Fundamentals of Heat Transfer
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Transcript of Fundamentals of Heat Transfer
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ME353HEATTRANSFER1
LectureNotes
Prof.MetinRenksizbuluti i i
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h i l i i
Heat Transfer:
Physical Origins
andRate Equations
Chapter One
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Quantity Meaning Symbol UnitsThermal Energy+ Energy associated with microscopic
behavior of matter
Temperature A means of indirectly assessing the
amount of thermal energy stored in matter
Heat Transfer Thermal energy transport due to
temperature gradients
Heat Amount of thermal energy transferred
over a time interval t 0
Heat Rate Thermal energy transfer per unit time
Heat Flux Thermal energy transfer per unit time
and surface area
orU u J or J/kg
T K or C
Q J
q W
q 2W/m
+
Thermal energy of system
Thermal energy per unit mass of system
U
u
DO NOT confuse or interchange the meanings ofThermal Energy, Temperature
and Heat Transfer
3
DEFINITIONS and NOMENCLATURE
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Conduction: Heat transfer in a solid or a stationary fluid (gas or liquid) due to
the random motion of its constituent atoms, molecules and /orelectrons.
Convection: Heat transfer due to the combined influence ofbulk and
random motion for fluid flow over a surface.
Radiation: Energy that is emitted by matter due to changes in the electron
configurations of its atoms or molecules and is transported as
electromagnetic waves
Conduction and convection require the presence of temperature variations in a material
medium.
Although radiation originates from matter, its transport does not require a material
medium and occurs most efficiently in a vacuum.
Modes of Heat Transfer
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MOLECULAR DIFFUSION
MOLECULAR DIFFUSION + ADVECTION
MODES OF HEAT TRANSFER
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Conductionthroughastagnantgasbymoleculardiffusion
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2 1x
dT T T q k k
dx L
1 2
x
T T
q k L
Heat rate (W): x xq q A
Application to one-dimensional, steady conduction across a
plane wall of constant thermal conductivity:
Conduction:
General (vector) form ofFouriers Law:
Heat flux
q k T
Thermal conductivity Temperature gradient2
W/m W/m K C/m or K/m
7
In this specific case, the
temperature profile is linear.
Heat transfer b molecular diffusion
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HEAT TRANSFER THROUGH A PLANE WALL
Calculate the heat transfer rate.
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Convection
Relation of convection to flow over a surface and developmentofvelocity and thermal boundary layers:
Newtons law of cooling:
sq h T T
2Convection heat transfer coeffici: (W/m Kent )h
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Heat transfer by conduction PLUS advection
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ExamplesofConvectiveHeatTransfer
Forced Convection
FreeConvection
BoilingC d ti
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THERMALRADIATION:heattransferbyelectromagneticwaTheelectromagneticspectrum:
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ThermalRadiation
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Radiation Heat transfer at a gas/surface interface involves radiation
emission from the surface and may also involve the
absorption of radiation incident from the surroundings
(irradiation, ), as well as convection if .sT T
Energy outflow due to emission:4
b sE E T
emissi:Surf vityace 0 1
blackbody: Emissive power of a (the perfect emit r)tebE
2Emissive powe: r W/mE
-8 2 4: Stefan-Boltzmann constant 5.6710 W/m K
Energy absorption due to irradiation:
absG G2
abs: incidAbsorbed radiatioent (Wn /m )G
absorpti: Surfa vityce 0 1 2Irradiation: W/mG
G
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Example:
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Transmissivity
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Special case of surface exposed to large
surroundings of uniform temperature, surT
4
sur surG G T
4 4rad sur
If , the from the
surface due to exchange with the surroundings is:
net radiation heat flux
b s sq E T G T T
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Alternatively,
rad sur
2
2 2
sur sur
Radiation heat transfe: W/mr coefficient K
r s
r
r s s
q h T T
h
h T T T T
For combined convection and radiation,
conv rad surs r sq q q h T T h T T
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Problem 1.40: Power dissipation from chips operating at a surface temperature
of 85C and in an enclosure whose walls and air are at 25C for
(a) free convection and (b) forced convection.
Schematic:
Assumptions: (1) Steady-state conditions, (2) Radiation exchange between a small surface and a large enclosure, (3)
Negligible heat transfer from sides of chip or from back of chip by conduction through the substrate.
Analysis:
elec co n v radP q q
(a) If heat transfer is by natural convection,
5/4 5/42 5/4 -4 2
conv
-4 2 -8 2 4 4 4 4
rad
elec
= 4.2W/m K 2.25 10 m 60K = 0.158W
0.60 2.25 10 m 5.6710 W/m K 358 298 K = 0.065W
0.158W + 0.065W = 0.223W
sq CA T T
q
P
(b) If heat transfer is by forced convection,
2 4 -4 2convelec
250W/m K 2.25 10 m 60K 3.375W
3.375W + 0.065W 3.44W
sq hA T T
P
4 4surs shA T T A T T
22 -4 20.015m 2.2510 mA L
Problem: Electronic Cooling
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use absolute temperaturein radiation calculations
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At an Instant of Time:
Note representation of system by a
control surface (dashed line) at the boundaries.
