A General Set of Bioheat Transfer Equations Based on the Volume Averaging Theory - Porous Media: Applications in Biological Systems and Biotechnology - page 30

1.7.3 Numerical Analysis Based on Enthalpy Method
The enthalpy method is often used for locating an interface in phase change
problems since it allows us to use a fixed mesh. An easy approach to imple-
ment the method is to include the latent heat by artificially increasing the
specific heat capacity around the freezing point, thus making it a function of
temperature as illustrated in Figure 1.10.
This simplest temperature function satisfies the obvious relationship
among the latent heat of solidification h sf , artificial maximum heat capac-
ity c max , and artificial temperature band ∆ T , namely, h sf = c max (2∆ T ). The
temperature band ∆ T should be set according to the mesh resolution. Natu-
rally, a finer grid system allows us to use a smaller ∆ T , which provides us a
sharper freezing front where T = T i . In this study, ∆ T was set to from 1 ◦ to 5 ◦ .
The temporal development of the freezing front is found fairly insensitive to
∆ T in this range.
Any standard scheme may be used to discretize the governing equation
(1.80). We shall use a finite volume method as proposed by Patankar (1980)
to obtain a two-dimensional finite volume expression. We consider a control
volume of size ∆ x ∆ y centering the node P (pole), as shown in Figure 1.11, and

( )

c max

c T

c c

c i

2 ∆ T

h sf

T i

T

FIGURE 1.10
Effective specific heat capacity.

N

n

δ y n

W

∆ y E

w e

x

δ

δ x e

P

δ y s

s

∆ x

S

FIGURE 1.11
Grid nomenclatures.