Page 18 - Bio Engineering Approaches to Cancer Diagnosis and Treatment

1.8 Principles of heat and fluid flow 15

Eq. (1.25) over the entire surface leads to average convection coefficient ( ) h for the h¯
entire surface:
1
h = hdA (1.26)
L ∫ A s s h¯=1L∫AshdAs
A thermal resistance is also defined for convection heat transfer from Eq. (1.27):

Q = ∆T = ∆T (1.27)
1/ hA R conv Q˙=∆T1/hA=∆TRconv

The convective thermal resistance (R ) is then:
conv
1
R = (1.28)
conv hA Rconv=1hA
Another important factor in convective heat transfer is friction coefficient (C ),
f
the characteristic of the fluid flow, which is:
τ
C f = w (1.29)
2
ρ u /2 Cf=τwρ∞u∞ /2
2
∞∞
1.8.2.3 Radiation heat transfer
Radiation heat transfer is the energy that is emitted by matter in the form of photons
or electromagnetic waves. Radiation can be important even in situations in which
there is an intervening medium. An example is the heat transfer that take place
between a living entity with its surrounding.
All bodies radiate energy in the form of photons. A photon is the smallest discrete
amount of electromagnetic radiation (i.e., one quantum of electromagnetic energy is
called a photon). Photons are massless and move in a random direction, with random
phase and frequency. The origin of radiation is electromagnetic and is based on the
Ampere law, the Faraday law and the Lorentz force. Maxwell analytically showed
the existence of electromagnetic wave. Electromagnetic waves transport energy at
the speed of light in empty space and are characterized by their frequency (ν) and
wavelength (λ) as follow:
C
λ = (1.30)
ν λ=Cν
where C is the speed of light in the medium.
The electromagnetic waves appear in nature for wavelength over an unlimited
range. Radiation with wavelength between 0.1 and 100 µm is in form of thermal
radiation and is called radiation heat transfer. Thermal radiation includes the entire
visible and infrared as well as a portion of ultraviolet radiation.
All bodies at a temperature above absolute zero emit radiation in all directions
over a wide range of wavelengths. The amount of emitted energy from a surface at a
given wavelength depends on the material, condition, and temperature of the body.