Surface Phenomena
,
in outenergy transfer across the control
surfa
: rate of thermal and/or mechanical
due to heat transfer, fluid flow and/or work interacc te ions.
E E
Volumetric Phenomena
: rate of due to conversion from another energy form
(e.g., electrical, nuclear, or chemical); energy conversion proc
thermal ener
ess occurs wi
gy generat
thin the s
ion
ystem.
gE
stenergy: storate of rage inchang the se o ysf .mteE
Conservation of Energy
in out st
stg
dE
dtE E E E
Each term has units of J/s or W.
APPLICATION TO A CONTROL VOLUME
Over a Time Interval
Each term has units of J.
in out stgE E E E
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Storage = Inflow - Outflow + Generation
CONSERVATION OF ENERGY (First Law of Thermodynamics)
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Example 1.4: Application to thermal response of a conductor with Ohmic
heating (generation):
Involves change in thermal energy and for an incompressible substance.
tdU dT Mcdt dt
Heat transfer is from the conductor
Generation may be viewed as electrical workdone on the system
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A special case for which no volume or mass is encompassed by the control surface.
Conservation of Energy
outin 0E E
Applies for steady-state and transient conditions.
Consider surface of wall with heat transfer by conduction, convection and radiation.
cond conv rad0q q q
4 41 2 2 2 2 sur 0T T
k h T T T T L
With no mass and volume, energy storage and generation are not pertinent to the energy
balance, even if they occur in the medium bounded by the surface.
THE SURFACE ENERGY BALANCE
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Storage = 0 always !
also, there may be heat generation directly at the surface
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On a schematic of the system, represent the control surface by
dashed line(s).
Choose the appropriate time basis.
Identify relevant energy transport, generation and/or storage termsby labeled arrows on the schematic.
Write the governing form of the Conservation of Energy requirement.
Substitute appropriate expressions for terms of the energy equation.
Solve for the unknown quantity.
METHODOLOGY OF FIRST LAW ANALYSIS
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PROBLEM 1.85
KNOWN: Solar collector designed to heat water operating under prescribed solar irradiation and loss
conditions.
FIND: (a) Useful heat collected per unit area of the collector, qu , (b) Temperature rise of the waterflow, T To i , and (c) Collector efficiency.
SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) No heat losses out sides or back of collector, (3)
Collector area is small compared to sky surroundings.
PROPERTIES: Table A.6, Water (300K): cp = 4179 J/kgK.
ANALYSIS: (a) Defining the collector as the control volume and writing the conservation of energy
requirement on a per unit area basis, find that
& & & & .E E E Ein out gen st + =
Identifying processes as per above right sketch,
=q q q qsolar rad conv u 0
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Problem 1.57: Thermal processing of silicon wafers in a two-zone furnace.
Determine (a) the initial rate of change of the wafer
temperature and (b) the steady-state temperature.
Problem: Silicon Wafer
KNOWN: Silicon wafer positioned in furnace with top and bottom surfaces exposed to hot
and cool zones, respectively.
FIND: (a) Initial rate of change of the wafer temperature from a value of 300 K,w,iT and (b)
steady-state temperature. Is convection significant? Sketch the variation of wafer temperature
with vertical distance.
SCHEMATIC:
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Problem: Silicon Wafer (cont.)
ASSUMPTIONS: (1) Wafer temperature is uniform, (2) Hot and cool zones have uniform
temperatures, (3) Radiation exchange is between small surface (wafer) and large enclosure
(chamber, hot or cold zone), and (4) Negligible heat losses from wafer to pin holder.
ANALYSIS: The energy balance on the wafer includes convection to the upper (u) and lower
(l) surfaces from the ambient gas, radiation exchange with the hot- and cool-zones and an energystorage term for the transient condition. Hence, from Eq. (1.12c ),
in out stE E E
or, per unit surface area
rad, rad, cv, cv,w
h c u ld T
q q q q cd dt
4 4 4 4
sur,sur,w
w c w u w l wh
d T
T T T T h T T h T T cd dt
(a) For the initial condition, the time rate of change of the wafer temperature is determined
using the foregoing energy balance with 300K,w w,iT T
8 2 4 4 4 8 2 4 4 4 440.65 5.67 10 W / m K 1500 300 K 0.65 5.67 10 W / m K 330 300 K
2 28 W / m K 300 700 K 4 W / m K 300 700 K
32700kg / m 875J / kg K 0.00078 m / w idT dt
104 K / sw idT /dt