Page 15 - Bio Engineering Approaches to Cancer Diagnosis and Treatment

12 CHAPTER 1 Introduction

viscous forces dominate and tend to damp out all disturbances, which leads to lami-
nar flow. At high Reynolds numbers, the disturbances appear and at high enough
Reynolds number the flow field eventually ends up in a chaotic state called turbulence.
Another important nondimensional number in biofluid mechanic is the Womer-
sley number (α), relating the pulsatile flow frequency in with viscous effects [50].
 ω  1/2 1/2
π
α = L   = (2Re St ) (1.13)
α=Lwν1/2=2πReSt1/2  ν 
The Strouhal number (St), is a dimensionless number describing the mechanism
of oscillating flow, and is given by [50]:

St = fL (1.14)
St=fLU U
where f is the frequency of vortex shedding, L and U are the characteristic lengths and
the flow velocity. The Euler number (Eu) is defined in hydrodynamic and described
the stream pressure versus inertia forces.

Eu = ∆P (1.15)
Eu=∆PρV 2 ρV 2
Also the Froude number (Fr) is defined as the ratio of the flow inertia to the exter-
nal field (such as gravity). This number is based on the speed-length ratio as follow:

Fr = U (1.16)
Fr=Ugl gl

1.8.2 Heat transfer
In physics, heat is defined as the transfer of thermal energy across a well-defined
boundary around a thermodynamic system. Heat transfer is a process function (or
path function). It means that the amount of heat transferred that changes the state of
a system depends on how that process occurs, not only the net difference between
the initial and final states of the process. The rate of heat transfer is dependent on the
temperatures of the systems and the properties of the intervening medium through
which the heat is transferred. The rate of heat transfer also depends on the proper-
ties of the intervening medium through which the heat is transferred. In engineering
contexts, the term heat is taken as synonymous to thermal energy. This usage has its
origin in the historical interpretation of heat as a fluid (caloric) that can be transferred
by various causes.
The transport equations for thermal energy (Fourier’s law), mechanical momen-
tum (Newton’s law for fluids), and mass transfer (Fick’s laws of diffusion) are
similar, and analogies among these three transport processes have been developed
to facilitate prediction of conversion from anyone to the others. The fundamental
modes of heat transfer are advection, conduction or diffusion, convection, and radia-
tion. Types of phase transition occurring in the three fundamental states of matter