# Fundamentals of Heat Transfer

Published on 2 weeks ago | Categories: Documents | Downloads: 4 | Comments: 0 | Views: 87
of x

## Content

ME353  HEAT TRANSFER 1

Lecture Notes

Prof. Metin Renksizbulut  Mechanical Engineering

Heat Transfer: Physical Physic al Origin Originss and Rate Equations Chapter One

1

•   What is heat is  heat transfer ? Heat transfer is thermal energy in transit due to a temperature difference.

•   What is thermal is  thermal energy? energy? Thermal energy is associated with the translation, rotation, vibration and electronic states of the atoms and molecules that comprise matter matter.. It represents the cumulati cumulative ve effect of  microscopic activities and is directly linked to the temperature of matter.

2

DO NOT  confuse or interchange the meanings of   Thermal Thermal Energy Energy,, Temperature DEFINITIONS and NOMENCLATURE

Heat Transfer  and Heat and Quantity

Meaning

Thermal Energy+

Temperature

Heat Transfer  Heat

Heat Rate

Heat Flux

Symbol

Energy associated with microscopic  behavior of matter

U or  u

A means means of indirectly indirectly assessing assessing the amount of thermal energy stored in matter

K or °C

Q

J

q

W

J or J/kg

Thermal energy transport due to temperature gradients

Amount of thermal energy transferred over a time interval    t    0

Thermal energy transfer per unit time

Thermal energy transfer per unit time and surface area

q

+ U   Thermal energy of system u

U Un nits

Thermal energy per unit mass of system 3

Modes of Heat Transfer  MODES OF HEAT TRANSFER

W/m2

Conductio Condu ction: n: Heat tra transfer nsfer in a solid or a stationary stationary flu fluid id (gas or liquid) liquid) due to the random the random motion of motion of its constituent atoms, molecules and /or  electrons.  MOLECULAR DIFFUSION Convection: Heat transfer due to the combined influe influence nce of   bulk bulk and random motion for motion  for fluid flow over a surface.  MOLECULAR DIFFUSION + ADVECTION Radiation Radi ation::

Ener Energy gy that is emitted is emitted by matter  due   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 originates from matter matter,, its transport does not require a material medium and occurs most efficiently in a vacuum. 4

5

Conduction through a stagnant gas by molecular diffusion

6

Conduction:

Heat transfe transferr b molecu molecular lar diffusi diffusion on

General (vector) form of   Fourier’s Fourier’s Law:

q  k T  Heat flux

W/m

2

Thermal conductivi ctivity ty Thermal condu

W/m  K

°C/m or K/m

Application to one-dimensional, to  one-dimensional, steady conduction steady  conduction across a  plane wall of constant thermal ther mal conductivity: con ductivity:

q x    k dT dx

  k  T2  T1

L

In this specific case, the temperature profile is linear.

q x   k

rate (W):  (W): Heat rate

qx

T1  T 2  L

 

qx A 7

HEAT TRANSFER THROUGH A PLANE WALL Calculate the heat transfer rate.

8

Convection

Heat transfer by conduction PLUS advection

Relation of convec Relation convection tion to flow over a surfac surfacee and develop development ment of   velocity and velocity  and thermal  thermal boundary layers:

Newton’ss law of cooling:  Newton’

q  h T

T

s

h : Convection heat transfer     2  K) coefficient (W/m

9

Examples of Convective Heat Transfer

Free

Convection

Forced Convection

Boiling

Condensation

10

11

12

THERMAL RADIATION: heat transfer by electromagnetic waves

The electromagnetic spectrum:

13

14

Heat transfer at a gas/surface interface involves radiation emission from emission from the surface and may also involve the radiation  incident from the surroundings absorption of radiation incident (irradiation, irradiation, G ), as we well ll as con conve vect ction ion  if T s  T   .  due to emission: to  emission: Energy outflow due Energy outflow 4  E   Eb   T s  E  : Emissive   power  r    W/m2   :Surf ace emissi   vity  0     1

E b : Emissive power of a  blackbody (the perfect emitter) 

: Stefan Stefan-B -Bol oltzm tzmann ann cons consta nt  5. 5.67 67×1 ×10 0-8 W/m W/m2  K 4    tant

due to irradiation: to  irradiation: Energy absorption due Energy absorption Gabs   G Gabs :Absorbed incident radiation ( W   /m 2 )

: Surface absorpti   vity  0     1 G : Irradiation  W/m 2 

15

Example:

