Heat Transfer in Biological Tissues - Selected Topics of Computational and Experimental Fluid Mechanics - page 305

(a)

(b)

Fig. 4 Temperature as a function time for different thermal Deborah numbers, a unperturbed b
perturbed De T ,with

ʾ = ∅ r = 0 , ∅ s = 0 . 3405

0,

4 Conclusions

The heat transfer process in biological tissues is studied numerically through a modi-
fied Pennes bioheat equation. This study showed that for very large times the temper-
ature distributions within the tissue can be well described by the classical Fourier law.
Nonetheless, the effects that occur on short time scales may not be equally predictable
with these theories. The Maxwell-Cattaneo model considers a relaxation time which
represents the time lag required to establish steady heat conduction, which is the time
that takes to transmit the signal from the stimulus to the whole structure of the tissue.
The energy transfer process in a biological tissue involves the interaction of multi-
ple internal mechanisms (i.e. metabolic activity and blood flow) and their response
to external stimulus. When blood perfusion increases, the energy transfer process
occurs faster and easily, until the system achieves thermal equilibrium. When the air
temperature is perturbed, the temperature profiles are constantly modified near the
upper boundary of the tissue, however they recover a linear trend along the system;
in addition to the timely behavior that presents a monotonous growth until it reaches
a steady state.

Acknowledgments This project was supported by the research grants SIP-IPN 20141466.

References

Chandrasekharaiah DS (1998) Hyperbolic thermoelasticity: a review of recent literature. Appl Mech
Rev 51:705-729
Deng Z-S, Liu J (2002) Analytical study on bioheat transfer problems with spatial or transient
heating on skin surface or inside biological bodies. J Biomech Eng 124:638-649