The rapidly growing needs for energy and their associated environmental problems have led to the formation of most challenging issue facing human civilization. This has massively signified the role of energy analysis and optimization in a wide range of engineering disciplines. Further, the recent advancement in manufacturing of small scale devices and introduction of synthetic materials has added new dimensions to energy analysis. Historically, thermal energy analysis included first law investigations or heat transfer analyses. Over the last two decades, it was demonstrated that such analyses could be lacking and do not provide a complete picture for many applications. Hence, combined first and second law analyses were conducted mostly on convective systems. More recently, the problems which chiefly involve conduction in complex media, such as porous or multilayer media, started to attract attention of the research community. This class of problems is essential in a number of applications including energy systems, energy storage, underground reservoirs, and micro- and nanoscale manufacturing. Optimization of combined conduction, convection, and radiation of heat and the resultant generation of entropy in these applications introduces a very rich and mostly unexplored problem. This special issue focuses on the mathematical aspects of such problem. Contributions from both analytical and numerical sides are welcome.

Potential topics include, but are not limited to:

• Novel analytical and numerical methods for first and second law analysis
• Application of computational fluid dynamics to combined first and second law analysis
• Application of the theory of optimization to second law analysis
• Mathematical aspects of non-Fourier conduction and inverse conduction
• Mathematical modelling of phase change heat transfer and entropy generation
• Mathematical modelling of heat transfer and entropy generation in porous media