Thermo 2 Final Exam Study Guide(Answered)

Stefan Jobe

4-30-11

Thermo 2

THERMO FINAL EXAM STUDY GUIDE

Internal Flow (pipe losses)o Laminar, transitional, and turbulent

Based on Reynolds # to determine what type of flow the fluid is. Transitional is also considered a turbulent flow due to lack of understanding

ℜ=ρV Dh

μ=V Dh

v Laminar flow Re ¿ 2300 Turbulent flow Re ¿10,000

o The friction coefficient in the fully developed flow region remains constant.o Pressure loss and head loss for all internal flows can be expressed as:

∆ P=f LD

ρV 2

2 and hL=

∆PL

ρg=f L

DV 2

2 g Pressure loss = a pressure drop that is due to viscous effects and represents an

irreversible pressure loss is indicated∆ PL. This ∆ PL is P1−P2. f is the friction factor which can be determined for a fully developed laminar flow in

a circular pipe f=64 /ℜ

Non-circular pipes the Hydraulic Diameter can be found using: Dh=4 Ac

p For turbulent flow the friction factor depends on the Reynolds # and the relative

roughness (εD

)

Using the Colebrook equation on page 569 in the texto Head Loss, hL

Total head loss for a system can be found using this: hL, total=hL,major+hL ,minor

o hL,major=f LD

V 2

2 g

o hL,minor=KLV 2

2g The K L (or Loss Coefficient) of a system can be found using:

K L=

hLV 2

(2 g) or K L=

∆PL

( 12 ρV 2 )

o The velocity boundary layer (or boundary layer) is the region that is most effected by the viscous shearing forces.

o Moody Chart represents the Darcy friction factor for pipe flow as a function of the Reynolds

# and the (εD

) over a wide range.

o **steady flow energy equation on page 560 may be important on the test. Heat Transfer (Forced & Natural Convection)

o The rate of convection heat transfer can be found by the following: Q=h A s (T s−T∞ )

o Reynolds # for ℜ=ρV Lc

μ For Flat plate

Laminar ℜ<5 x 105

Turbulent 5 x105≤ℜ≤107

o Nusselt Number= Nu=h Lc

k Nu =1 (means the heat transfer is purely conduction).

o Prandtl Number = Pr=Molecular diffusivity of momentumMolecular diffusivityof heat

= vα

=μ cpk

The higher the Pr # the slower the rate of heat dissipationo Parallel Flow over flat plates (section 19-3, has some equations on pages 782-784 that may

be useful)o Flat plate with Unheated Starting Length (has some equations on page 784 that may be

useful)o Uniform heat flux (two equations on page 785 that may be helpful)o The conservation of energy equation for the steady flow of a fluid in a tube can be

expressed as: Q=mc p(T e−T i)o Constant surface temperature

Q=h A s∆T avg

o logarithmicmeantemperature difference Look on page 801 for equation

o Constant heat flux can be expressed as:dT m

dx=

2 q s

ρV avg cp R=constant

o Bulk mean temperature: equation can be found on page 804 in text.o For fully developed laminar flow in a circular tube subjected to constant surface heat flux,

the Nusselt Number is constant. Nu=4.36o Bunch of equation for sections 19.7-19.8 for laminar and turbulent flow in tubes

o The Grashof Number GrL=gβ (T s−T ∞)Lc

3

v2

Represents the ratio of the buoyancy force to the viscous force acting on a fluid.

o Rayleigh Number = GrLPr=gβ(T s−T∞)Lc

3

v2Pr

Rayleigh Number is the product of Grashof and Prandtl numberso There are a lot of equations for natural convection for finned surfaces and for inside

enclosures on the summary page 861 in the text. External Flow

o Lift = The force a flowing fluid exerts on a body in the flow directiono Drag = The sum of the components of the pressure and wall shear forces in the direction

normal to the flow

o Lift and Drag Coefficients: CD=FD

1 /2 ρV 2 A and CL=

FL

1/2 ρV 2 Ao Flow separation = at high velocities the fluid stream detaches itself from the surface of the

bodyo More equations on flow over flat plates and other geometries which can be found on the

summary pages 612-613 2nd Law of Thermodynamics

o The 2nd law of thermodynamics states that processes occur in a certain direction, not in any direction. A process does not occur unless both the 1st and 2nd laws of thermodynamics are satisfied. (**The 1st law of thermodynamics is simply an expression of the energy principle or energy balance. The energy that goes into a system must go out the system. Also called the conservation of energy equation.)

o Bodies that can absorb or reject finite amounts of heat isothermally are called thermal energy reservoirs or heat reservoirs.

o Source =A reservoir that supplies energy in the form of heat o Sink = A reservoir that absorbs energy in the form of heat o Heat Engines:

Device or system that converts heat into output work Net work output = W net out=QH−QL

Thermal Efficiency = nth=Net work outputHeat Input

=W netout

QH

o Refrigerator: Device or system that uses input work to transfer energy from lower temperature

region Net work output = W net out=QH−QL

Coefficient of Performance = COPR=DesiredOutputwork input

=QL

W net ,∈¿¿o Heat Pump:

A device that transfers heat from a low-temperature medium to a high-temperature one.

