Inverse problem of estimating space and time dependent hot surface heat flux in transient transpiration cooling process

Shi, Junxiang; Wang, Jianhua

doi:10.1016/j.ijthermalsci.2008.11.019

Cited by 20 publications

(6 citation statements)

References 19 publications

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“…For the direct problem where the initial condition f (x) is specified, the problem given by equation (1)(2)(3)(4) is concerned with the determination of the temperature distribution u(x, t) in the interior region of the solid as a function of time and position.…”

Section: The Direct Problemmentioning

confidence: 99%

“…Inverse heat conduction problems have many applications in various branches of science and engineering,mechanical and chemical engineers, mathematicians and specialists in many other sciences branches are interested in inverse problems (see [1,2,3,4,5]),each with different application in mind. The main difficulty in the treatment of inverse problems is the instability of their solution in the presence of noise in the observed (measured) data, that is, the ill-posed nature Received: September 11, 2012 c 2013 Academic Publications, Ltd.…”

Section: Introductionmentioning

confidence: 99%

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Inverse Estimation of the Initial Condition for the Heat Equation

Tao¹,

Geng²,

Ren³

2013

Int. J. of Pure and Appl. Math.

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In this work,we investigate the inverse problem in the heat equation involving the recovery of the initial temperature from measurements of the final temperature. This problem is known as the backward heat problem and is severely ill-posed. We show that this problem can be converted into the first Fredholm integral equation, and an algorithm of inversion is given using the Tikhonov's regularization method. The Newton root-finding algorithm for obtaining the regularization parameter is presented. We also present numerical computations that verify the accuracy of our approximation.

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Section: The Direct Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Inverse Estimation of the Initial Condition for the Heat Equation

Tao¹,

Geng²,

Ren³

2013

Int. J. of Pure and Appl. Math.

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“…Inverse heat conduction problems have many applications in various branches of science and engineering (see [1][2][3][4]). In summary, one could classify the inverse heat problems into five classes based on the type of causal characteristics to be determined: initial value inverse problem [5]; boundary value inverse problem [6]; coefficient inverse problem [7]; source inverse problem [8]; shape inverse problem.…”

Section: Introductionmentioning

confidence: 99%

“…a Dirichlet boundary condition on S 0 u = g, on S 0 × (0, T) =: (S 0 ) T (4) and a homogeneous initial condition…”

Section: Introductionmentioning

confidence: 99%

The direct and inverse problem for an inclusion within a heat-conducting layered medium

Guo

Yan

Zhou

2015

Applicable Analysis

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This paper is concerned with the problem of heat conduction from an inclusion in a heat transfer layered medium. Making use of the boundary integral equation method, the well-posedness of the forward problem is established by the Fredholm theory. Then an inverse boundary value problem, i.e. identifying the inclusion from the measurements of the temperature and heat flux on the accessible exterior boundary of the medium is considered in the framework of the linear sampling method. Based on a careful analysis of the Dirichlet-to-Neumann map, the mathematical fundamentals of the linear sampling method for reconstructing the inclusion are proved rigorously. ARTICLE HISTORY

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“…Important applications for inverse heat conduction problem solutions include, for example, controlled cooling of electronic components, estimation of jet-flow rate of cooling in machining or quenching, determination of conditions at the interface between the mold and metal during metal casting or a rolling process [3], and heat flux estimation in the surface of a wall subjected to fire or the inside surface of a combustion chamber [4], in surfaces where ablation takes place, or in surfaces going through a welding process [5]. Some other applications of the IHCP are prediction of the inner wall temperature of a reactor, determination of the heat transfer coefficient and outer surface conditions in the re-entry of a space vehicle, and modeling of the temperature or heat flux at the tool-work interface of machine cutting [6] and in transpiration cooling control [7]. There are many different methods for solving inverse heat conduction problems.…”

mentioning

confidence: 99%

Time-Dependent Heat Flux Estimation in Multi-Layer Systems by Inverse Method

Mohammadiun

2016

Journal of Thermophysics and Heat Transfer

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In this paper, the conjugate gradient method, coupled with the adjoint problem, is used to solve the inverse heat conduction problem and to estimate the time-dependent heat flux, using temperature distribution at a point in a threelayer system. Also, the effect of noisy data on the final solution is studied. The numerical solution of the governing equations is obtained by employing a finite difference technique. For solving this problem, the general coordinate method and body-fitted coordinate method are used. The irregular region in the physical domain (r, z) is transformed into a rectangle in the computational domain (ξ, η). The present formulation is general and can be applied to the solution of boundary inverse heat conduction problems over any region that can be mapped into a rectangle. The obtained results show the good accuracy of the presented method. Also, the solutions have good stability even if the input data includes noise. The problem is solved in an axisymmetric case. Applications of this model are in the thermal protection systems and heat shield systems. Nomenclature A; B; C = material names in computational plane c = constant C p = specified thermal capacity d k t = direction of descent e rms = root mean square error G est t i = estimated function at t i G ex t i = exact function at t i I = number of measurements i; j = node positions in computational plane J = Jacobian transformation k = thermal conductivity n = normal vector to the surface qt = time-dependent heat flux R = radial distance from center R i = inner radius R o = outer radius S = objective function r = normal distance from the z axis T = temperature t = time w = wall z = symmetric axis α; β; γ = computational coefficients β k = search step size γ k = conjugate coefficient η = vertical axis in computational plane λ = adjoint temperature ξ = horizontal axis in computational plane ρ = density σ = standard deviation of measurement error ω = normal distribution

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Inverse problem of estimating space and time dependent hot surface heat flux in transient transpiration cooling process

Cited by 20 publications

References 19 publications

Inverse Estimation of the Initial Condition for the Heat Equation

Inverse Estimation of the Initial Condition for the Heat Equation

The direct and inverse problem for an inclusion within a heat-conducting layered medium

Time-Dependent Heat Flux Estimation in Multi-Layer Systems by Inverse Method

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