Chapter 1 Chee 318 1 Reminder: The General Balance Equation mulation = Creation – Destruction + Flow in – Flow Rate Equation Rate of Rate of Rate of tion = Creation – Destruction + Flow in – Flow out Applicable to any extensive property: mass, energy, entropy, momentum, electric charge
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Chapter 1 Chee 318 1
Reminder: The General Balance Equation
Accumulation = Creation – Destruction + Flow in – Flow out
Rate Equation
Rate of Rate of Rate of Rate of Rate of Accumulation = Creation – Destruction + Flow in – Flow out
Applicable to any extensive property: mass, energy, entropy, momentum, electric charge
Chapter 1 Chee 318 2
Reminder: System and Control Volume
• A system is defined as an arbitrary volume of a substance across
whose boundaries no mass is exchanged. The system may
experience change in its momentum or energy but there is no transfer
of mass between the system and its surroundings. The system is
“closed”.
• A control volume is an arbitrary volume across whose boundaries
mass, momentum and energy are transferred. The control volume
may be stationary or in motion. Mass can be exchanged across its
boundaries. Useful in fluid mechanics, heat and mass transfer
Chapter 1 Chee 318 3
Reminder: Approaches for Analysis of Flow
In analyzing fluid motion we may take two paths:
1. Working with a finite region (=the control volume), making a
balance of flow in versus flow out and determining flow effects
such as forces, or total energy exchange. This is the control
volume method. This approach is also called “macroscopic” or
“integral method of analysis”.
2. Analysing the detailed flow pattern at every point (x,y,z) in the
field. This is the differential analysis, sometimes also called
“microscopic”.
Chapter 1 Chee 318 4
Conservation of Energy
• Energy conservation on a rate basis:
Control Volume (CV)
Surroundings, S
Boundary, B (Control Surface, CS)
-Accumulation (Storage)
-GenerationAdditionthrough inlet
Lossthrough outlet
stst
outgin Edt
dEEEE
inE outE
gEstE
Inflow and outflow are surface phenomena Generation and accumulation are volumetric phenomena
Units W=J/s(1.1)
Chapter 1 Chee 318 5
The Energy Balance
Chapter 1 Chee 318 6
The Energy Balance
Rate of Energy Flow into CV: ininint WqmzgV
u
in2
2
Rate of Energy Flow out of CV: outoutoutt WqmzgV
u
out2
2
Rate of Energy Accumulation: CV
zg
Vum
dt
dt 2
2
ut :internal energy, V: velocity, z: potential energy, q: heat rate, W: work
Chapter 1 Chee 318 7
The Energy Balance
02
2
2
2
outoutout
out
t
ininint
WqmzgV
u
WqmzgV
u
in
Substituting in equation (1.1) and assuming steady-state conditions:
Convention
inoutoutnet
outininnet
WWW
qqq
,
,q is positive when transferred from surroundings to system.
W is positive when transferred from system to surroundings
Chapter 1 Chee 318 8
The Energy Balance
• For steady-state conditions the energy balance reduces to:
022
22
outnetout
out
tint WqmzgV
umzgV
u ,
in
(1.2)
The net work is:
inout, ]m ) [(]m ) [(P PWW shaftoutnet
Injection Work
The work term is divided in two contributions: Flow work, associated to pressure forces (=p, where is the specific volume) and (shaft) work done by the system.
Chapter 1 Chee 318 9
Steady-Flow Energy Equation
pui t
0
22
22
shaft
out
Wq
zgV
pumzgV
pum
in
Recall:
m
VA
VAm
c
c
Mass flow rate (kg/s)
Volumetric flow rate (m3/s)
Units of [J/s]
Enthalpy per unit mass:
and )()( outinpoutin TTcii
Chapter 1 Chee 318 10
Simplified steady-flow energy equation
• For steady state conditions, no changes in kinetic or potential energy, no thermal energy generation, neglible pressure drop:
)( inoutp TTCmq
Chapter 1 Chee 318 11
Example (Problem 1.36 textbook)In an orbiting space station, an electronic package is housed in a compartment having a surface area As=1 m2, which is exposed to space. Under normal operating conditions, the electronics dissipate 1kW, all of which must be transferred from the exposed surface to space.
(a) If the surface emissivity is 1.0 and the surface is not exposed to the sun, what is its steady-state temperature?
(b) If the surface is exposed to a solar flux of 750 W/m2 and its absorptivity to solar radiation is 0.25, what is its steady-state temperature?
Chapter 1 Chee 318 12
Surface Energy Balance
For a control surface:
0
0
"""
radconvcond
outin
qqq
or
EE
T
x
T1
T2
T
qcond”qrad”
qconv”
Chapter 1 Chee 318 13
Example (Problem 1.55 textbook)The roof of a car in a parking lot absorbs a solar radiant flux of 800 W/m2, while the underside is perfectly insulated. The convection coefficient between the roof and the ambient air is 12 W/m2.K.
a) Neglecting radiation exchange with the surroundings, calculate the temperature of the roof under steady-state conditions, if the ambient air temperature is 20°C.
b) For the same ambient air temperature, calculate the temperature of the roof it its surface emissivity is 0.8
Chapter 1 Chee 318 14
Chapter 1: Summary
Modes of Heat Transfer:
Conduction Convection Radiation
dx
dTkqx " )("
TThq Sx)( 44"
sursrad TTq
)( sursrrad TTAhq
qx”(W/m2) is the heat flux qx (W=J/s) is the heat rate
Energy Balances – written on a rate basis (J/s):
Conservation of Energy for a Control Volume Surface Energy Balance (does not consider volumetric phenomena)