Coefficient of Performance = COPHP=DesiredOutputWork Input

=QH

W net ,∈¿¿ Also another COP equation on page 263 in text.

o Kevin-Planck Statement = Heat engine can’t produce output work by only energy interactions with a hot reservoir

o Clausius statement = Refrigerator can’t have energy interactions from cold to hot reservoir without requiring input work

o Reversible Process = a process that can be reversed without leaving any trace on the surroundings. (These processes do not occur in nature)

o Irreversible Process = a process that is not reversible Irreversibilities = friction, unrestrained expansion, mixing of two fluids, heat transfer

across a finite temperature difference, electric resistance, etc.o Internally reversible process = a process where no irreversibilities occuro Carnot Cycle = best known reversible cycle, four reversible processes, 2 isothermal and 2

adiabatic. Four processes:

Isothermal expansion Adiabatic expansion Isothermal compression

Adiabatic compression

o

o The cycle can be reversed to give a refrigeration cycleo Carnot Heat Engine :

Thermal efficiency = nth=1−QL

QH

Thermal efficiency of a reversible heat engine = nth=1−T L

T H

o More equations on COP of carnot refrigerator and heat pump Check summary page 285 in text.

Entropyo Entropy = a quantitative measure of microscopic disorder for a system

Heat transferred to a system increases the entropy and heat transferred from a system decreases it.

For an Isentropic process (s2=s1), and the ∆ S=0 also.o The Clausius Inequality

Whenever a system completes a cyclic process, the integral of dQ/T around the cycle is less than zero or in the limit is equal to zero. (*pretty much the integral of dQ/T has to be zero or less)

o Increase of entropy principle states that the entropy generated during a process must be equal or greater than zero. Sgen≥0

o Entropy generation = the entropy generated during a process.

∆ Ssys=S2−S1=∫1

2 δQT

+Sgen

Sgen>0 ;irreversible Sgen=0 ; reversible Sgen<0 ;impossible

o If property is adiabatic + reversible =isentropic Where entropy = constant

o Isentropic efficiencies of steady flow devices equations can all be found of page 355 in the text.

o Entropy balance states that entropy change of a system during a process is equal to the net entropy transfer through the system boundary and the entropy generated within the system.

S¿−Sout+Sgen=∆ Ssystem

Power Cycleso 1st law of cycles = Qnet=W net

Determines Q or W for the component Used to find thermal efficiency or coefficient of performance of cycle

o Ideal cycle Assumes reversible processes and isentropic expansions and compressions

o Actual cycle Includes isentropic efficiencies of the components (e.g., turbines or compressors)

o Carnot cycle: 1→2: isothermal heat addition 2→3: isentropic expansion 3→4: isothermal heat rejection 4→1: isentropic compression

o Thermal efficiency = nth=1−Qout

Q¿

o nth ,carnot=1−T L

T H

o Air standard assumptions?o Cold air assumptions?o Compression ratio, ro Otto Cycle: Spark-ignition engine (closed system)

Air-fuel mixture ignited by spark plug processes

1→2: isentropic compression 2→3: constant volume heat addition 3→4: isentropic expansion 4→1: constant volume heat rejection

o q¿=u3−u2=cv (T3−T2)o qout=u4−u1=cv (T 4−T 1)o Diesel Cycle: Compression-ignition engine (closed system)

Air compressed first then fuel added to self-igniteo cycle processes

1→2: isentropic compression 2→3: constant pressure heat addition 3→4: isentropic expansion 4→1: constant volume heat rejection

o q¿=h3−h2=c p (T 3−T 2 )o qout=u4−u1=cv (T 4−T 1)

o Cut-off ratio, rc=V 3

V 2

Ratio of volume after and before combustiono Brayton Cycle: Gas turbine engines (steady-flow system)

Can be closed or open cycleo cycle processes

1→2: isentropic compression (compressor) 2→3: constant pressure heat addition 3→4: isentropic expansion (turbine) 4→1: constant pressure heat rejection

o q¿=h3−h2=c p(T 3−T 2)o qout=h4−h1=c p(T 4−T1)

o Pressure ratio = r p=P2P1

oo

These are the thermal efficiencies of each cycle VAPOR CYCLES:

o Rankine Cycle:

o Ideal cycle processes 1→2: isentropic compression (pump) 2→3: constant pressure heat addition (boiler) 3→4: isentropic expansion (turbine) 4→1: constant pressure heat rejection (condenser)

o

o Vapor-Compression Refrigeration Cycle:o cycle processes

1→2: isentropic compression (compressor) 2→3: constant pressure heat rejection (condenser) 3→4: constant enthalpy throttling (expansion valve) 4→1: constant pressure heat addition (evaporator)

Transient Conductiono Lumped system analysis

Where an object can be modeled to have the same temperature throughout the object.

