Mathematical modelling of moisture transport into electronic enclosure under non-isothermal conditions

Significance Statement

The use of electronic gadgets in climatically harsh areas result in moisture-related issues and failures, which are mainly corrosion due to water layer formation, leakage currents and open circuits caused by electrochemical migration. These are some of the primary issues found in outdoor electronic applications such as renewable energy devices and automotive applications. In a bid to increase reliability of electronic devices and components, it therefore becomes necessary to understand moisture transport into an electronic device enclosure under environmental conditions.

Adequate design of these electronic enclosures currently depends on years of practical exposures and experience as opposed to scientific knowledge. The major push towards breaking this trend is in the development of a set of more knowledge based modeling tools that can fortify further the quest for optimal design and humidity control alternatives. It is a good idea to have fast modeling tools considering that the computational time is important in the design, particularly in the preliminary product development stage.

FEM and CFD are useful tools that are widely used for moisture modeling; unfortunately, these methods are time consuming owing to computational effort. It is for that reason desirable to develop an adequately precise method with optimally reduced spatial resolution to compute the moisture response in the electronic systems within practical timeframes.

Zygimantas Staliulionis and colleagues at the Technical University of Denmark have built an in-house code based on the resistor-capacitor method for simulating coupled heat as well as mass transport into a closed electronic enclosure under non-isothermal conditions (fig. 1). Thereafter, the authors were able to predict the amount of moisture as well as heat transported through diffusion and heat conduction based on the developed code. Their research work is published in Microelectronics Reliability.

The authors’ in-house code based on resistor-capacitor method combines a 1-dimensional description of critical features of electronic enclosures with lumped components for describing the interiors of the polycarbonate enclosure. The 1-dimensional description of heat and mass transport in the enclosure walls was based on a finite volume method (FVM) discretization of heat conduction equation and Fick’s second law. Simultaneously, a lumped capacitance component demonstrated the enclosure volume. The authors then compared simulation results with experimental results and found a good agreement.

After the authors validated the code, they investigated material properties such as diffusivity, conductivity and solubility for their role in moisture control inside an enclosure. The next simulations ran in a bid to investigate the response of moisture as well as temperature inside a closed box.

The developed in-house code was very fast with less spatial resolution, and significantly less time consuming as compared to commercial CFD codes. This code could be improved further to incorporate condensation and couple with evaporation process – the direction of current research by the authors. The authors observed that the interior temperature responded fast to the ambient temperature owing to small thermal time constant. In addition, the latter showed a buffer effect in short period counting on wall thickness and the size of the box.

The moisture response inside a box was slow given that the time constant for the mass transport was larger. Analyzing the diffusivity and solubility indicated that both parameters were necessary for moisture control. For this reason, material choice needed to be done consistent with the application case. Thermal conductivity had negligible effects compared to solubility and diffusivity in controlling interior moisture response.

Mathematical modelling of moisture transport into an electronic enclosure under non-isothermal conditions-Advances in Engineering

Coupled RC thermal and moisture circuits. Blue arrows show the coupling between nodal points of concentration and temperature

About The Author

Zygimantas Staliulionis was born in 1987 in Kaunas, Lithuania. He received the B.Sc. degree in 2011 and M.Sc. degree in 2013, both in electronics engineering from Kaunas University of Technology in Lithuania, and has submitted his Ph.D. dissertation in Mechanical Engineering this year (2017) at Technical University of Denmark, Denmark.

His research interests include the development of semi-empirical models for predicting climate inside electronic enclosures. His PhD project was carried out in close collaboration with companies in order to provide practical solutions for increasing the reliability and lifetime of electronics. He is currently working as a specialist in product compliance group in FORCE Technology, Denmark and focusing on humidity and reliability issues of electronics.

About The Author

Sankhya Mohanty draws upon 6 years of experience in multi-physics numerical modelling in performing his tasks at the Process Modelling Group at DTU Mechanical Engineering. Leveraging an equal experience in model-based optimization with continuing pioneering activities in model-based uncertainty quantification as well as reduced-order model generation, he develops platforms for integrating multi-scale, multi-physics simulation-assisted design & process planning to enable industrial implementation. He acquired his Bachelors & Masters degree in Mechanical Engineering from the prestigious Indian Institute of Technology (IIT) situated at Kharagpur in India. During his recent involvement at DTU, he has participated in 4 Danish innovation consortiums, 1 pan-European project and has established several active national and international collaborations. 

About The Author

Dr Masoud Jabbari is Chartered Engineer and a member of the Institution of Mechanical Engineers (MIMechE). After completing his PhD in 2014 in the Section of Manufacturing, Department of Mechanical Engineering at the Technical University of Denmark (DTU), where he was working on computational approaches for optimising manufacturing of ceramics/composites for Solid Oxide Fuel Cells (SOFCs), Masoud worked as a Post.Doc. (2014-2015) and a Researcher (2015-2016) in the same institute. In DTU, he undertook a number of collaborative research projects between companies and institutes in the area of humidity control and thermal management of electronic enclosures as well as ceramics and composites manufacturing. Masoud Joined WMG, University of Warwick in 2016 where he is lecturing in Energy & Thermofluids.

His current research areas focus on isothermal/non-isothermal flow in porous media for ceramic/composite manufacturing, thermal management and CFD modelling in fuel cells and batteries. Masoud serves as a guest editor of special issues of Applied Mathematical Modelling (Elsevier), Journal Porous Media and a member of the review board for several international journals.

About The Author

Jesper H. Hattel, born in Copenhagen, Denmark 1965, obtained his M.Sc. in structural engineering in 1989 and his Ph.D. in mechanical engineering in 1993 both from the Technical University of Denmark (DTU). Following this, he held various positions at DTU as post.doc., assistant professor, associate professor and finally full professor which he was appointed in 2006. In 1994-1995 he obtained an EU Marie Curie individual mobility fellowship which was spent at MAGMA GmbH, Aachen, Germany during which he initiated the development of the later MAGMAstress Module.

He currently is head of Section for Manufacturing Engineering at the Department of Mechanical Engineering, DTU and holds a full professorship in modeling of manufacturing processes at the department. His research interests are multiphysics modeling of manufacturing processes like casting, joining, composites manufacturing as well as additive manufacturing. This involves the use of computational methods within the disciplines of heat transfer, fluid dynamics, solid mechanics as well as materials science. Applications range from microelectronics over automotive industry to large structures like wind turbines. Jesper Hattel has been PI or COI on applications of more than 15MEuro and has more than 300 publications including journal papers as well as contributions to conference proceedings.


Ž. Staliulionis, S. Mohanty, M. Jabbari, J.H. Hattel. Mathematical modelling of moisture transport into an electronic enclosure under non-isothermal conditions. Microelectronics Reliability, Available online 15 May 2017.

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