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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.

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.

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.

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.

A numerical study of a two‐dimensional turbulent flow in a partially open rectangular cavity such as a room is carried out. The turbulent flow is induced by the energy input due to a localized heat source positioned on the floor of the cavity. This flow is of interest in enclosure fires where the flow in the cavity interacts with the environment through the opening or vents. The focus is on the stable, thermal stratification that arises in the room and on the influence of the opening height. A finite‐difference method is employed for the solution of the problem, using a low Reynolds number k — ε turbulence model for the turbulent flow calculations. This model is particularly suitable for flows in which the possibility for relaminarization exists. It was found that, for high Grashof numbers and for relatively small opening heights, particularly for doorway openings, a strong stable thermal stratification is generated within the cavity, with a cooler, essentially uniform, layer underlying a warmer, linearly stratified, upper layer. As a consequence, turbulence is suppressed and the flow in the upper region of the cavity becomes laminar with turbulence confined to locations such as the fire plume above the source and the shear layer at the opening. The penetration distance and the height of the interface are both found to decrease with a reduction in the opening height. The Nusselt number for heat transfer from the source is seen to be affected to a small extent by the opening height. The basic trends are found to agree with those observed in typical compartment fires. Comparisons with results available in the literature on turbulent buoyancy‐driven enclosure flows indicate good agreement, lending support to this model and the numerical scheme.

This paper seeks to discuss the numerical modeling of the transport processes that frequently arise in practical thermal systems and involve complexities such as property variations with temperature or with the shear rate in the flow, complicated regions, conjugate mechanisms, chemical reactions and combined mass transfer, and intricate boundary conditions.

The basic approaches that may be adopted in order to study such processes are discussed. Considerations for accurate numerical modeling are also discussed. The link between the process and the resulting product is critical in many systems such as those in manufacturing. The computational difficulties that result from the non‐Newtonian behavior of the fluid or from the strong temperature dependence of viscosity are considered in detail. Similarly, complex geometry, free surface flow, moving boundaries, combined mechanisms, and simulation of appropriate boundary conditions are important in several processes and are discussed.

Some of the important techniques to treat the problems that arise in numerical simulation are presented. Common errors that lead to inaccurate or invalid results are outlined. A few practical processes are considered in greater detail to quantify and illustrate these approaches. Validation of the numerical model is a particularly important aspect and is discussed in terms of existing results, as well as development of experimental arrangements to provide inputs for satisfactory validation.

Practical thermal processes involve a wide variety of complexities. The paper presents some of the important ones and discusses approaches to deal with them. The paper will be of particular value to the numerical simulation of complicated thermal processes in order to design, control or optimize them to achieve desired thermal processing.

Experimental results play a crucial role in the validation of mathematical and numerical models for a variety of basic and applied thermal transport problems. The purpose of this paper is to focus on the role played by experimentation in an accurate numerical simulation of thermal processes and systems.

The paper takes the form of a numerical simulation combined with experimentation. The paper presents various circumstances where the numerical simulation may be efficiently combined with experimentation, and indeed driven by experimental data, to obtain accurate, valid and realistic numerical predictions.

The paper demonstrates validation and accuracy of numerical simulation.

This paper is an important first step in combining experiments and simulation for complex thermal systems.

The numerical simulation of practical thermal processes is generally complicated because of multiple transport mechanisms and complex phenomena that commonly arise. In addition, the materials encountered are often not easily characterized and typically involve large property changes over the ranges of interest. The boundary conditions may not be properly defined and or may be unknown. However, it is important to obtain accurate and dependable numerical results from the simulation in order to study, design, and optimize most practical thermal processes of current and future interest. The purpose of this paper is to focus on the main challenges that are encountered in obtaining accurate numerical simulation results on practical thermal processes and systems.

A wide range of thermal systems is considered and the challenges faced in the numerical simulation are outlined. The methods that may be used to meet these challenges are presented in terms of grid, solution strategies, multiscale modeling and combined mechanisms. The models employed must be validated and the accuracy of the simulation results established if the simulation is to form the basis for improving existing systems and developing new ones.

Of particular interest are concerns like verification and validation, imposition of appropriate boundary conditions, and modelling of complex, multimode transport phenomena in multiple scales. Additional effects such as viscous dissipation, surface tension, buoyancy and rarefaction that could arise and complicate the modelling are discussed. Uncertainties that arise in material properties and in boundary conditions are also important in design and optimization. Large variations in the geometry and coupled multiple regions are also discussed.

The paper is largely focused on numerical modeling and simulation. Experimental data are considered mainly for validation and for physical insight.

A wide variety of practical systems, ranging from materials processing to energy, cooling, and transportation is considered.

Future needs in this interesting and challenging area are also outlined in the paper.

Multiple length and time scales arise in a wide variety of practical and fundamental problems. It is important to obtain accurate and validated numerical simulation results, considering the different scales that exist, in order to predict, design and optimize the behavior of practical thermal processes and systems. The purpose of this paper is to present modeling at the different length scales and then addresses the question of coupling the different models to obtain the overall model for the system or process.

Both numerical and experimental methods to obtain results at the different length scales, particularly at micro and nanoscales, are considered. Even though the paper focusses on length scales, multiple time scales lead to similar concerns and are also considered. The two circumstances considered in detail are multiple length scales in different domains and those in the same domain. These two cases have to be modeled quite differently in order to obtain a model for the overall process or system. The basic considerations involved in such a modeling are discussed. A wide range of thermal processes are considered and the methods that may be used are presented. The models employed must be validated and the accuracy of the simulation results established if the simulation results are to be used for prediction, control and design.

Of particular interest are concerns like verification and validation, imposition of appropriate boundary conditions, and modeling of complex, multimode transport phenomena in multiple scales. Additional effects such as viscous dissipation, surface tension, buoyancy and rarefaction that could arise and complicate the modeling are discussed. Uncertainties that arise in material properties and in boundary conditions are also important in design and optimization. Large variations in the geometry and coupled multiple regions are also discussed.

The paper is largely focussed on multiple-scale considerations in thermal processes. Both numerical modeling/simulation and experimentation are considered, with the latter being used for validation and physical insight.

Several examples from materials processing, environmental flows and electronic systems, including data centers, are given to present the different techniques that may be used to achieve the desired level of accuracy and predictability.

Present state of the art and future needs in this interesting and challenging area are discussed, providing the impetus for further work. Different methods for treating multiscale problems are presented.

The purpose of this paper is to reveal the characteristics of the temperature field under different types of heat sources, which are significant to the temperature control encountered in practical manufacturing processes.

The temperature fields in an infinite slab under line or plane heat source are calculated numerically by control volume approach and ADI scheme, and the numerical results of the temperature rise have been compared among the different types of the heat sources.

The numerical results show the different changing patterns of temperature fields under line and plane heat source, respectively, and demonstrate that the magnitude of temperature rise depends strongly on the type of the heat sources. The order of temperature rise from high to low is point, line and plane heat source base on the same input heat.

The study is original and findings are new, which demonstrate the different changing patterns of temperature fields and the magnitude of temperature rise under line and plane heat source. The numerical solution is significant for the temperature control in practical manufacturing processes.