Data Centers’ Temperature Profile Simulation Optimized by Finite Elements and Discretization Methods

Nowadays, data center industry faces strong challenges for increasing the speed and data processing capacities while at the same time is trying to keep their devices a suitable working temperature without penalizing that capacity. Consequently, the cooling systems of this kind of facilities use a large amount of energy to dissipate the heat generated inside the servers, and developing new cooling techniques or perfecting those already existing would be a great advance in this type of industry. The installation of a temperature sensor matrix distributed in the structure of each server would provide the necessary information for collecting the required data for obtaining a temperature profile instantly inside them. However, the number of temperature probes required to obtain the temperature profiles with sufficient accuracy is very high and expensive. Therefore, other less intrusive techniques are employed where each point that characterizes the server temperature profile is obtained by solving differential equations through simulation methods, simplifying data collection techniques but increasing the time to obtain results. In order to reduce these calculation times, complicated and slow computational fluid dynamics simulations are replaced by simpler and faster finite element method simulations which solve the Burgers‘ equations by backward, forward and central discretization techniques after simplifying the energy and enthalpy conservation differential equations. The discretization methods employed for solving the first and second order derivatives of the obtained Burgers‘ equation after these simplifications are the key for obtaining results with greater or lesser accuracy regardless of the characteristic truncation error.

• José Alberto García Fernández
• Zhimin Du
• Xinqiao Jin

• Burgers’ equations
• CFD simulation
• data center
• discretization methods
• FEM simulation
• temperature profile.

[1] Charles Hirsch. Fundamentals of Computational Fluid Dynamics. Volume 1.Second edition. Numerical Computation of Internal and External Flows. Butterworth-Heinemann (2007).
[2] T.J Chung. University of Alabaman in Huntsville. Computational Fluid Dynamics. Second Edition. Cambridge University Press. (2014).
[3] Roland W.Lewis. University of Wales Swansea, UK. Perumal Nithiarasu. University of Wales Swansea, UK. Kankanhalli N. Seetharamu. Universiti Sains Malaysia, Malaysia. Fundamentals of the Finite element Method for Heat and Fluid Flow. John Wiley & Sons, Ltd. (2004). Chapters from 1 to 7.
[4] Young W. Kwon, Hyochoong Bang. The Finite Element Method using Matlab. Second Edition. CRC Press (2000). Chapters from 1 to 5.
[5] William F. Ames. Numerical Methods for Partial Differential Equations. Academic Press. Second Edition (2014).
[6] Sandeep Nagar. Introduction to Python for Engineers and Scientists: Open Source Solutions for Numerical Computation. Apress (2017).
[7] T. J. Barth M. Griebel D.E. Keyes R.M. Nieminen D. Roose T. Schlick, A Primer on Scientific Programming with Python. Editorial Board. Fourth Edition (2010).
[8] Chih-Wei Chang, Nam T. Dinh. Classification of machine learning frameworks for data-driven thermal fluid models. International Journal of Thermal Sciences. 135 (2019) 559-579.
[9] Enrico Fonda, Ambrish Pandey, Jörg Schumacher, and Katepalli R. Sreenivasan. Deep learning in turbulent convection networks. Proceedings of the National Academy of Sciences .PNAS. 116 (18) (2019) 8667-8672.
[10] Qiyin Lin, Jun Hong, Zheng Liu, Baotong Li, Jihong Wang. Investigation into the topology optimization for conductive heat transfer based on deep learning approach. International Communications in Heat and Mass Transfer. 97 (2018) 103-109.
[11] Chun Chen, Wei Liu, Chao-Hsin Lin, Qingyan Chen. A Markov chain model for predicting transient particle transport in enclosed environments. Building and Environment. 90 (2015) 30-36.
[12] Abad, A. & Barrio, R. & Marco-Buzunariz, M. & Rodríguez, M. Automatic implementation of the numerical Taylor series method: A MATHEMATICA and SAGE approach. Applied Mathematics and Computation. 268 (2015) 227-245.