Page 71 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

48 BIOMECHANICS OF THE HUMAN BODY

Guarded Hot Plate. Thermal conductivity can be measured directly by using steady-state methods,
such as the guarded hot plate. This method is invasive in that it requires the excision of the specimen
for in vitro measurement. It typically involves imposing a constant heat flux through a specimen and
measuring the temperature profile at specific points in the specimen after a steady-state temperature
field has been established. Once a simple one-dimensional steady-state temperature field is estab-
lished in the specimen, the thermal conductivity may be easily found by the expression based on the
linear temperature profile in a one-dimensional wall
′′
qL
k = (2.14)
T − T
1 2
where q″ is the heat flux passing through the specimen, T and T are temperature values at any two
1 2
measurement locations in the axial direction (or the direction of the heat flux), and L is the axial dis-
tance between these two temperature measurements.
Biological materials typically have moderate thermal conductivities and therefore, require exten-
sive insulation to ensure a unidirectional heat flow in the one-dimensional wall. The contact resis-
tance between the specimen and the plate is also difficult to be minimized. In addition, this method
cannot be used to obtain in vivo measurements. Once the tissue specimen is cut from the body, dehy-
dration and temperature-dependent properties may need to be considered. It is also a challenge to
accurately measure the thickness of the tissue sample.
Flash Method. The transient flash method, first proposed by Parker et al. (1961), is the current
standard for measuring the thermal diffusivity of solids. A schematic diagram of this method is
shown in Fig. 2.6. The front face of a thin opaque solid, of uniform thickness, is exposed to a burst
of intense radiant energy by either a high-energy flash tube or laser. The method assumes that the
burst of energy is absorbed instantaneously by a thin layer at the surface of the specimen. Adiabatic
boundary conditions are assumed on all other surfaces and on the front face during the measurement.
The transient temperature at the rear surface is then measured by using thermocouples or an infrared
detector.
An analytic expression for the rear surface temperature transient in the one-dimensional temper-
ature field is given by
22
Q ⎡ ∞ ⎛ n π ⎞ ⎤
n
Tl t) − Tl(, ) = 1 ⎢ + 2 ∫ (−1 ) exp − t α ⎥ (2.15)
(,
0
⎜
⎟ ⎟
ρ Cl ⎣ ⎢ n =1 ⎝ l 2 ⎠ ⎥ ⎦
Radiant Energy Q

l Sample
Adiabatic Adiabatic

Thermocouple

FIGURE 2.6 Schematic diagram of a flash apparatus for sample diffusivity
measurements.