me 1521 energy transfer by heat, work, and mass cengel & boles, chapter 3
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ME 152 2
Energy Transfer
• Energy transfer to/from closed systems– Heat (Q)
– Work (W)
• Energy transfer to/from open systems (control volumes)– Heat (Q)
– Work (W)
– Mass flow )( m
ME 152 3
Heat
• Heat (Q) is the transfer of energy due to a temperature difference– a system w/o heat transfer is an
adiabatic system– SI units: kJ
• Heat rate, , (kJ/s or kW)
• Heat per unit mass, q = Q/m
• Sign convention:– Q > 0: heat transferred to system from
surroundings– Q < 0: heat transferred from system to
surroundings
Q
ME 152 4
Heat Transfer Modes
• Conduction– transfer of heat through a material due
to random molecular or atomic motion; most important in solids
• Radiation– transfer of heat due to emission of
electromagnetic waves, usually between surfaces separated by a gas or vacuum
• Convection– transfer of heat between a solid surface
and fluid due to combined mechanisms of i) fluid conduction at surface; ii) fluid flow within boundary layer
ME 152 7
Radiation Heat Transfer
• Stefan-Boltzmann law of radiation (between a small surface A of emissivity and large surroundings):
44surrsrad TTAQ
ME 152 8
Work
• Work (W) is the energy transfer associated with a force acting through a distance:
• Work rate or power
• Work per unit mass, w = W/m
• Sign convention– W > 0: work done by system on
surroundings
– W < 0: work done on system by surroundings
(kJ) sdFW
kW)or (kJ/s VFW
ME 152 9
Types of Work
• Moving boundary (compression/expansion) work
• Shaft work• Spring work• Electrical work• Other forms; work associated with:
– Acceleration– Gravity– Polarization– Magnetization– Solid deformation– Liquid film stretching
ME 152 10
Moving Boundary Work
• Associated with a volume change of a fluid system (aka compression-expansion work)
2
1
2
1
2
1
PdVW
PAdxFdxW
b
x
x
x
x
ME 152 11
Moving Boundary Work, cont.• Expansion: dV > 0, Wb > 0
• Compression: dV < 0, Wb < 0
• Work processes on P-V diagram:
curves betweenarea
)( curve 1-2under area
(-) curve 2-1under area
exp
1
221,exp
2
112,
WWW
PdVWW
PdVWW
compcycle
b
bcomp
ME 152 12
Moving Boundary Work, cont.• Special cases:
1) if V = constant, Wb = 0
2) if P = constant, Wb = P(V2-V1)
3) if PVn = constant (known as a polytropic process),
(see pp. 135-136 for derivation)
)1( ln
)1( 1
1
211
1122
nV
VVPW
nn
VPVPW
b
b
ME 152 13
Shaft Work
• Associated with a rotating shaft
unit time)per srev' ( 2
s)revolution of no. ( 2
thenconstant, if
torque) ( 2
1
2
1
nnW
nnW
dFrdW
sh
sh
sh
ME 152 14
Spring Work
• Associated with the extension or compression of a spring; if spring is linear, then force obeys Hooke’s law,
21
222
1
2
1
and
constant) spring (
xxk
kxdxW
kkxF
sp
sp
ME 152 15
Electrical Work
• Associated with the motion of electrons due to an electromotive force
V
V
VV
IW
ItI
N
NsdEN
sdFW
e
e
current) (
voltage) (
charge) electric ( 2
1
2
1
ME 152 16
Work and Heat
• Both are energy transfers• Both are path-dependent functions
• P and V are properties, because
• Q and W are path functions, because
BA
BA
PPPP
VVVV
)()(
)()(
1212
1212
BABA WWQQ )()( , )()( 12121212
ME 152 17
Conservation of Mass
• “Mass can neither be created nor destroyed” – mass and energy can be converted to
each other according to Einstein’s E=mc2, but this effect is negligible except for nuclear reactions)
• For closed systems, this principle imposes m = constant since mass cannot cross the system boundary
• For control volumes, the mass entering and leaving the system may be different and must be accounted for
ME 152 18
Mass and VolumeFlow Rates
• Mass flow rate: fluid mass conveyed per unit time [kg/s]
where Vn = velocity normal to area [m/s]
= fluid density [kg/m3]
A = cross-sectional area [m2]
A ndAm V
ME 152 19
Mass and VolumeFlow Rates, cont.
• For most pipe flows, = constant and the average velocity (V) is used:
• Volume flow rate is given by
v
Am
Am ave
V
V
or
v
VVm
AV
then
V
)(V
ME 152 20
Conservation of Mass Principle - Control Volume
• Net mass transfer during a process is equal to the net change in total mass of the system during that process
where i = inlet, e = exit, 1 = initial state, 2 = final state
• in rate form:
• In fluid mechanics, this is often referred to as the continuity equation
systemei mmmm )( 12
dt
dmmm system
ei
ME 152 21
Steady-Flow Processes
• Steady-flow or steady-state – a condition where all fluid and flow properties, heat rates, and work rates do not change with time.
– mathematically:
– applied to mass balance:
0dt
d
0dt
dmsystem
ME 152 22
Steady-Flow Processes, cont.
• Conservation of mass during a steady-flow process:
• If control volume is single-stream (i.e., one inlet, one exit), then
ei mm
2
22
1
11
21
or
v
AV
v
AV
mmm
ME 152 23
Incompressible Flow
• If = constant, then the mass flow is considered incompressible
– for steady-flow:
– for single-stream, steady-flow:
ei VV
2211
21
or
VV AA
VV
ME 152 24
Total Energy of a Flowing Fluid
• A flowing fluid contains internal, kinetic, and potential energies:
• Fluid entering or leaving a control volume has an additional form of energy known as flow energy, which represents the work required to “push” the fluid across a boundary:
gzue
gzumE
2
21
221 or , )(
V
V
mPvPVW flow energyflow
ME 152 25
Total Energy of a Flowing Fluid, cont.
• The total energy of a flowing fluid (on a unit-mass basis, ) becomes
• Using the definition of enthalpy (h),
Pvgzu 221 V
gzh 221 V
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