Characteristic length can be found by dividing the specific volume by the area

Fourier Number, Fo: is the dimensionless time τ=αtL2

1-D transient conduction One-term approximation analytical solutions

Heisler and Gröber charts Multi-dimensional systems

Product solutions using results of 1-D analysis

Solutions using a one-term approximation for τ>0.2

***Mark off figures 18-15 and 18-17

What is diffuse radiation? Radiation occurs equally in all directions

What is a specular surface? Surface for which reflected angle for radiation equal to incoming angle

The fraction is known as the view factor, Fi→j fraction of radiation leaving surface i that reaches surface j directly how much of other surface is “seen” by the originating surface

**(tab this in book) View factors for common geometries given in Tables 21-3 & 21-4 and Figures 21-33 to 21-36

Summation rule Sum of view factors for from a surface to all others in an enclosure equals 1

Superposition rule

View factor to a composite surface is equal to the sum of view factors to each portion of the composite surface

Symmetry rule View factor from surface for to symmetrical orientation of other surfaces

are same

When an object has zero radiation leaving it’s surface Then all incoming radiation gets emitted by surface Known as a reradiating surface

Heat Exchangerso To exchange heat between two fluidso Overall heat transfer coefficient, U

o Total Thermal resistance, R

o Fouling factor, Rf Accounts for deposits and build-up within tubes during operation of the device Becomes additional variable for resistance in the thermal network

QUESTIONS:

• Someone claims that the shear stress at the center of a circular pipe during fully developed laminar flow is zero. Do you agree with this claim?

• Piping system has 2 pipes with same diameter but different lengths connected in parallel. How do the pressure drops in these two pipes compare? Pressure drop is the same in both pipes.

• How would the pressure drops compare if the roughness of these two pipes were different?

• The pressure drops would still be the same due to the head losses being the same in both pipes.

• What causes the indicated motion in this chimney-type cooker? (just a chimney cooker with flames underneath and heat in the up direction)

• Convection

• A hot object is in a spacecraft that is filled with air at atmospheric pressure and temperature at all times. Will the object cool faster or slower when the spacecraft is in outer space or still on the ground on Earth?

• Gravity

• What is an isolated system?

• It is closed to the surrounding environment

• What would be the change in entropy for an isolated system?

• Always increases or remains constant

• What is known about entropy generation?

• Must be greater than zero (positive)

• Which of the following processes result in an overall increase in entropy?

• 1) braking an automobile

• 2) gradual slowing of automobile as it rolls uphill without friction

• 3) lifting water with a frictionless electric pump from a well to an elevated reservoir

• Is it possible for the entropy change of a closed system to be zero during an irreversible process?

• Can’t be zero (only for reversible)

• The work in a pump to increase the pressure is small compared to the work in an air compressor for the same pressure increase. Why?

• The

• The refrigeration cycle can be viewed as a power cycle operated with reversed flow of the working fluid. For the vapor cycles, why isn’t it advantageous to use a turbine for the expansion process in the refrigeration cycle?

• dsfa

• What is a quasi-equilibrium process?

• Quasi = Italian for “about” and this type of process is almost in equilibrium and is used to do analytical studies of certain processes even know they aren’t in complete equilibrium. This is allowed because it is fairly close to equilibrium.

• Is it possible for a heat engine to have 100% thermal efficiency?

• Heat is hardly ever converted to work. It is the other way around. For example a turbine does work and releases heat to the environment.

• Would a heat engine with 100% thermal efficiency violate the 1st Law of Thermodynamics?

• Yes

• Can a Carnot heat engine have 100% thermal efficiency?

• No. look at equation 7-18 on page 279 in text.

• Can you create a reversible cycle that is more efficient than a Carnot cycle operating between the same temperature limits?

• No because the Carnot cycle is the most efficient reversible engine cycle possible

• How could you increase the thermal efficiency of a heat engine?

• Be able to convert more heat to work and reduce the irreversibility

IMPORTANT INFORMATION:

Warmer (less dense) fluid rises and replaced by colder (more dense) fluid Adiabatic = no heat transfer Isothermal = Isentropic =