Download ENT 211 Week 1 - Introduction to Thermal-Fluid

INTRO TO FLUID MECHANICS
• Define and explain fluid properties such as density,
shear stress, velocity and etc.
• Define, explain and derive viscosity, and explain its
correlation with human blood. Viscosity measurement.
• Define and explain the surface tension and capillary
effect.
• Explain the effect of surface tension in biomedical
engineering.
THERMAL-FLUID
Science that deal with energy, and the transfer,
transport, and conversion of energy.
Fluid Mechanics + Thermodynamics + Heat Transfer
CIRCULATION SYSTEM
Heart, bloods, human body (Fluid Mechanics)
Energy conversion, body cells, body heat rejected
(Thermodynamics)
Human comfort, rate of metabolic heat ejection.
Control of heat transfer, clothes (Heat Transfer).
THERMODYNAMICS
Thermo (heat) & Dynamic (force)
In earlier days, the capacities of hot bodies,
work.
Nowadays, broader scope, the science that
studies energy and the transformation of
energy into work, or moving things around.
Energy
Ability to cause changes.
Thermal, mechanical, kinetic, potential, electric,
magnetic, chemical, nuclear energy.
THERMODYNAMICS
The Zeroth law
Temperature measurement.
The First law
Conservation of energy principle (energy change from
on state to another).
The Second law
Energy has quality and quantity, actual processes occur
in the direction of decreasing quality of energy.
HEAT TRANSFER
Heat
A form of energy that can be transferred from one
system to another as a result of temperature
difference.
Heat Transfer & Thermodynamics
Thermodynamics – the amount of heat transfer
from one equilibrium state to another.
Heat Transfer – How long the heat transfer process
will take, due to temperature difference,
nonequilibrium.
BETWEEN T’DYNAMICS AND HEAT TRANSFER
Thermodynamics tells us:
– how much heat is transferred (δQ)
– how much work is done (δW)
– final state of the system
– equilibrium
Heat transfer tells us:
– how (with what modes) δQ is transferred
– at what rate δQ is transferred
– temperature distribution inside the body
– Non equilibrium
DIMENSIONAL HOMOGENEOUS
What is the different between Weight and
Mass? (Definition & Units.) - Quiz
Every terms in an equation must have the
same dimensions.
Spotting Errors in unit
E (kJ) = 25 kJ + 7 kJ/Kg
Fundamental Dimension: M,L,T
Obtain formulas from unit
ρ = 850kg/m3; V = 2 m3
FLUID MECHANICS
Fluid
– A substance in the gas or liquid phase.
– A liquid takes the shape of the container, free surface
under gravity.
– Gases cannot form a free surface
SOLID AND FLUID
Solid
Resist an applied shear stress by deforming.
Stress proportional to strain.
Fluid
Deforms continuously under the influence of
shear stress.
Stress proportional to strain rate.
MECHANICS - QUIZ
Statics?
Dynamics?
Kinetics?
Kinematics?
Normal Stress?
Shear Stress?
Weight?
Mass?
FLUID MECHANICS- CATEGORIES
Fluid Statics & Dynamics
The motion of fluids that are incompressible
(density constant), HYDRODYNAMICS.
GAS DYNAMICS, compressible (density
change significantly) fluid flow, nozzles at
high speed.
AERODYNAMICS, flow of gases over
bodies, aircraft, automobiles.
FLUID PROPERTIES
Any characteristic of a system is called a
property.
– Familiar: pressure P, temperature T, volume V,
and mass m.
– Less familiar: viscosity, thermal conductivity,
modulus of elasticity, thermal expansion
coefficient, vapor pressure, surface tension.
FLUID PROPERTIES
Density (mass/unit volume)
Symbol: ρ --- rho
Blood density, 1060kg/m3; water
(1000kg/m3),
Specific weight (Weight/Volume)
Symbol: γ --- Gamma
Water on earth is 9807Nm-3 at 5ºC
FLUID PROPERTIES
Specific volume is defined as,
v = 1/r = V/m (m3/kg)
Specific gravity,
(Ratio of the density of a substance to the
density of water at 4°C - relative density)
Sg = ρ object / ρwater at 4°C = γobject/γwater at 4°C
Unit: dimensionless or unitless, Blood????
EXAMPLE 1
Calculate the weight of a reservoir
of oil if it has a mass of 825 kg.
ANSWER 1
EXAMPLE 2
If the reservoir from Example 1 has a
volume of 0.917m3, compute the density,
the specific weight, and the specific
gravity of the oil.
ANSWER 2
EXAMPLE 3
Glycerine at 20°C has a specific
gravity of 1.263. Compute its
density and specific weight.
