Mathematical modeling of flow

Mathematical models of flow processes are non-linear, coupled partial differential equations. Analytical solutions are possible only for some simple cases. For most flow processes which are of interest to a reactor engineer, the governing equations need to be solved numerically. A brief overview of basic steps involved in the numerical solution of model equations is given in Section 1.2. In this chapter, details of the numerical solution of model equations are discussed. 

I have made an attempt to provide sufficient information to understand and to define the specific role of computational flow modeling in reactor engineering applications. Discussions on the main features of reactor engineering, computational flow modeling and their interrelationship will help to select appropriate models, and to apply these computational models to link reactor hardware to reactor performance. Mathematical modeling of flow processes (including turbulent flows, multiphase flows and reactive flows) and corresponding numerical methods to solve these model... 

S.D. Kolev, Mathematical modeling of flow-injection systems, Anal. Chim. Acta 308 (1995) 36. 

Reddy N.P. and Patel K. 1995. A mathematical model of flow through the terminal lymphatics. Med. Eng. Phys. 17 134. 

The effect of changes in weave pattern on flow throu the fabric will be discussed in the section dealing with mathematical modelling of flow flirou monofilaments. 

This division of flow has technical inq>ortance in those circumstances where the fine particles present are small enough to follow the flow into the yam. Once inade the yam, removal of these particles is effected with great difficulty. A tightfy twisted, closely woven cloth will approach the constractional and filtration characteristics of a monofilament cloth hut also will generally exhibit better mechanical properties. The effect of cloth constmction is discussed in detail below in the section dealing with mathematical models of flow in filter fabrics. 

Mathematical Models of Flow Through Filter Media... 

Mathematical Models of Flow Throtigh Filter Media 143... 

McDougall, S. R., A. R. Anderson, M. A. Chaplain, and J. A. Sherratt. 2002. Mathematical modelling of flow through vascular networks imphcations for tumour-induced angiogenesis and chemotherapy strategies. Bull Math Biol 64 673-702. 

There have through the years been various mathematical models of flow in separated rotor internal mixers [48,49,60 to 65]. Generally the internal mixer is considered completely filled. Many of the studies use hydrodynamic lubrication theory. Hu and White [64,65] sought to model flow in various rotor designs and predict differences in the rate of mixing. 

M. K. Choudhary. Mathematical modeling of flow and heat-transfer phenomena in glass furnace channels and forehearths. J. Am. Ceram. Soc. 74 (12), 1991, 3091. 

---