A General Set of Bioheat Transfer Equations Based on the Volume Averaging Theory - Porous Media: Applications in Biological Systems and Biotechnology - page 38

6000

ω eff = 0.004/sec

5000

4000

Numerical

3000

Analytical

2000

R lim = 29.92 mm

1000

0

0 10 20 30

R i [mm]

(a)

3000

ω eff = 0.004/sec

Numerical

2000

Analytical

1000

R lim = 12.82 mm

0

0 5 10 15

R i [mm]

(b)

FIGURE 1.15
Time required for freezing the tumor: (a) low perfusion rate, (b) high perfusion
rate.

1.8 Conclusions
In this chapter, a general set of bioheat transfer equations for blood flows
and its surrounding biological tissue was derived using a VAT established in
the field of fluid-saturated porous media. Unknown correlations were mod-
eled in terms of macroscopic determinable quantities. It has been shown that
the resulting two-energy equation model reduces to existing empirical models
such as the Pennes model, the Wulff model, and their modifications, under
appropriate conditions. Subsequently, the two-energy equation model has been
extended to the three-energy equation model, so as to account for the effect of
countercurrent heat transfer between closely spaced arteries and veins in the