Accurate Thermal Diffusivity Measurements Using a Modified Ångström's Method With Bayesian Statistics

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Yuan Hu ◽  
Timothy S. Fisher
Keyword(s):  
Thermal Diffusivity ◽  
Probability Distribution Function ◽  
Transfer Problem ◽  
Temperature Fluctuations ◽  
Infinite Medium ◽  
One Dimension ◽  
Ambient Conditions ◽  
Diffusivity Measurements ◽  
Inverse Heat Transfer ◽  
Inverse Heat Transfer Problem

Abstract This work reports a custom instrument that employs a modified Ångström's method to measure the thermal diffusivity of foil-like materials in which heat propagates in one dimension. This method does not require a semi-infinite medium assumption as compared to the original Ångström's method, which also has been typically performed in vacuum. However, in this work, temperature measurements are performed in laboratory ambient conditions, which are more convenient for most experiments. To quantify and reduce uncertainties due to temperature fluctuations in noisy ambient conditions, a Bayesian framework and Metropolis algorithm are employed to solve the inverse heat transfer problem and to obtain a probability distribution function for thermal diffusivity. To demonstrate the effectiveness of the custom instrument, the thermal diffusivity of a copper 110 foil (25.0 mm long, 7.0 mm wide, and 76.2 μm thick) was measured in ambient conditions, and the results match well with previous studies performed in vacuum conditions on much longer samples.

scholarly journals Estimation of Functional Form of Time-Dependent Heat Transfer Coefficient Using an Accurate and Robust Parameter Estimation Approach: An Inverse Analysis

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 5073
Author(s):  
Farzad Mohebbi ◽  
Mathieu Sellier
Keyword(s):  
Heat Transfer ◽  
Parameter Estimation ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Inverse Analysis ◽  
Functional Form ◽  
Transfer Problem ◽  
Function Estimation ◽  
Inverse Heat Transfer ◽  
Inverse Heat Transfer Problem

This paper presents a numerical method to address function estimation problems in inverse heat transfer problems using parameter estimation approach without prior information on the functional form of the variable to be estimated. Using an inverse analysis, the functional form of a time-dependent heat transfer coefficient is estimated efficiently and accurately. The functional form of the heat transfer coefficient is assumed unknown and the inverse heat transfer problem should be treated using a function estimation approach by solving sensitivity and adjoint problems during the minimization process. Based on proposing a new sensitivity matrix, however, the functional form can be estimated in an accurate and very efficient manner using a parameter estimation approach without the need for solving the sensitivity and adjoint problems and imposing extra computational cost, mathematical complexity, and implementation efforts. In the proposed sensitivity analysis scheme, all sensitivity coefficients can be computed in only one direct problem solution at each iteration. In this inverse heat transfer problem, the body shape is irregular and meshed using a body-fitted grid generation method. The direct heat conduction problem is solved using the finite-difference method. The steepest-descent method is used as a minimization algorithm to minimize the defined objective function and the termination of the minimization process is carried out based on the discrepancy principle. A test case with three different functional forms and two different measurement errors is considered to show the accuracy and efficiency of the used inverse analysis.

scholarly journals Inverse heat transfer problem in digital temperature control in plate fin and tube heat exchangers

2011 ◽  
Vol 32 (4) ◽  
pp. 17-32 ◽  
Author(s):  
Dawid Taler ◽  
Adam Sury
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Temperature Control ◽  
Heat Exchangers ◽  
Pid Controller ◽  
Transfer Problem ◽  
Heat Transfer Problem ◽  
Inverse Heat Transfer ◽  
Inverse Heat Transfer Problem ◽  
Exit Temperature

Inverse heat transfer problem in digital temperature control in plate fin and tube heat exchangersThe aim of the paper is a steady-state inverse heat transfer problem for plate-fin and tube heat exchangers. The objective of the process control is to adjust the number of fan revolutions per minute so that the water temperature at the heat exchanger outlet is equal to a preset value. Two control techniques were developed. The first is based on the presented mathematical model of the heat exchanger while the second is a digital proportional-integral-derivative (PID) control. The first procedure is very stable. The digital PID controller becomes unstable if the water volumetric flow rate changes significantly. The developed techniques were implemented in digital control system of the water exit temperature in a plate fin and tube heat exchanger. The measured exit temperature of the water was very close to the set value of the temperature if the first method was used. The experiments showed that the PID controller works also well but becomes frequently unstable.

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