Biomedical Engineering Reference
In-Depth Information
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Fundamentals of Bioheat Transfer
1.1 Introduction .................................................................................................................................3
1.2 Heat Transfer Principles .............................................................................................................3
Thermodynamics and the Energy Balance • Conduction Heat Transfer • Convection Heat
Transfer • Radiation Heat Transfer
1.3 Special Features of Heat Transfer in Biomedical Systems ...................................................19
Blood Perfusion Effects • Thermal Properties of Living Tissues
Acknowledgments .................................................................................................................................21
References ...............................................................................................................................................21
Kenneth R. Diller
University of Texas
1.1 Introduction
more routine problems. For that reason, you will find numerical
methods applied for the solution of many bioheat transfer prob-
lems, including a large number in this topic. he objective of this
chapter is to provide a simple introduction of bioheat transfer
principles without attempting to delve deeply into the details
of the very large number of specific applications that exist. The
following chapters will provide this particular analysis where
appropriate.
The science of heat transfer deals with the movement of ther-
mal energy across a defined space under the action of a tem-
perature gradient. Accordingly, a foundational consideration
in understanding a heat transfer process is that it must obey
the law of conservation of energy, or the first law of
thermody-
namics
. Likewise, the process must also obey the second law
of thermodynamics, which, for most practical applications,
means that heat will flow only from a region of higher tempera-
ture to one of lower temperature. We make direct and repeated
use of thermodynamics in the study of heat transfer phenom-
ena, although thermodynamics does not embody the tools to
tell us the details of how heat flows across a spatial temperature
gradient.
A more complete analysis of heat transfer depends on fur-
ther information about the
mechanisms
by which energy is
driven from a higher to a lower temperature. Long experi-
ence has shown us that there are three primary mechanisms
of action:
conduction
,
convection
, and
radiation
. The study of
heat transfer involves developing a quantitative representa-
tion for each of the mechanisms that can be applied in the
context of the conservation of energy in order to reach an
overall description of how the movement of heat by all of the
relevant mechanisms inf luences changes in the thermal state
of a system.
Biological systems have special features beyond inanimate
systems that must be incorporated in the expressions for the
heat transfer mechanisms. Many of these features result in
effects that cause mathematical nonlinearities and render the
analytical description of bioheat transfer more complex than
1.2 Heat transfer principles
In this section we will review the general principles of heat
transfer analysis without reference to the special characteristics
of biological tissues that influence heat transfer and the energy
balance. These matters will be addressed in the next section.
Here we will first consider the energy balance as it applies to all
types of heat transfer processes and then each of the three heat
transport mechanisms.
1.2.1 thermodynamics and the Energy Balance
The starting point for understanding the movement of heat
within a material is to consider an energy balance for the sys-
tem of interest. When an appropriate system has been identified
in conjunction with a heat transfer process, an energy balance
shows that the rate at which the internal energy storage within
the system changes is equal to the summation of all energy
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