8,9] and in numerous other papers by the same author. Continuing the analytical approach we have the theoretical stability analysis of papers [16,17,18,19,20,21]. Examples of regularization strategies to battle against the ill-posedness are found in [10,11,12,13,14,15].…”

Section: Literature Reviewmentioning

confidence: 99%

Detection of time-varying heat sources using an analytic forward model

Tamminen¹

2020

Journal of Computational and Applied Mathematics

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Section: Literature Reviewmentioning

confidence: 99%

Detection of time-varying heat sources using an analytic forward model

Tamminen¹

2020

Journal of Computational and Applied Mathematics

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“…Find f (x) if an additional boundary observation of u, for example, in case of the Dirichlet boundary condition (1.9), we require the Neumann condition be given in a subset of S, [4,6,7,8,9,10,14,21,22,23,53,56,57].…”

Section: Introductionmentioning

confidence: 99%

Determination of a term in the right-hand side of parabolic equations

Hào

Huong

Oanh

et al. 2017

Journal of Computational and Applied Mathematics

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The inverse problem of determining a term in the right hand side of parabolic equations from integral observations is investigated. The observations can be regarded as generalized interior point observations which are collected in practice. The problem is then reformulated as a least squares problem in coupling with a Tikhonov regularization term. It is proved that the Tikhonov functional is Fréchet differentiable and a formula for the gradient is derived via an adjoint problem. The variational problem is discretized by the finite element method, the convergence of which is proved. The discretized variational problem is numerically solved by the conjugate gradient method. Some numerical examples are presented for showing the efficiency of the method.

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“…Christian et al, [12] examined the mechanical, optical, and physical properties of Thermally Modified Timber (TMT) with its impact on high heat flow. Dang et al, [13] constructed a regularized solution of the source energy data prediction by using the interpolation and the truncated Fourier series method. [14] investigated the different effectiveness of heat and mass exchangers by using NTU correlation numerical models.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Economic TEHES-Tube Material Evaluation by Absorbability Index under O-S-Dimensions for Minimizing Global Warming and Air Pollution by Exploring Dominance Theory: Green Management Initiative

Prabhu

Kottala

Anbazhagan³

et al. 2022

Adsorption Science & Technology

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It is investigated that the Global Warming and Air Pollution (GWAP) issues are highly prioritized around the world. There is a high magnitude of contaminated hot heat (CHH) from hot fluids such as contaminated water, oils, and mixed oils; toxic oils increase the GWAP ON emission. Such GWAP can be controlled by applying the methods-techniques for optimizing the energy processes, evaluating the high energy absorption material among available materials and technological advancement in energy flow devices, optimizing design of energy systems and low heat emission strategy, etc. It is observed that nowadays, Thermal Energy Heat Exchanger Systems (TEHESs) are utilized in many industries for transferring the energy between two mineral or contaminated liquids, separated by walls. It is found that TEHESs are constructed by tube materials, might be contributed to control the GWAP if TEHESs are fabricated with composite material, and have a high absorbability index. The evaluation of the Energy Absorbability Index (EAI) of TEHES composite tube materials provides the two innovative solutions to TEHES designers such as choose the economic/cost TEHESs and initiate to green management (reducing minimizing the GWAP). On literature survey, a few research documents are found by authors, which focused on mathematical modelling of either O- (objective-) or S- (subjective-) dimensions of composite TEHES tube material evaluation models for computing EAI. It is also probed that those models are simulated by single or nondynamic material evaluation methods. Therefore, it is summarized that there are no still research document pertaining to integrated/mixed mathematical modelling of O-S- (objective-subjective-) dimensions of composite TEHES tube materials with dominance theory for computing EAI of composite TEHES tube materials. Said research gaps are respected as major research defies (help to minimize the GWAP or green management). To fulfil the said research defies, the authors developed and proposed the TEHES-O-S-composite tube material evaluation model by conducting literature and real industrial survey, consisting of seven TEHES-O and four TEHES-S tube material dimensions. The O-dimensions are framed by available O-rating/data, while S-dimension is framed S-rating. The TFNs (triangular fuzzy numbers) are used by a team of experts for assigning the appropriateness ratings vs. four TEHES-S composite tube material dimension, and priority weights are assigned vs. entire TEHES-O-S tube material dimensions. After data modelling of the TEHES-O-S-composite tube material evaluation model, defuzzification is carried out to normalize O-S-data. Later, the authors’ implemented integrated optimization technique “crisp VIKOR combined FMF technique” to evaluate the EAI of composite TEHES tube materials. As the reliability of results is an enormous concern, dominance theory is applied by conducting the comparative analysis among evaluated results and delivering the accurate and reliable results. The evaluated beast composite TEHES tube materials based on EAI linked to green management and economic concern of material. The research can be used by TEHES designers to minimize the GWAP across the universe.

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Determine the special term of a two-dimensional heat source

Cited by 9 publications

References 14 publications

Detection of time-varying heat sources using an analytic forward model

Detection of time-varying heat sources using an analytic forward model

Determination of a term in the right-hand side of parabolic equations

Economic TEHES-Tube Material Evaluation by Absorbability Index under O-S-Dimensions for Minimizing Global Warming and Air Pollution by Exploring Dominance Theory: Green Management Initiative

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