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Über dieses Buch

This book develops continuum modeling skills and approaches the topic from three sides: (1) derivation of global integral laws together with the associated local differential equations, (2) design of constitutive laws and (3) modeling boundary processes. The focus of this presentation lies on many practical examples covering aspects such as coupled flow, diffusion and reaction in porous media or microwave heating of a pizza, as well as traffic issues in bacterial colonies and energy harvesting from geothermal wells. The target audience comprises primarily graduate students in pure and applied mathematics as well as working practitioners in engineering who are faced by nonstandard rheological topics like those typically arising in the food industry.



Chapter 1. Scaling and Estimation of Physical Systems

To introduce the idea of measuring physical quantities, we need concepts like units, dimensions, and characteristic scales. This chapter briefly introduces the reader to these concepts by means of a few examples referring to traffic of cars on motorways, droplets rolling on surfaces, and to the voice of the dragon. Key working tools are dimension renormalization, nondimensionalization, and scaling.
Adrian Muntean

Chapter 2. Balance Equations in Continuum Physics

In this chapter, we present the basic equations of continuum physics both in global and local formulations. The local balance laws together with the global Clausius–Duhem inequality define the class of admissible thermodynamic processes. Boundary conditions and discontinuities appear as prominent issues. We give a few examples of constitutive equations for the stress tensor and for the transport fluxes. A set of worked-out practical modeling scenarios is emphasized.
Adrian Muntean

Chapter 3. Transport Fluxes

This chapter introduces the concept of flux of matter in the context of conservation laws—the playground of the local balance laws derived in Chap. 2. The attention moves to presenting two averaging techniques for guessing the structure of two distinct transport fluxes. First, the concern falls on the derivation of the Darcy law for two particular cases of microstructures: (i) a periodic array of cells and (ii) randomly distributed cells. Then a possible derivation for the structure of the thermodiffusion flux is given. The considerations extend immediately to the cross-diffusion case.
Adrian Muntean


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