ANSWER 3
VISCOSITY
Density & specific weight, measures heaviness
Additional properties to distinguish flow, fluidity
(how easy it flows).
Internal resistance of fluid to motion.
A measure of the resistance of a fluid to deform under
shear stress.
FRICTIONAL FORCE
Solid & Solid
F = µ N, µ: Friction coefficient
Analogous,
Fluid & Solid, Fluid & Fluid.
Move in air, walk in water, higher
resistance.
VISCOSITY
y
u=V
Moveable Plate
B
F
B’
h
A
Fluid at t=0
dγ (small deformation)
Fixed Plate A
u=0
Velocity gradient , dV/dy = V/h
No slip condition
VISCOSITY
Based on the experimental analysis,
F∝AV/h or F/A∝V/h
Shear Stress acting on fluid layer is defined as,
τ = F/A
Finally,
τ∝V/h ∝ du/dy----(1)
VISCOSITY
y
u=V
F
h
u=0
In STEADY operation, the fluid velocity between the plates
varies linearly between 0 and V
Thus create velocity profile,
U(y)/y = V/h ; dU/dy=V/h ----------(2)
VISCOSITY
y
da
N
N’
u=V
F
h
dӨ
M
u=0
During differential time interval dt, fluid particles
along vertical line MN rotate through a differential
angle dӨ, while the upper plate moves a differential
distance da = Vdt.
VISCOSITY
y
da
N’
N
u=V
F
h
dӨ
M
u=0
For small displacement,
dƔ=da/h=tan(dӨ)=Vdt/h=du/dy * dt ----(3)
Therefore, shear strain rate is,
.
Ɣ = du/dy ----(4)
VISCOSITY
From (1) ,
τ ∝V/h ∝ du/dy
From (4),
.
du/dy = Ɣ
Then, it is understand that shear stress is also
proportional to the rate of shearing.
Therefore,
.
τ ∝ du/dy ∝ Ɣ
DYNAMIC VISCOSITY
.
τ =µdu/dy = µ Ɣ;
µ: Dynamic Viscosity
Fluid with constant µ is called
Newtonian Fluid

KINEMATIC VISCOSITY  
r
– why do we need kinematic viscosity?
– When shear stress and shear rate is influenced by fluid
density.
– An example of this is the measurement of viscosity using
gravity techniques such as a cup with a small orifice in the
bottom. With this type of measurement device, a specific
volume of fluid passes through the orifice and the time it
takes for the volume of fluid to pass through the orifice is
proportional to the fluid viscosity.
– However, it also depends on the density of the fluid since
the more dense the fluid, the faster it will flow through the
orifice. The property being measured in this example is then
the kinematic viscosity and not the dynamic viscosity.
– Unit m2/s and stoke (1 stoke = 1 cm2/s = 0.0001 m2/s)
GAS AND LIQUID KINEMATIC VISCOSITY
Resistance to deformation,
internal friction force
develop between fluid
layers.
Liquids, cohesive forces
between the molecules.
Collisions in gas molecules.
Liquid, Temp increase,
Viscosity Decrease.
Gas, Temp increase,
Viscosity Increase.
GAS AND LIQUID KINEMATIC VISCOSITY
• Liquid, molecules posses more energy at
higher temperature, and oppose the large
cohesive intermolecular force more
strongly.
• Gas, intermolecular forces are negligible,
high temperature, gas move at higher
velocities. More molecular collisions per
unit volume per unit time and higher
resistance to flow.
FIG 2.4 SHOWS THE ROTATING-DRUM VISCOMETER
VISCOMETRY
• How is viscosity measured?
A rotating viscometer.
– Two concentric cylinders
with a fluid in the small gap
ℓ.
– Inner cylinder is rotating,
outer one is fixed.
MEASUREMENT OF VISCOSITY
T  FR
-----(1)
du
F  A  A
dy
V
F  A
A  2RL
l
V  R
  2N
2
3
4 R NL
T 
l
VISCOSITY
NEWTONIAN & NON NEWTONIAN
τ
Bingham Plastic – Toothpaste and Mayonnaise
Shear thinning - Latex
Newtonian - Oil, Water
Shear thickening - quicksand
dƔ/dt
• Newtonian – constant viscosity
• Non-Newtonian (apparent viscosity)
Shear thinning – viscosity , shearing rate (velocity gradient)
Shear thickening – viscosity , shearing rate (velocity gradient)
• Bingham plastic – constant viscosity but at certain amount shear stress,
fluid starts shearing
BLOOD
• Blood is a living tissue composed of
blood cells suspended in plasma. It
consists of aqueous and cellular
phase.
