IFTIKHAR, M. Analýza nejistot inverzního problému vedení tepla ve dvou prostorových souřadnicích [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2025.

Posudek vedoucího

Boháček, Jan

The thesis addresses the inverse heat conduction problem (IHCP) in two spatial dimensions, focusing on the reconstruction of the heat transfer coefficient (HTC) at the surface of a die insert in high-pressure die casting (HPDC) using internal temperature measurements. The work applies a finite-volume approach with OpenFOAM, employs synthetic numerical experiments, and uses the BOBYQA optimization algorithm to estimate the HTC distribution. The thesis also investigates the sensitivity of the inverse problem to uncertainties, particularly sensor misplacement, and discusses the role of regularization. Strengths: - A thorough literature review is provided as outlined in the thesis objectives, covering methods for the inverse heat conduction problem (IHCP). Moreover, the significance of IHCP is demonstrated through its application to a relevant engineering problem. - The methodology is generally well-conceived: the use of synthetic data, finite-volume modeling (despite the steep learning curve of OpenFOAM), and a derivative-free optimization approach are appropriate choices for the problem addressed. - The thesis offers a clear and structured presentation of the mathematical and computational framework, detailing the governing equations, boundary conditions, and optimization setup. - The sensitivity analysis on sensor misplacement is well-justified, effectively highlighting a crucial challenge in the practical application of IHCP techniques. - The work is supported by relevant literature, and the obtained results are meaningfully discussed in the context of their potential industrial application. Weaknesses, Reservations, Question: - The thesis does not fully achieve all the objectives outlined in the assignment. Specifically, while the development and implementation of a methodology for determining the regularization parameter is discussed in theory, it is not practically carried out. - The uncertainty analysis is predominantly limited to the effect of sensor misplacement. Other significant sources of uncertainty — such as measurement noise, model simplifications, or numerical errors — are not systematically addressed. - Certain reasoning presented in the thesis is incorrect or misleading. For instance, on page 36: “When sensors are shifted away from the surface, their thermal response is delayed, causing the inverse algorithm to overestimate the HTC. Conversely, shifting sensors closer to the surface results in underestimation due to the faster thermal response.” - What if, instead, a piece-wise constant interpolation of HTC was considered? How would this affect the stability of the IHCP calculation, and why? Summary and Conclusion In conclusion, the thesis demonstrates the student’s ability to work with the relatively user-unfriendly open-source CFD software OpenFOAM and to apply numerical and optimization methods to address an inverse heat conduction problem. The student successfully processed large data sets and learned to visualize the results using the open-source visualization toolkit ParaView. A valuable sensitivity study on sensor placement was carried out in relation to the inherent uncertainties of the IHCP. However, the thesis does not fully meet the assignment’s objectives, particularly in the area of regularization methodology, which is only discussed without any evident attempt at implementation. Additionally, the uncertainty analysis would have benefited from more thorough attention and depth. Overall, I recommend the thesis for defense and propose a grade of “C”.

Posudek oponenta

Štoudková Růžičková, Viera

There were 5 objectives for the thesis, and from these not all were fulfilled. Objectives 1, 2: the literary research and description of the IHCP problem are presented.  Objectives 3, 4: the OpenFOAM code was used and numerical experiments were performed, but the only analysis of uncertainties was the calculation of relative errors of HTC determination that occur when the positions of thermocouples are shifted towards or away from the surface. The last objective, which required to work with regularization term and make more sophisticated mathematical calculations, was not met at all, the regularization techniques are mentioned only briefly (p. 37). Formally, the work is within required standard, there are only a few typos, but I found several inconsistencies, e.g.: Fig. 3.4, 5.2: dimensions are not stated. The original distances of thermocouples from the surface are not given, on p. 22, there is only written that it is “approximately 1 mm”. They are later shifted by 0.05 mm, so the original position should be given more accurately. Also, the shifting to half distance is not clear – what is this “half distance”? Fig. 3.6 – 3.8: there is missing description what the color scale means. References: item 7 is same as item 18, item 17 is incomplete, etc. I evaluated this thesis with grade E, but I have doubts that it meets the requirements for a degree in Applied and Interdisciplinary Mathematics. The only mathematics that I found in the work was derivation of equation for temperature at the surface (p. 18) and calculation of relative errors (p. 35).

eVSKP id 166038