16

17

Transmissivity

18

Special case of case  of surface exposed to large to  large surroundings of surroundings  of uniform temperature, T

sur

G G sur

4

  T

sur

If 

  ,

the net radiation heat flux from the

surface surfa ce due to exchange with the surroundings is: qrad

  Eb

Ts    G    T  s4  Tsu4r 

<<< a very useful approximation

19

Alternatively,

hr Ts

 Tsur



hr : Radiation heat transfer coefficient  W/  m 2  K  hr

 

Ts  Tsur  Ts2  Tsu2r  

q  qconv

h T s

 T  hr

20

Ts  Tsur  

21

Problem: Electronic Cooling

Problem Proble m 1.40: Power diss dissipation ipation from chips operati operating ng at a surfac surfacee temperatur temperaturee of 85C and in an enclosure whose walls and air are at 25 C for  (a) free convection and (b) forced convect convection. ion. Schematic:

conditions, (2) Radiation exchange between a small surface and a large a  large enclosure, (3) enclosure,  (3) Assumptions: (1) Steady-state (1) Steady-state conditions,  Negligible heat transfer  from   from sides of chip or from back of chip by chip  by conduction through the substrate. Analysis:

Pe le c

q co n v

A  L2

 0.015m 

q ra d 2

4 hA T s  T    A  Ts4  Tsur   

2.25×10-4 m 2

(a) If heat transfer is by natural by  natural convection, 5/ 4

 CA

T s  T  

5/ 4

= 4.2W  /m 2  K 5/4  2.25 1 0-4 m 2   60K 

0.60  2 2..25 10 m -4

2

 5.67×10

-8

W W//m

2

K

4

358

4

 298

4

K

= 0.158W 4

= 0.065W

use absolute temperature in radiation calculations

P elec

0.158W + 0.065W = 0.223W

(b) If heat transfer is by forced by  forced convection,

qconv  P

hA T s

 T   

3.375W 5W  3.37

250W /m 2  K 4  2.25 1 10 0-4 m 2   60K   3.375W

+ 0.065W 0.065W  3.44W 3.44W

elec

22

CONSERVATION OF ENERGY (First Law of Thermodynamics)

ROL L VO VOLU LUME ME APPLICA APPL ICATION TION TO A CONT CONTRO •

At an  Instant of Time:  Note representation repr esentation of system by a line) at  at the boundaries. boundaries. control surface (dashed line)

Surface Phenomena

 in  out : ,

E E

rate of thermal and/or m mechanic echanical al energy transfer across the control   surface due to heat transfer, fluid   flow and/or work interac tions.

Volumetric Phenomena

  g  :  E

rate of thermal ener gy generation due to conversion from another energy form (e.g., electrical, nuclear, or chemical); energy conversion proc ess occurs within the system.

 st :

rate of  chang     e o f  energy  storage   in the system.

Conservation of Energy  in  E out  E  g   dE st  E   st dt

Each term has units of J/s or W. • Ov Over er a  Time Interval

Storage = Inflow - Outflow + Generation

Ein  Eout  E g   E st Each term has units of J. 23

Examplee 1.4: Appli Exampl Application cation to thermal respon response se of a conductor with Ohmic heating (generation):

energy and  and for an incompressible substance. • Involves Involves change change in thermal in thermal energy

dU t  dt

  Mc

dT   dt

• Heat transfer transfer is from the conductor  conductor   done on the system • Genera Generation tion may may be viewed viewed as electrical as electrical work  done

24

25

26

THE SURFACE ENERGY BALANCE A specia speciall case for which no volume or mass is encompasse encompassed d by the control surf surface. ace. Conservation of Energy

out  Ein  E    0

also, there may be heat generation directly at the surface

Storage = 0 always !

• With With no mass and volume, volume, energy storage and generation generation are not pertinent pertinent to the energy  balance, even if they occur in the medium bounded by the surface. Considerr surface of wall with heat transfer Conside transfer by conduction, conduction, convection convection and radiation.

qcond  qconv  qrad   0 k

T1  T 2

27

L



 h T2  T    2  T24  Ts4ur      0

28

METHODOLOGY OF FIRST LAW LAW ANAL ANALYSIS YSIS • On a  schematic  schematic of  of the system, represen representt the the control  control surface surface by  by dashed line(s).

• Choose the app appropriat ropriatee time basis. basis.

storage  terms •  Identify relevant energy transport, energy  transport, generation and/or storage terms  by labeled  by  labeled arrows on arrows  on the schematic.