• The cellular phase is (95% red
blood cells, 0.13% white blood
cells and 4.9% platelets ) about
45% of the red blood cells.
BLOOD
• The Plasma (aqueous phase) is
about 55% (Water 92%,
miscellaneous elements and 7%
protein – fibrinogen, globulin and
albumin).
BLOOD VISCOSITY
• Plasma shows Newtonian, however, whole blood
•
exhibits non-Newtonian behaviour [A].
Blood behaves as:
– Newtonian fluids in (> 100s-1), in large arteries where
shear rate is above 100s-1 blood is assumed to have
constant viscosity at 3.5 cP.
– In the microcirculation (small arteries and capillaries)
and in veins where the shear rates is low, blood is
treated as non Newtonian fluid.
– Bingham plastic – The yield stress for blood is very small,
approximately 0.005 to 0.01N/m2
FACTORS AFFECTS BLOOD VISCOSITY
• The percentage of red blood cell in blood
•
(Hematrocit). Higher Red Cell, Higher Viscosity .
A normal Hematrocit in human males is 42 to 45%.
A hematocrit of 40%, the relative viscosity is 4.
At a hematocrit of 60%, the relative viscosity is about
8. Therefore, a 50% increase in hematocrit from a
normal value increases blood viscosity by about 100%.
Such changes in hematocrit and blood viscosity occur
in a patients with polycythemia (more than 50%)
FACTORS AFFECTS BLOOD VISCOSITY
• The effect of temperature on the viscosity of bloods is
still not clearly established. The normal practice is to
measure the viscosity at body temperature [1].
Temperature decrease, viscosity increase. Viscosity
increases approximate 2% for each °C decrease in
temperature.
Implications:
When a person's hand is cooled by exposure to a cold
environment, the increase in blood viscosity contributes
to the decrease in blood flow (along with neuralmediated thermoregulatory mechanisms that constrict
the vessels).
FACTOR AFFECT BLOOD VOSCOSITY
The apparent viscosity increases with the increase of tube
diameter [3], Fahraeus-Lindqvist effect.
Larger Arteries
RBCs have great random motion: some move horizontally, others vertically, and
others with an angle. Thus, internal friction is great, which increases viscosity.
Smaller Arteries
RBCs have no random motion: each RBC must move singly, one after the other.
Thus, internal friction is minor, which decreases viscosity.
FACTOR AFFECT BLOOD VOSCOSITY
• Protein content in Plasma.
• Globulin, Albumin has significant effects where
fibrinogen effect is minimal [1].
BLOOD VISCOELASTICITY [4]
Blood plasma shows viscosity only, while whole
blood shows viscous and elastic.
Viscosity - Energy dissipated during flow due to
sliding and deformation of red blood cell and its
aggregates.
Elasticity - Energy stored during flow due to
orientation and deformation of red blood cells.
BLOOD VISCOELASTIC [4]
The viscosity of the viscoelastics material gives the
substance a strain rate dependent on time.
Elastic
Viscoelastics
BLOOD VISCOELASTICITY [4]
Blood Structure Vs Viscoelasticy
Low shear rates - RBC’ cells, large aggregates, Viscoelasticity is dominated by the
aggregation properties of RBC. Deformability play lesser role.
Moderate shear rates - RBC’s cells disaggregate, cells orient in flow direction and
moves. The influence of aggregation on viscoelasticity diminish, and deformability
increase.
Higher shear rates – Normal RBC’s cells stretch and deform and align with flow. RBC
layers slide on plasma. Deformability dominates viscoelasticity.
AGGREGATION,VISCOELASTICITY [4]
The viscosity and elasticity of blood with low aggregation tendencies (RED) are
below the values for normal blood (BLUE) at low shear rates. The viscosity and
elasticity of blood with elevated aggregation tendencies (GREEN) are above
those for normal blood at low shear rates. But, in the region of high shear rates,
where aggregation effects no longer dominate, the viscosity and elasticity
approach the same values in each case.
DEFORMABILITY,VISCOELASTICITY [4]
The idealized example shows how the viscoelasticity blood
containing cells with low deformability (RED) can differ from the
viscoelasticity of blood with normal cells (BLUE).
VISCOELASTICITY, CLINICAL CONDITIONS [4]
As an example, the viscoelasticity of an individual's blood
with sickle cell disease is markedly different from the
viscoelasticity of normal blood. This is clearly seen at high
shear rates where the Patient's Elasticity (Red) is
significantly higher than the Normal Elasticity (BLACK).
SURFACE TENSION
SURFACE TENSION
The cohesive forces between molecules down into a liquid
are shared with all neighboring atoms and balance each other
because of symmetry.
