Predicting System Performance and Estimating Parameters for Systems Burdened With Uncertainties and Noise Using Bayesian Inference

2008 ◽  
Author(s):  
A. F. Emery ◽  
D. Bardot
Keyword(s):  
Heat Transfer ◽  
Bayesian Inference ◽  
System Performance ◽  
Taylor Series Expansion ◽  
Substantial Effect ◽  
Simple Problem ◽  
Transfer Coefficients ◽  
Strong Function ◽  
Heat Transfer Coefficients ◽  
Transfer Problems

The precision of estimates of system performance and parameter estimation is often based upon the standard deviation obtained from the usual equation for the propagation of variances derived from a Taylor series expansion [1]. With increasing computing power, it is often suggested that the more complex Bayesian inference approach may yield improved estimates of the precision. The Bayesian approach has not been widely used in the heat transfer and fluid mechanics communities. The paper develops the necessary equations and applies them to two typical heat transfer problems. It is shown that, even for the simple problem of heat loss from a fin, that the predicted performance can be a strong function of relatively minor changes in the heat transfer coefficients or the thermal conductivity and as a consequence that the form of the parameter variability has a substantial effect.

Predicting Thermal System Performance and Estimating Parameters for Systems Burdened With Uncertainties and Noise Using Hierarchical Bayesian Inference

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
A. F. Emery ◽  
D. Bardot
Keyword(s):  
Heat Transfer ◽  
System Performance ◽  
Taylor Series Expansion ◽  
Heat Losses ◽  
Thermal System ◽  
Computing Power ◽  
Bayesian Hierarchical ◽  
Hierarchical Bayesian Inference ◽  
Transfer Problems ◽  
The Bayesian Approach

The precision of estimates of system performance and of parameters that affect the performance is often based upon the standard deviation obtained from the usual equation for the propagation of variances derived from a Taylor series expansion. With ever increasing computing power it is now possible to utilize the Bayesian hierarchical approach to yield improved estimates of the precision. Although quite popular in the statistical community, the Bayesian approach has not been widely used in the heat transfer and fluid mechanics communities because of its complexity and subjectivity. The paper develops the necessary equations and applies them to two typical heat transfer problems, measurement of conductivity with heat losses and heat transfer from a fin. Because of the heat loss the probability distribution of the conductivity is far from Gaussian. Using this conductivity distribution for the fin gives a very long tailed distribution for the heat transfer from the fin.

Determination of Non-Uniform Heat Transfer Coefficients Around a Solid Aluminum Alloy Complex Shape During Quenching by Using an Inverse Method

2002 ◽  
Author(s):  
Pen-Chung Chen ◽  
Deborah A. Kaminski ◽  
Robert W. Messler
Keyword(s):  
Heat Transfer ◽  
Gas Turbine ◽  
Inverse Method ◽  
Flux Measurement ◽  
Transient Temperature ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Uniform Heat ◽  
The Cost ◽  
Transfer Problems

Gas turbine systems include complex heat transfer problems. Especially, the cooling efficiency is critical to the operation of gas turbine. In order to achieve the desired cooling condition, one needs to know the distribution of heat transfer on the components; however, the cost to implement a full-scale gas turbine test is tremendous. Therefore, many researchers used simplified models to acquire the test data; certain experiments can provide heat flux measurement, whereas other techniques can measure heat transfer coefficients. The direct measurement of heat transfer coefficients on the surface of components is extremely difficult. In such situations, the inverse method using transient temperature measurements taken within the part can be used to determine heat transfer coefficients. By combining experiments and numerical modeling, this presentation attempts to provide an effective and robust method to determine heat transfer coefficients on the part’s surface during cooling. Though the setting of the present paper is the quenching of a part, the technique presented is proposed for in-service heat load. To characterize the present situation, i.e., non-uniform heat transfer coefficients occurring during quenching, a unique methodology for employing inverse heat conduction was developed to obtain heat transfer coefficients from temperature responses. In conventional inverse approaches, the heat transfer coefficient is assumed to be uniform around the periphery, but this approach sometimes is unrealistic, especially for complex shaped parts. In this study, experimental data were used to find parameters in a heat transfer correlation, rather than to determine the coefficients directly. The resulting analysis provided an improved fit to measurements compared to conventional inverse approaches. The method developed was robust and is extendable to parts of arbitrary shape.

scholarly journals Why heat transfer coefficients are unnecessary and undesirable, and how heat transfer problems are solved without them.

2020 ◽  
Author(s):  
EUGENE ADIUTORI
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Thermal Behavior ◽  
Convection Heat Transfer ◽  
Nonlinear Function ◽  
Convection Heat ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Transfer Problems

Abstract Heat transfer coefficients (h) are unnecessary and undesirable . They are unnecessary because heat transfer problems are readily solved without them. They are undesirable because they greatly complicate problems that concern nonlinear thermal behavior. In order to understand why heat transfer coefficients are unnecessary and undesirable, it is necessary to know precisely what h is. The nomenclature in every heat transfer text should state “ h is a symbol for q/ D T ”. (Note that q = h D T and h = q/ D T are identical .) Problems in convection heat transfer are conventionally solved using q, h, and D T —ie using q, q/ D T, and D T . It is self-evident that any problem that can be solved using q, q/ D T , and D T can also be solved using only q and D T . Therefore h (ie q/ D T ) is unnecessary. h (ie q/ D T ) is undesirable because, when q is a nonlinear function of DT (as in free convection, condensation, and boiling), h (ie q/ D T ) is a third variable , and it greatly complicates problem solutions. The text includes example problems that support the conclusion that h (ie q/ D T ) is unnecessary and undesirable.

Status, Challenges, and Potential for Machine Learning in Understanding and Applying Heat Transfer Phenomena

2021 ◽  
Author(s):  
Matthew T. Hughes ◽  
Girish Kini ◽  
Srinivas Garimella
Keyword(s):  
Heat Transfer ◽  
Machine Learning ◽  
Large Scale ◽  
Computationally Efficient ◽  
Transfer Coefficients ◽  
Thermal Systems ◽  
Reduced Order ◽  
Heat Transfer Coefficients ◽  
Real Time Analysis ◽  
Transfer Problems

Abstract Machine learning (ML) offers a variety of techniques to understand many complex problems in different fields. The field of heat transfer, and thermal systems in general, are governed by complicated sets of governing physics that can be made tractable by reduced-order modeling, and by extracting simple trends from measured data. Therefore, ML algorithms can yield computationally efficient models for more accurate predictions or to generate robust optimization frameworks. This study reviews past and present efforts that use ML techniques in heat transfer from the fundamental level to full-scale applications, including the use of ML to build reduced-order models, predict heat transfer coefficients and pressure drop, real-time analysis of complex experimental data, and optimize large-scale thermal systems in a variety of applications. The appropriateness of different data-driven ML models in heat transfer problems is discussed. Finally, some of the imminent opportunities and challenges that the heat transfer community faces in this exciting and rapidly growing field are identified.

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