TRANSFER: BASICS OF MASS AND HEAT TRANSFER - Biomass as a Sustainable Energy Source for the Future - page 100

n component in direction normal to wall
p particle
P Planck mean
r radiation
s slip
s surface
sat saturation
Ttar
T thermal

w at wall, or gas - solid interface

∞ position at large distance

Superscripts

HC Hirschfelder - Curtis approximation

4.1 INTRODUCTION

Heat and mass transfer are essential in most biomass conversion processes. In this
chapter, abasic introduction to the theoreticalmodelingof heat andmass transfer isgiven.
The explanation of heat andmass transfer phenomena starts from the transport equations
presented inChapter 3. The general principles are illustratedwithsome specific examples
concerning evaporation of ethanol droplets and devolatilization of wood particles. The
subject is very broad. For topics not covered here and more detailed treatment including
tables of basic physical data, we refer to the textbooks listed in the bibliography.

4.2 TRANSPORT TERMS IN THE GOVERNING EQUATIONS

4.2.1 Mass Transfer

When a system contains two or more components, these components in general have a
slightly different velocity. Otherwise, mixing would not occur. The velocity of a com-
ponent relative to the average velocity of the mixture is called the diffusion velocity.
The relative velocity in general gives rise to the transport of a component from a
region of higher concentration to a region of lower concentration, called mass transfer
(see Welty et al., 2001, Ch. 24).
The diffusion velocity is a factor in the diffusive mass flux j ! = V ! appearing in the

transport equation for species mass fractions presented as Equation (3.22) in Chapter 3:

ρ

j ! +

=

∂ ρ Y i

∂

*

!

* Y i

+ r ρ − r ω i for i = 1, … ,N ð Eq : 4 : 1 Þ

t

The four terms in this equation, respectively, are the transient term, the advection term,
the diffusion term, and the source term. The advection term describes transport of
quantities carried with the fluid velocity, defined as mass-weighted average of the