# Perspectives on Engineering Estimation via the Heat Transfer Dunking Problem

#### Keywords

Advanced Numerical Methods for Scientific Computing

**Speaker:**

Anthony T. Patera

**Affiliation:**

Department of Mechanical Engineering, Massachusetts Institute of Technology

**When:**

Friday 14th October 2022

**Time:**

14:00:00

**Where:**

Online seminar: https://mox.polimi.it/mox-seminars/?id_evento=2185

**Abstract:**

We consider the dunking problem: a solid body, initially at thermal equilibrium in a first environment at temperature Ti, is abruptly placed - “dunked” - at time t = 0 in a second environment, characterized by farfield fluid/enclosure temperature Too. The Quantities of Interest (QoI) describe the spatial distribution of the temperature as a function of time.
The high-fidelity mathematical model for the dunking problem - a very detailed conjugate heat transfer formulation - is not practical for typical engineering studies. However, the QoI can be predicted, inexpensively and reasonably accurately, by well-established engineering Estimation procedures: simplification of the high-fidelity mathematical model; subsequent approximate solution of the simplified mathematical model, often informed by archived experimental data.
In this talk we present error estimates for the engineering Estimation QoI predictions.
In fact, dunking is one example of a heat transfer problem class: a problem description for which the instances arise - in response to a particular ubiquitous need - very often in practice. Other heat transfer problem classes include wall and fin, each of which also admit Estimation procedures and associated error estimates. The collective scope of the problem classes in concert with the guidance provided by the error estimates can ultimately be incorporated in an autonomous heat transfer Estimation framework. We close with a preliminary demonstration of autonomous heat transfer Estimation: the software (a) accepts a non-prescriptive problem statement in the form of English text and an associated geometry figure, (b) identifies and instantiates the appropriate heat transfer problem class, (c) develops the simplified mathematical model and associated approximate solution, the latter incorporating asymptotic techniques as well as computational and experimental data, and (d) provides a summary of the Estimation QoI prediction and associated justifications.
Acknowledgements: work performed in collaboration with Kento Kaneko, MIT, Claude Le Bris, ENPC, Max Kessler, MIT (2020), and undergraduate students in MIT heat transfer subject 2.51; work funded by the Office of Naval Research, grant monitor Reza Malek-Madani.
Contatto: alfio.quarteroni@polimi.it

**Note:**

Anthony T. Patera is Professor of Mechanical Engineering and Ford Professor of Engineering at the Massachusetts Institute of Technology (MIT). Professor Patera received his SB and SM degrees in Mechanical Engineering and his PhD degree in Applied Mathematics, all from MIT. Professor Patera’s research interests include fluid dynamics and heat transfer, partial differential equations, variational techniques, computational methods, model reduction, and numerical analysis.