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Numerical modeling of multiple length scales in thermal transport processes

Yogesh Jaluria (Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, New Jersey, USA)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 29 April 2014




Multiple length and time scales arise in a wide variety of practical and fundamental problems. It is important to obtain accurate and validated numerical simulation results, considering the different scales that exist, in order to predict, design and optimize the behavior of practical thermal processes and systems. The purpose of this paper is to present modeling at the different length scales and then addresses the question of coupling the different models to obtain the overall model for the system or process.


Both numerical and experimental methods to obtain results at the different length scales, particularly at micro and nanoscales, are considered. Even though the paper focusses on length scales, multiple time scales lead to similar concerns and are also considered. The two circumstances considered in detail are multiple length scales in different domains and those in the same domain. These two cases have to be modeled quite differently in order to obtain a model for the overall process or system. The basic considerations involved in such a modeling are discussed. A wide range of thermal processes are considered and the methods that may be used are presented. The models employed must be validated and the accuracy of the simulation results established if the simulation results are to be used for prediction, control and design.


Of particular interest are concerns like verification and validation, imposition of appropriate boundary conditions, and modeling of complex, multimode transport phenomena in multiple scales. Additional effects such as viscous dissipation, surface tension, buoyancy and rarefaction that could arise and complicate the modeling are discussed. Uncertainties that arise in material properties and in boundary conditions are also important in design and optimization. Large variations in the geometry and coupled multiple regions are also discussed.

Research limitations/implications

The paper is largely focussed on multiple-scale considerations in thermal processes. Both numerical modeling/simulation and experimentation are considered, with the latter being used for validation and physical insight.

Practical implications

Several examples from materials processing, environmental flows and electronic systems, including data centers, are given to present the different techniques that may be used to achieve the desired level of accuracy and predictability.


Present state of the art and future needs in this interesting and challenging area are discussed, providing the impetus for further work. Different methods for treating multiscale problems are presented.



The author acknowledges the partial support from NSF under grant number 1067141, and from industry for this study and the work done by several graduate students.


Jaluria, Y. (2014), "Numerical modeling of multiple length scales in thermal transport processes", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 24 No. 4, pp. 781-796.



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