kuliah-3 fundamental of convection3

8/12/2019 Kuliah-3 Fundamental of Convection3

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Nazaruddin SinagaLaboratorium Efisiensi dan Konservasi Energi

Fakultas Teknik Universitas iponegoro


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2

Convection

Bulk movement of thermal energy in fluids


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3

Hot Water Baseboard Heating and

Refrigerators


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Cold air sinks

Where is thefreezercompartment put in

a fridge?

Freezercompartment

It is put at the top,because cool air

sinks, so it cools thefood on the way

down.

It is warmer at

the bottom, sothis warmer air

rises and aconvection

current is set up.


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Convection

What happens to the particles in a liquid or a gas when you

heat them?

The particles spread out and becomeless dense.

This effects fluid movement.


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Fluid movement

Cooler, more dense, fluids sinkthrough warmer, less dense fluids.

In effect, warmer liquids and gases rise up.

Cooler liquids and gases sinks


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7

Convectionis the process in which heat is carried from

place to place by the bulk movement of a fluid.

Convection currentsare set up when a pan of water is

heated.

Convection


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Why is it windy at the seaside?


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Theory of Convection Heat Transfer : Newtons

Law & Nusselts Technology


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Concept of Solid Fluid Interaction : Maxwells Theory

Diffuse reflection

U2

UU

U2

U1

U1

U2

Specular reflection

Perfectly smooth surface (ideal surface) Real surface

The convective heat transfer is defined for a combined solid and fluid

system.

The fluid packets close to a solid wall attain a zero relative velocity close to

the solid wall : Momentum Boundary Layer.


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The fluid packets close to a solid wall come to thermal

equilibrium with the wall.

The fluid particles will exchange maximum possible energy

flux with the solid wall.

A Zero temperature difference exists between wall and

fluid packets at the wall.

A small layer of fluid particles close the the wall come to

Mechanical, Thermal and Chemical Equilibrium With solid

wall.

Fundamentally this fluid layer is in Thermodynamic

Equilibrium with the solid wall.


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Physical Mechanism of

Convection Heat Transfer

Convection is the mechanism of heat transfer inthe presence of bulk fluid motion.

It can be classified as:

1) Natural or free convection:The bulk fluid motion is due to buoyant force caused by densitygradient between the hot and cold fluid regions. The temperature &velocity distributions of free convection along a vertical hot flatsurface is shown in figure below.

Ts

T T


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13

2) Forced convection :

The bulk fluid motion is caused by external means, suchas a fan, a pump or natural wind, etc.

u

U


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14

The properties of the flow fields

Due to the properties of fluid both velocity and thermalboundary layers are formed. Velocity boundary layer iscaused by viscosity and thermal boundary layer iscaused by both viscosity and thermal conductivity of the

fluid.

Internal versus external flow

- External flow : the solid surface is surrounded by the

pool of moving fluid- Internal flow : the moving fluid is inside a solid channel

or a tube.


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The properties of the flow fields

Laminar flow versus turbulent flow

- Laminar flow: the stream lines are approximately parallel toeach other

- Turbulent flow: the bulk motion of the fluid is superimposed

with turbulence

u


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Heat Transfer in Equilibrium Layer

The thickness of stagnant layer decides the magnitude of normal temperaturegradient at the wall.

And hence, the thickness of wall fluid layer decides the magnitude of convectiveheat transfer coefficient.

Typically, the convective heat transfer coefficient for laminar flow is relativelylow compared to the convective heat transfer coefficient for turbulent flow.

This is due to turbulent flow having a thinner stagnant fluid film layer on theheat transfer surface.

At the wall for fluid layer :

layermequilibriuAcross,

TThA

y

TAk wallfluidfluid

TT

yTk

hwall

wall

fluid

At Thermodynamic equilibrium

wallwallfluid TT ,


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Estimation of Heat Transfer

Coefficient

TT

yTk

h wall

wall

fluid


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0

''

y

Acrosss y

TkTThq

Non-dimensional Temperature:

TT

TT

s

Non-dimensional length:

L

yy *

0

*

0 *scaleLength

scaleeTemperatur

yy yy

T


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0

**

y

sfluids

yL

TTkTTh

fluidy k

hL

y

0

**

0* *

y

fluid

yL

kh


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This dimensionless temperature gradient at the wall is named as

Nusselt Number:

resistanceConvection

resistanceConduction

1

h

k

L

k

hLNu

fluid

fluid

fluidy k

hLy

Nu

0

**

Local Nusselt Number


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Average Nusselt Number

avgfluid

avg

avgk

LhNu

,

Estimation of heat transfer coefficient is basically

computation of temperature profile at the wall.

A general theoretical and experimental study isessential to understand how the stagnant layer is

developed.

The global geometry of the solid wall and flow

conditions will decide the structure of stagnant layer.

Basic Geometry : Internal Flow or External Flow.


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22

The governing parameters of convection

heat transfer

Newtons law of cooling

The main objective to study convection heat transfer is todetermine the proper value of convection heat transfercoefficient for specified conditions. It depends on thefollowing parameters:

- The Bulk motion velocity, u, (m/s)- The dimension of the body, L, ( m)

- The surface temperature, Ts,oC or K

- The bulk fluid temperature, T,oC or K

( )sQ hA T T


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The governing parameters of convection

heat transfer (Cont.)

