Page 19 - Bio Engineering Approaches to Cancer Diagnosis and Treatment

16 CHAPTER 1 Introduction

A surface is said to be diffuse if its surface properties are independent of direction
and gray if its properties are independent of wavelength.
A black body is an ideal thermal radiator. It absorbs all incident radiation (absorp-
tivity, α = 1), regardless of wavelength and direction. It also emits maximum radia-
tion energy in all directions (diffuse emitter). The energy radiated per unit area is
given by Joseph Stefan as [51]:

Q˙″b=σT 4 Q b ′′= σT 4 (1.31)
Eq. (1.31) is called Stefan-Boltzmann law, σ is the Stefan-Boltzmann constant
2
−8
×
4
2
5.67×10−8 W/m K 4 and is equal to 5.67 10 W/mK , E is blackbody emissive power, and T is the
b
absolute temperature. Real bodies radiate less effectively than black bodies. The rate
of real body radiation energy per unit area is defined by [51]:
ε ′′=
Q˙″=εQ˙″b=εσT 4 Q ′′ = Q b εσT 4 (1.32)
where ε is a property and is called the emittance. Values of emittance vary greatly for
different materials. The emissivity of the human body is 0.97 for incident infrared
radiation. They are near unity for rough surfaces such as ceramics or oxidized metals,
and roughly 0.02 for polished metals or silvered reflectors.
Radiation energy can be absorbed, reflected, or transmitted when reaches a sur-
face in human body. The sum of the absorbed, reflected, and transmitted fraction of
radiation energy is equal to unity:
+
α + ρ τ = 1
α+ρ+τ=1 (1.33)
where α is absorptivity (fraction of incident radiation that is absorbed), ρ is reflectiv-
ity (fraction of incident radiation that is reflected), and τ is transmissivity (fraction
of incident radiation that is transmitted). Reflective energy may be either diffuse or
specular (mirror-like). Diffuse reflections are independent of the incident radiation
angle. For specular reflections, the reflection angle equals the angle of incidence.

1.8.3 Thermodynamic
Thermodynamics are consisted of two words: thermo (heat) and dynamics (power).
It is a branch of science, deals with conversion of heat to work. It is established in the
19th century [52]. Historically, it dealt only with work generated by hot body (heat
engine) and efforts to make it a more efficient heat engine. Today, thermodynamics
deal mostly with energy and its relationship between properties of substances.
Thermodynamics generally starts with several basic concepts and lead to differ-
ent thermodynamics laws. A thermodynamic system is a quantity of matter, which is
defined by its boundary. Everything outside the boundary is called the surroundings
or environment. The environment often contains one or more idealized heat reser-
voirs—heat sources with infinite heat capacity enabling them to give up or absorb
heat without changing their temperature. The boundary can be real or imaginary,
fixed or movable. There are two types of systems: closed and open system. Closed
system (control mass) is a system with fixed quantity of matters. Thus, no mass