The attractive forces acting on the surface molecule are not
symmetric, and the attractive forces applied by the gas
molecules above are very small. It experiences forces only
sideways and downward, which creates the surface tension
effect.
SURFACE TENSION?
It can also be defined as the tendency of
liquids to reduce their exposed surface to
the smallest possible area
[The Columbia Encyclopedia, Sixth Edition. Copyright 2008
Columbia University Press]
It is denoted by σs, has units of force per
unit length or energy per unit area. Since it
is energy per area, it also represent the
work perform to create a new surface.
The unit of the surface tension is N/m or in
energy terms as Nm/m2
SURFACE TENSION
The external pressure is Po, and the
pressure inside the drop is Pi. A force
balance yields
(Pi-Po) * Pi * R2 – Ɣ*2*Pi*R = 0
ΔP = Pi – Po,
ΔP = 2Ɣ/R ---- Law of Laplace
The smaller the R, the higher Delta P is
required to inflate the surface.
THE IMPORTANCE OF SURFACE TENSION IN
ENGINEERING/SCIENCE APPLICATIONS
Automobile Engineering
Surface preparation before painting to ensure that
the paint will stick to the surface.
Food Engineering
To dissolve powders such as milk or cocoa.
Life Science
Wetting of the eye. The cornea is by nature very
hydrophobic, yet a normal eye is wet ! Proteins
(called mucins), present in tears, turn the surface of
the eye hydrophilic, stabilizing the lachrymal film. If
one accidentally smears a fatty cream on the eye, it
dries up, causing considerable discomfort.
LUNG PHYSIOLOGY AND PATHOLOGY
Respiration System
Lung physiology and pathology
Alveoli
–
–
–
–
–
Gas exchange from lung to the blood or vice versa
Spherical in shape and are connected to terminal bronchi in lung
Size vary widely
Law of Laplace; ΔP = 2Ɣ/R
Pressure to inflate smaller alveoli > larger alveoli
Lung physiology and pathology
SURFACE TENSION has tendency to
collapsed the alveoli
SURFACTANTS (lipoprotein-rich
phospholipid) is secreted to prevent
collapsed of alveoli (exhale) and avoid
overdistension of alveoli (inhale)
Lung physiology and pathology
In developing fetuses, surfactant is not produced
until last six weeks before normal delivery
Danger to premature infant, respiratory distress
syndrome (hard to breath) due to lack of
surfactant.
Labored breathing and incomplete expansion of
the lungs. Death?? Synthetic surfactants.
SURFACE TENSION
• Table 1.5 shows the surface tension of water.
CAPILLARY EFFECT
• Capillary effect is the
•
W  mg  rVg  rg (R h)
Fsurface  2R s cos 
•
2 s
h
cos 
rgR
2
rise or fall of a liquid in
a small-diameter tube.
The curved free surface
in the tube is call the
meniscus.
Force balance can
describe magnitude of
capillary rise.
For water-glass in atmospheric air, Ø = 0
CAPILLARY EFFECT
• When the attractive forces are between
unlike molecules, they are said to be
adhesive forces. The adhesive forces
between water molecules and the walls of
a glass tube are stronger than the
cohesive forces (attraction between like
molecules) lead to an upward turning
meniscus at the walls of the vessel and
contribute to capillary action.
ASSIGNMENT
Find 3 articles that related to the applications of the
following fields in solving Biomedical Engineering
related problems:
1.
2.
3.
Fluid Mechanics.
Thermodynamics.
Heat Transfer.
2 of the articles must include the application of fluid
mechanics concepts and the other article can be any one
of the other listed field.
Try to sort out the fundamental principles used in the
article. Summarize and explain how the principles is used
to solved related problems.
ASSIGNMENT
The report should not be less than 5 pages.
The format are as follow:
1. Single spacing
2. Times New Roman - font size – 12
3. Should include:
Introduction (Overall and related information on the problems) - 10 marks
Problem Statement (What is the problem) - 15 marks
Thermofluid Principles (What are the principles use?) – 15 marks
How the problem were solved? – 5 marks
References – 5 marks
SUBMISSION – 11th of August 2008.
LATE SUBMISSION – MINUS 25% MARKS
PLAGIARISM – MINUS 75% MARKS
***PLAGIARISM IS NOT ALLOWED***
REFERENCE
1.
2.
3.
4.
Biofluid Mechanics: The Human Circulation
Thermal-Fluid Sciences, Yunus A. Cengel, Robert H. Turner, John M. Cimbala
http://en.wikibooks.org/wiki/Biomechanics/Hemodynamics
http://www.vilastic.com/FAQ_Blood.htm