Fundamentals of Heat Transfer

7/30/2019 Fundamentals of Heat Transfer

1/38

ME353HEATTRANSFER1

LectureNotes

Prof.MetinRenksizbuluti i i


2/38

h i l i i

Heat Transfer:

Physical Origins

andRate Equations

Chapter One

1


3/38


4/38

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


5/38

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

4

MOLECULAR DIFFUSION

MOLECULAR DIFFUSION + ADVECTION

MODES OF HEAT TRANSFER


6/38


7/38

Conductionthroughastagnantgasbymoleculardiffusion


8/38

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


9/38

HEAT TRANSFER THROUGH A PLANE WALL

Calculate the heat transfer rate.


10/38

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

9

Heat transfer by conduction PLUS advection


11/38

ExamplesofConvectiveHeatTransfer

Forced Convection

FreeConvection

BoilingC d ti


12/38
http://www.wiley.com/college/bergman/0470501979/image_gallery/ch01/pages/table_01_02.htm


13/38


14/38

THERMALRADIATION:heattransferbyelectromagneticwaTheelectromagneticspectrum:


15/38

ThermalRadiation


16/38

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

15


17/38

Example:


18/38


19/38

Transmissivity


20/38

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

19


21/38

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

20


22/38
http://www.wiley.com/college/bergman/0470501979/image_gallery/ch01/pages/tableun_01_01.htm


23/38

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

22

use absolute temperaturein radiation calculations


24/38

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

23

Storage = Inflow - Outflow + Generation

CONSERVATION OF ENERGY (First Law of Thermodynamics)


25/38

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

24


26/38


27/38


28/38

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

27

Storage = 0 always !

also, there may be heat generation directly at the surface


29/38


30/38

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

29


31/38


32/38

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


33/38

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:

32


34/38

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

Fundamentals of Heat Transfer

Documents

Transcript of Fundamentals of Heat Transfer