ME 152 1

Energy Transfer By Heat, Work, and Mass

Cengel & Boles, Chapter 3

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 5

Conduction Heat Transfer

• Fourier’s law of conduction:

dx

dTkAQcond

ME 152 6

Convection Heat Transfer

• Newton’s law of “cooling”, or convection:

)( fsconv TThAQ

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

ME 152 26

Energy Transport by Mass

• Amount of energy transport:

• Rate of energy transport:

)( 221 gzhmmEmass V

)( 221 gzhmmEmass V