01. introduction overview of mechanisms

7/28/2019 01. Introduction Overview of Mechanisms

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1. INTRODUCTION

Examples of Heat Transfer Problems

(1) Slide Projector,

(2) Ice Storage(3) Re-entry Aerodynamic Heating

(4) Pot Handle

(5) Under-window radiator of heating system

(6) Refrigerator

Focal Point in Heat Transfer

Determination of the temperature distribution in a region


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Modes of Heat Transfer

(ii) Convection: by mass motion

(iii)Radiation: by electromagnetic waves

Conduction: Fourier's LawS= wall area

L L = wall thickness

siT T1= inside surface temperature

soT T2= outside surface temperature

Is proportional toS? How?Q&

Is proportional toL ? How?x

Q&

Is proportional to (T1 - T2)? How?Q&

(i) Conduction: by molecular or atomic activity

Fig.1.1

x

xq

L

dx

siTsoT

A

0

Q&

S [m2]

T1 T2


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is called thermal conductivity, a property of material Equation (1.1) is valid for: (i) steady state, (ii) one-

dimensional conduction and (iii) constant .Reformulation of (1.1): Apply (1.1) to an element dx:

dx

T(x)dx)+T(xS=

dx

dx)+T(xT(x)S=Q

x

&

dxT(x),T1 dx),T(xT2 +

L

TTSQ 21

x

=& 1.1.[W]

Heat Transfer Rate (tepeln tok)


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(1.2) becomes

dxdTq

x=& (1.4)

For 3-D:

Equation (1.5) is known as Fourier's law

,x

Tq

x

=& ,

y

Tq

y

=&

z

Tq

z

=& (1.5)

Definition: Heat flux (mrn tepeln tok)x

q&

(1.2)dx

dTS=Q

x& [W]

S

Qq x

x

&

& = (1.3)[W/m2]


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Convection: Newton's Law of Cooling

Convection: Energy is transported by means of massmotion

Classification:

(1) Free convection

(2) Forced convection

Heat exchange between a surface and a fluid movingover it

TTq

ww&

where

wT = surface temperature

T = fluid temperature far away from the surface

wq& = surface (wall) flux [W/m2] (mrn tepeln tok)

T

sTw

Twq&


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Rewrite:

(1.6)= TTq ww

This isNewton's law of cooling.

NOTE:(1) is called heat transfer coefficient

(2) It is a defined quantity

(3) It depends on geometry, fluid properties and

motion

(4) To determine , the temperature distribution in the

fluid must be known

(5) Major objective in convection: Determination of

(souinitel pestupu tepla)


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Typical Values of Table 1.1Typical values of

5 - 30

20 - 1000

20 - 300

50 - 20,000

5,000 - 50,000

2,000 - 100,000

5,000 - 100,000

Free Convection

Gases

Liquids

Forced ConvectionGases

Liquids

Liquid metals

Phase change

Boiling liquids

Condensation

(W/m2 K)ProcessImportant:

problems.solve

tovaluestheseusenotDoonly.guide

aastablethisUse


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Radiation: Stefan-Boltzmann Law Transmission by electromagnetic waves

No medium is needed. Best in a vacuum

Maximum possible radiation: By an idealsurfacecalled blackbody.

Stefan-Boltzmann law for blackbody radiation flux:

T = surface temperature, measured in absolute degrees

(Kelvin)

=Stefan-Boltzmann constant

(1.7)4

0TE = [W]

= blackbody radiation flux (zivost)0E


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= 5.67 x 10-8

W/m2

-K4 (1.8)

Real surface:

E= radiation flux (zivost edho povrchu)

Emissivity, , a surface property defined as(1.9)

0E

E=

Combining (1.7) and (1.9)

4TE= (1.10)


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12Q& = Energy exchange between two surfaces

Absorptivity (absorptance) a : Fraction of radiationincident on a surface which is absorbed

Simplified model: Gray surface: = aSpecial case: A small gray surface enclosed by a much

larger surface

(1.11))T(TSQ 42

4

11112=&

( )1= small surface, ( )

2= large surface

Energy Exchange Between Two Bodies:

A Simplified Model


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Properties

Heat transfer depends on material and surface

properties as:

Conductivity Density

Viscosity

Specific heat Emissivity


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Example: Application of Problem SolvingMethodology

Square transistor is mounted

on a circuit board. Transistorsurface is cooled by convection.

Size, dissipated power, heat

transfer coefficient and ambienttemperature are known.

(1) Observations

(i) Schematic diagram

Determine surface

temperature.

T sT

board

transistor

1.3Fig.


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(ii) Dissipated electric energy is removed by

convection and radiation

(iii) Surface temperature is higher than ambient

temperature

(iv) Increasing dissipated power increases surface

temperature

(2) Problem DefinitionFind the relationship between power and surface

temperature

(3) Solution Plan

Apply Newton's law of cooling to the surface of the

transistor.


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(4) Plan Execution

(i) Assumptions(1) Steady state

(2) Dissipated electric energy leaves transistorsurface (no energy leaves from the back side)

(3) Negligible heat loss by radiation

(4) Uniform surface temperature

(5) Uniform heat transfer coefficient

(6) Constant ambient temperature

(ii) Analysis

Newton's law of cooling:

T sT

board

transistor

1.3Fig.


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= heat transfer coefficient = 8 K][W/m2

wq& = surface heat flux, 2W/m

wT = ? surface temperature, Co

T = ambient air temperature = 26 Co

Conservation of energy and assumptions (2) and (3):

surfacefromremovedHeatpowerDissipated =

wqSP &= (b)

S= surface area = 1 (cm) 1 (cm) = 1 = 0.0001 m2

(a)

= TTqww

&


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P= power dissipated in transistor = 0.04 W

(b) into (a)

)T(TS

Pw = (c)

Solving forw

T

S

TT

w

+=

(d)

(iii) Computations

(d) gives

C768.0,0001

0,0426

wT

o

=+=


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(iv) Checking

Dimensional check: Equation (d) is dimensionallycorrect. Each term has units of temperature.

Qualitative check: Equation (d) behaves correctly:

wT Decreasing the surface area increases

Decreasing increasesw

T

Limiting checks: Power off (P= 0): surface temperature = ambient

temperature

IncreasingPincreasesw

T

(d)S

PTT

w+=

If = 0 ( no heat is removed) then wT


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(5) Learning and Generalizing

< 85

o

CwT(i)

(ii) Examine assumptions (2) and (3):

Heat removed from the back side lowerscalculated

w

T

Radiation heat loss lowers calculatedw

T

(2) no energy leaves from the back side

(3) negligible heat loss by radiation


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)dt

dum

dt

dU(

dt

dEEEEE akakoutgin ====+&&&& [W]

Requirements for Energy Conservation

a) Balance for Energy flux

in every moment, [W].

b) Balance for amount

of heat, [J]. akoutginEEEE =+ [J]

Energy Conservation for a Control Volume


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Requirements for Energy Conservation

Energy Conservation for a Control Surface

0EEoutin

= &&

01. introduction overview of mechanisms

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