Accurate Numerical Modeling of Complex Thermal Processes: Impact of Professor Spalding’s Work

  • Yogesh JaluriaEmail author


Practical thermal processes and systems, in application areas such as energy, manufacturing, environmental control, heating/cooling, thermal management of electronics, and transportation, generally involve combined transport mechanisms and many different complex phenomena. The materials of interest are also frequently difficult to characterize, and their properties could involve large changes with temperature, concentration, and pressure. The boundary conditions are often unknown or not well defined. The configuration and the geometry are frequently quite complicated. However, in order to study, predict, design, and optimize most practical thermal processes, it is important to obtain accurate and realistic numerical results from the simulation. The mathematical and numerical models must be verified and validated to establish the accuracy and reliability of the simulation results if these are to be used for improving existing systems and developing new ones. This paper focuses on the main considerations that arise and approaches that may be adopted to obtain accurate numerical simulation results on practical thermal processes and systems. A wide range of systems is considered, including those involved in materials processing, energy, heat removal, and safety. Verification and validation, imposition of realistic boundary conditions, modeling of complex, multimode, transport phenomena, multiscale modeling, and time dependence of the processes are discussed. Additional aspects such as viscous dissipation, surface tension, buoyancy, and rarefaction that arise in several systems are also considered. Uncertainties that arise in material properties and in boundary conditions are also important in design and optimization. The methodology to treat these is outlined. Large variations in the geometry and coupled multiple regions are also of interest. The methods that may be used to address these issues are discussed, along with typical results for a range of important processes. Future needs in this interesting and important area are also presented. In many of these studies, the work done by Professor Spalding and his research group has been particularly valuable, since it has guided many of the simplifications and approaches that have been adopted. This paper is a brief tribute to the extraordinary contributions of Professor Spalding to the field of computational fluid dynamics and heat transfer.


Professor Spalding Practical systems Thermal processes Thermal systems Numerical simulation Accuracy Complexities Challenges 



The author acknowledges the support of the National Science Foundation, through several grants, and of the industry for the work reported here. The author also acknowledges the interactions with several collaborators and the work done by several students that made it possible to present this review. Finally, the inspiration provided by Professor Spalding is gratefully acknowledged.


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of Mechanical & Aerospace EngineeringRutgers UniversityPiscatawayUSA

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