Solution of the inverse jet in a crossflow problem by a predictor–corrector technique

VanderVeer, Joseph R.; Jaluria, Yogesh

doi:10.1016/j.ijheatmasstransfer.2015.05.037

Cited by 8 publications

(2 citation statements)

References 11 publications

(25 reference statements)

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“…It is important to determine the location and strength of the source and measurements downstream may be used to obtain these (Knight et al , 2007). A predictor-corrector method is developed to solve the inverse convection problem of a plume or jet in a cross-flow (Vanderveer and Jaluria, 2013, 2014, 2015). The inverse problem involves the prediction of the strength and location of the jet or heat source by using a few selected data points downstream, as shown in Figure 4.…”

Section: Resultsmentioning

confidence: 99%

Strategies for solving inverse problems in thermal processes and systems

Jaluria

2020

HFF

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Purpose This paper aims to discuss inverse problems that arise in a variety of practical thermal processes and systems. It presents some of the approaches that may be used to obtain results that lie within a small region of uncertainty. Therefore, the non-uniqueness of the solution is reduced so that the final design and boundary conditions may be determined. Optimization methods that may be used to reduce the uncertainty and to select locations for experimental data and for minimizing the error are presented. A few examples of thermal systems are given to illustrate the applicability of these methods and the challenges that must be addressed in solving inverse problems. Design/methodology/approach In most analytical and numerical solutions, the basic equations that describe the process, as well as the relevant and appropriate boundary conditions, are known. The interest lies in obtaining a unique solution that satisfies the equations and boundary conditions. This may be termed as a direct or forward solution. However, there are many problems, particularly in practical systems, where the desired result is known but the conditions needed for achieving it are not known. These are generally known as inverse problems. In manufacturing, for instance, the temperature variation to which a component must be subjected to obtain desired characteristics is prescribed, but the means to achieve this variation are not known. An example of this circumstance is the annealing, tempering or hardening of steel. In such cases, the boundary and initial conditions are not known and must be determined by solving the inverse problem to obtain the desired temperature variation in the component. The solutions, thus, obtained are generally not unique. This is a review paper, which discusses inverse problems that arise in a variety of practical thermal processes and systems. It presents some of the approaches or strategies that may be used to obtain results that lie within a small region of uncertainty. It is important to realize that the solution is not unique, and this non-uniqueness must be reduced so that the final design and boundary conditions may be determined with acceptable accuracy and repeatability. Optimization techniques are often used for minimizing the error. This review presents several methods that may be applied to reduce the uncertainty and to select locations for experimental data for the best results. A few examples of thermal systems are given to illustrate the applicability of these methods and the challenges that must be addressed in solving inverse problems. By considering a variety of systems, the paper also shows the importance of solving inverse problems to obtain results that may be used to model and design thermal processes and systems. Findings The solution of inverse problems, which frequently arise in thermal processes, is discussed. Different strategies to obtain the conditions that lead to the desired result are given. The goal of these approaches is to reduce uncertainty and obtain essentially unique solutions for different circumstances. The error of the method can be checked against known conditions to see if it is acceptable for the given problem. Several examples are given to illustrate the use of these methods. Originality/value The basic strategies presented here for solving inverse problems that arise in thermal processes and systems, as well as the optimization techniques used to reduce the domain of uncertainty, are fairly original. They are used for certain challenging problems that have not been considered in detail earlier. Several methods are outlined for considering different types of problems.

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Section: Resultsmentioning

confidence: 99%

Strategies for solving inverse problems in thermal processes and systems

Jaluria

2020

HFF

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“…Inverse heat transfer problems encompass a spectrum of classifications, including inverse heat conduction problems (the most prevalent), inverse heat convection problems, inverse heat radiation problems, and inverse heat conjugation problems. Researchers have comprehensively explored inverse problems related to heat conduction [1][2][3][4][5][6][7][8][9], heat convection [10][11][12][13][14][15][16], and heat radiation [17][18][19], employing diverse algorithms. However, investigations into inverse conjugate heat transfer problems [20][21][22] remain notably scarce within the available literature.…”

Section: Introductionmentioning

confidence: 99%

An Inverse Problem for Estimating Spatially and Temporally Dependent Surface Heat Flux with Thermography Techniques

Huang,

Fang

2024

Mathematics

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In this study, an inverse conjugate heat transfer problem is examined to estimate temporally and spatially the dependent unknown surface heat flux using thermography techniques with a thermal camera in a three-dimensional domain. Thermography techniques encompass a broad set of methods and procedures used for capturing and analyzing thermal data, while thermal cameras are specific tools used within those techniques to capture thermal images. In the present study, the interface conditions of the plate and air domains are obtained using perfect thermal contact conditions, and therefore we define the problem studied as an inverse conjugate heat transfer problem. Achieving the simultaneous solution of the continuity, Navier–Stokes, and energy equations within the air domain, alongside the heat conduction equation in the plate domain, presents a more intricate challenge compared to conventional inverse heat conduction problems. The validity of our inverse solutions was verified through numerical simulations, considering various inlet air velocities and plate thicknesses. Notably, it was found that due to the singularity of the gradient of the cost function at the final time point, the estimated results near the final time must be discarded, and exact measurements consistently produce accurate boundary heat fluxes under thin-plate conditions, with air velocity exhibiting no significant impact on the estimates. Additionally, an analysis of measurement errors and their influence on the inverse solutions was conducted. The numerical results conclusively demonstrated that the maximum error when estimating heat flux consistently remained below 3% and higher measurement noise resulted in the accuracy of the heat flux estimation decreasing. This underscores the inherent challenges associated with inverse problems and highlights the importance of obtaining accurate measurement data in the problem domain.

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An experimental inverse problem in determining spatially varying surface heat flux using measured temperature readings

Huang

2023

Case Studies in Thermal Engineering

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Solution of the inverse jet in a crossflow problem by a predictor–corrector technique

Cited by 8 publications

References 11 publications

Strategies for solving inverse problems in thermal processes and systems

Strategies for solving inverse problems in thermal processes and systems

An Inverse Problem for Estimating Spatially and Temporally Dependent Surface Heat Flux with Thermography Techniques

An experimental inverse problem in determining spatially varying surface heat flux using measured temperature readings

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