View factor geometric expressions

Radiaton heal transfer between surfaces depends on the orientation of the surfaces relative to each other. In a radiation. analysis, this effect is accounted for by the geometric parameter vie.iv facior. The vretv factor ftoni a surface i to a. surface j is denoted by or F j, and is defined as the fraction of the radiation leaving surface i that strikes surface j directly. The view factors between differential and finite surfaces are expressed as... 

The concept of view factors is quite convenient in the analysis of diffuse and gray radiation exchanges. Under these assumptions, the view factor, Fu2, is purely a geometric quantity. Physically, it means the fraction of radiative energy leaving surface 1 that reaches surface 2. In other words, it describes how much surface 1 sees surface 2, thus the name view factor. Due to the restricted nature of this chapter, the expression for the view factors will not be derived here. Instead, the expression will be given here and the reader will be referred to a more-detailed discussion in References 2, 18, and 19. Mathematically, the view factor is defined as... 

To understand heat conduction, diffusion, viscosity and chemical kinetics the mechanistic view of molecule motion is of fundamental importance. The fundamental quantity is the mean-free path, i. e. the distance of a molecule between two collisions with any other molecule. The number of collisions between a molecule and a wall was shown in Chapter 4.1.1.2 to be z = CNQvdtl6. Similarly, we can calculate the number of collisions between molecules from a geometric view. We denote that all molecules have the mean speed v and their mean relative speed with respect to the colliding molecule is g. When two molecules collide, the distance between their centers is d in the case of identical molecules, d corresponds to the effective diameter of the molecule. Hence, this molecule will collide in the time dt with any molecule centre that lies in a cylinder of a diameter 2d with the area Jid and length gdt (it follows that the volume is Jtd gdt). The area where d is the molecule (particle) diameter is also called collisional cross section a. This is a measure of the area (centered on the centre of the mass of one of the particles) through which the particles cannot pass each other without colliding. Hence, the number of collisions is z = c n gdt. A more correct derivation, taking into account the motion of all other molecules with a Maxwell distribution (see below), leads to the same expression for z but with a factor of V2. We have to consider the relative speed, which is the vector difference between the velocities of two objects A and B (here for A relative to B) ... 

---