• Wr Write ite the go governing verning fform orm of the the Conservation  Conservation of Energy Energy requirement.  requirement.

• Subst Substitute itute appropr appropriate iate expres expressions sions for terms of the energ energy y equation.

• Solve for th thee unknown qua quantity ntity.. 29

30

PROBLEM 1.85 KNOWN:

Solar collector designed to heat heat water operating under pres prescribed cribed solar irradiation and loss loss

conditions. FIND:

(a) Useful heat collected per unit area of the collector, collector, q ′′ u ,  (b) Temperature rise of the water

flow, To − Ti , and (c) Collector efficiency.  SCHEMATIC:

ASSUMPTIONS:

(1) Steady-state conditions conditions,, (2) No heat losses out sides o orr back of collector, (3) Collector area is small compared to sky surroundings.

PROPERTIES:  Table A.6 ,

Water (300K): c p = 4179 J/kg⋅K.

ANALYSIS:

(a) Defining the collector as the the control volume and writi writing ng the conservation of energy requirement on a per unit area basis, find that & E in

& −E out +

& E gen

=

& E st .

Identifying processes as per above right sketch,

q s′′ola  r

−q   ′′ ′′ rad  − q  c′′on v − q  ′′  u =

0

where q s′′ola  r = 0.9  q s′′; that is, 90% of the solar flux flux is absorbed in the collecto collectorr (Eq. 1.6). Using the appropriate rate equations, the useful heat rate per unit area is

(

)

4 − h ( Ts − T∞ ) 0.9 qs′′ − εσ  Tc4p − Tsky   W W W o − 0.94 × 5.67 ×10 q′u′   = 0.9 × 700 10−8 3034 − 2634 K 4 − 10  30 − 25 ) C ( m2 m2 ⋅ K 4 m2 ⋅ K

q′u′

=

(

q ′′  ′′ u   = 630 W / m

2

− 194

2

W/m

− 50

W/m

2

=

)

2

386 W / m .

u ⋅ A.   Defining a control volume about the water tubing, the (b) The total useful heat collected is q ′′ useful heat causes an enthalpy enthalpy change of the flowing water. That is,  & c (T q′u′   ⋅ A=m p i

− To

)

or

( Ti − To ) = 386 W/m2 × 3m 2 / 00..01kg/s × 4179J/kg ⋅ K=27.7

2

2

o

C.

(

(c) The efficiency is  η  =  q u / qS = 386 W/m COMMENTS:

)  / ( 700 W  /m )

=

0.55 or 55%.

Note how the sky has been treated as large surroundings at a uniform uniform temperature

Tsky.

31

Problem: Silicon Wafer

Problem Proble m 1.57: Therma Thermall processi processing ng of silicon wafers in a two-zone furnace. furnace. Determine (a) the initial rate of change of the wafer  temperature and (b) the steady-state temperature.

KNOWN:   Silicon

wafer positioned positioned in furnace with top and bottom surfaces exposed exposed to hot and cool zones, respectively. FIND:   (a)

Initial rate of change of the wafer temperature from a value of  T w,i     300K,   and (b)

steady-state temperature. Is convection significant? steady-state significant? Sketch the variation of wafer temperature with vertical distance. distance.

SCHEMATIC:

32

Problem: Silicon Wafer (cont.) ASSUMPTIONS:   (1)

Wafer temperatu temperature re is uniform, (2) Hot and cool zones have uniform 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 include includess convection to the upper (u) and lower  (l) surfaces from the ambient gas, radiation exchange exchange with the hot- and cool-zones and an energy storage term for the transient condition. Hence, from Eq. (1.12c ),

 st  E in  E out  E

Notice how the convection terms are handled.

or, per unit surface area

d T w qrad, h  qrad,c  qcv,u  qcv,l       cd   dt  

4 4 4  Tw4     Tsur,   u Tw  T   hl Tw  T   c   Tw   h Tsur, h  

 cd

d T w     dt

(a) For the initial condition, the time rate of change of the wafer temperature temperature is deter determined mined using the foregoing energy balance with Tw   T w,i  300K, 0.65  5.67  10

8

2

W / m K

4

15004   3004  K4  0.65  5.67  108 W / m2  K 4 3304   3004  K4

300  700  K   8 W / m2  K  33000  700  K  4 W / m2  K  30 27 2700kg 00kg / m3  87 875J 5J / kg  K 0.00   078 m  dTw / dt   /dt  t     104 K / s  dTw /d i

<

## Recommended

#### Heat Transfer

Or use your account on DocShare.tips

Hide