- The density of the fluid, , kg/m3

- The thermal conductivity of the fluid, kf, (W/m.K)

- The dynamic viscosity of the fluid, , (kg/m.s)

- The specific heat of the fluid, Cp, (J/kg.K)

- The change in specific weight, , (kg/(m2s2) or (N/m3)

- The shape and orientation of the body, S

The convection heat transfer coefficient can be written as

h = f( u, L, Ts, T, , kf, , Cp, , S)


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It is impossible to achieve a correlation equation forconvection heat transfer in terms of 10 variables. A betterway to reduce the number of variables is required.

Dimensionless analysis

There are 11 parameters with 4 basic units (length, m), (mass,

kg), (temperature, oC or K) , and (time, s).

Applying the method of dimensional analysis, it can be

grouped into 11- 4 = 7 dimensionless groups, they are:

3 2

2( , , , , , )

p s

p

c ThL uL g L uF S

k k T c T


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1. Nusselt number : =

2. Eckert number : =

3. Reynods number : =

4. Temperature ratio: s =

5. Grashof number : =

6. S : shape of the surface

7. Prandtl number: =

hL

k

uL

3

2

g L

pc

k

2

p

u

c T

sT

T

LNu

ReL

LGr

Pr

kE


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The Governing Parameters of

Convection Heat Transfer

The convection heat transfercoefficient can be written as:

Nu= f( Ek, ReL, s, GrL, Pr, S)


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To find Reynolds numberChoosing density (), dimension (L), surface temperature (Ts), anddynamic viscosity () as the 4 basic parameters, and velocity (u) as the

input parameter. The dimensionless number is obtained by solving the 4constants, a, b, c, & d.

13

0

( ) ( ) ( ) ( )

3 1 0

0

0

1 01, 0, 1, 1

Re

a b c d

s

a b o c d

o

L

L T u

kg kg LL C

L sL sL a b d

kg a d

C c

s dd c a b

Lu


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Simply the dimensionless equations !!!

Now we have reduced the equation involving 11

variables into a 7 dimensionless group equation.

However, 7 dimensionless groups is still too large, we

need neglecting the unimportant dimensionlessgroups.

Eckert number is important for high speed flow. It can be

neglected for our application.

If the average fluid temperature is used for getting the fluid

properties, the temperature ratio can also be discarded.


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Nu= f( Ek, ReL, s, GrL, Pr, S)

After neglecting the two unimportant

dimensionless groups, the generalconvection equation is

(Re , Pr, , )L L LNu F Gr S


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Forced Convection: the density change is very small, theGrashoff number is neglected

Natural Convection: there is no bulk fluid motion induced byexternal means, u = 0, Reynolds number is disappeared.

(Re , Pr, )L LNu F S

( , Pr, )L LNu F Gr S


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The Physical Meaning of

The Dimensionless Numbers

Nusselt NumberIt is the ratio of convection heat transfer

rate to the conduction heat transfer rate.

Consider an internal flow in a channel of

height L and the temperatures at the lowerand upper surfaces are T1 & T2, respectively.

The convection heat transfer rate is

The conduction heat transfer rate is

The ratio

&Qcov

hA(T1T

2)

&Qcond

kA

L(T

1 T

2)

NuL

&Qcov

&Qcond

hA

kA

L

hL

k

u

T1

T2

L


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The Reynolds Number

It is the ratio of inertia force to viscous force of the

moving fluid.

- Inertia force

- The viscous force

- The ratio

3 2 2 2 2

2 ( )i

L LF ma L L L u

s s

2 2

v

u uF A L L uL

y L

ReLuL uL uL


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The Prandtl Number

It is the ratio of the momentum diffusivity to the thermal

diffusivity. The momentum diffusivity is the kinematic viscosity andit

controls the rate of diffusion of momentum in a fluid

medium.

Thermal difusivity controls how fast the heat diffuses in amedium. It has the form

The ratio of the two is called Prandtl number.

Pr p

p

c

k k

c

p

k

c


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The Thermal Expansion Coefficient

It is defined as

The negative sign results from the fact that, for gases, the

change of density with respect to temperature under constant

pressure process is always negative. From ideal gas law

For ideal gas, the thermal expansion coefficient is the inverse

of the absolute temperature

1( )p

T

0p RT dp RdT RTd ( )pd

dT T

1

T


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Grashoff Number

The Grashoff number represents the ratio of

the buoyant force to the viscous force.

3

2

g LGr


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Grashof number

The change of density is

Substituting into Grashof number

The subscript L means that the characteristic length of the

Grashof number. It may be the length of the surface. Forideal gas, GrLis

( ) ( )T T T T T

3 33

2 2 2

( ) ( )L

g T T L g T T Lg LGr

3

2

( )L

g T T LGr

T

Ts

T T

Buoyant force

Viscous force


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Chapter 1 Chee 318 37

Example

Air at 20C blows over a hot plate, which is maintained ata temperature Ts=300C and has dimensions 20x40 cm.

CT 20

q

CTS300

Air

The convective heat flux is proportional to

TTq Sx"


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Chapter 1 Chee 318 38

The proportionality constant is the convection heattransfer coefficient, h (W/m2.K)

)(" TThq Sx Newtons law of Cooling

For air h=25 W/m2.K, therefore the heat flux is qx= 7,000

W/m2

The heat rate, is qx= qx. A = qx. (0.2 x 0.4) = 560 W.

In this solution we assumed that heat flux is positive when heatis transferred from the surface to the fluid

How would this value change if instead of blowing air we hadstill air (h=5 W/m2.K) or flowing water (h=50 W/m2.K)


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The nd

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kuliah-3 fundamental of convection3

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