Nazaruddin Sinaga

Laboratorium Efisiensi dan Konservasi Energi

Fakultas Teknik Universitas Diponegoro

2

Convection

• Bulk movement of thermal energy in fluids

3

Hot Water Baseboard Heating and Hot Water Baseboard Heating and RefrigeratorsRefrigerators

Cold air sinks

Where is the freezer

compartment put in a fridge?

Freezer compartment

It is put at the top, because cool air sinks, so it cools the food on the

way down.

It is warmer at the bottom, so this warmer air

rises and a convection

current is set up.

ConvectionConvectionWhat happens to the particles in a liquid or a gas when you heat them?

The particles spread out and become less dense.

This effects fluid movement.

Fluid movement

Cooler, more dense, fluids sink through warmer, less dense fluids.

In effect, warmer liquids and gases rise up.

Cooler liquids and gases sinks

7

Convection is the process in which heat is carried from place to place by the bulk movement of a fluid.

Convection currents are set up when a pan of water is heated.

ConvectionConvection

Why is it windy at the seaside?

Theory of Convection Heat Transfer : Newton’s Law & Nusselt’s Technology

Concept of Solid Fluid Interaction : Maxwell’s Theory

Diffuse reflection

U2

U U

Φ

U2

Φ

U1

U1

Φ

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.

• 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 in the 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 density gradient between the hot and cold fluid regions. The temperature & velocity distributions of free convection along a vertical hot flat surface is shown in figure below. Ts

T∞

T∞

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2) Forced convection : The bulk fluid motion is caused by external means, such as a fan, a pump or natural wind, etc.

u

U

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The properties of the flow fields

• Due to the properties of fluid both velocity and thermal boundary layers are formed. Velocity boundary layer is caused by viscosity and thermal boundary layer is caused 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 to

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

with turbulence

u

Heat Transfer in Equilibrium LayerHeat Transfer in Equilibrium Layer

• The thickness of stagnant layer decides the magnitude of normal temperature gradient at the wall.

• And hence, the thickness of wall fluid layer decides the magnitude of convective heat transfer coefficient.

• Typically, the convective heat transfer coefficient for laminar flow is relatively low compared to the convective heat transfer coefficient for turbulent flow.

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

At the wall for fluid layer :

layer mequilibriu Across,

TThAyTAk wallfluidfluid

TT

yTk

hwall

wall

fluid

At Thermodynamic equilibrium

wallwallfluid TT ,

Estimation of Heat Transfer Estimation of Heat Transfer CoefficientCoefficient

TT

yTk

hwall

wall

fluid

0

''

yAcrosss y

TkTThq

Non-dimensional Temperature:

TTTT

s

Non-dimensional length:Lyy *

0*

0 *scaleLength scale eTemperatur

yy yyT

0

**

y

sfluids yL

TTkTTh

fluidy khL

y

0*

*

0*

*

y

fluid

yLk

h

This dimensionless temperature gradient at the wall is named asNusselt Number:

resistance Convectionresistance Conduction

1

h

kL

khLNu fluid

fluid

fluidy khL

yNu

0

**

Local Nusselt Number

Average Nusselt Numberavgfluid

avgavg k

LhNu

,

• Estimation of heat transfer coefficient is basically computation of temperature profile at the wall.

• A general theoretical and experimental study is essential 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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The governing parameters of convection heat transfer

• Newton’s law of cooling

• The main objective to study convection heat transfer is to determine the proper value of convection heat transfer coefficient for specified conditions. It depends on the following 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, ρ , kg/m3

- The thermal conductivity of the fluid, kf, (W/m.K) - The dynamic viscosity of the fluid, μ , (kg/m.s) - The specific heat of the fluid, Cp , (J/kg.K) - The change in specific weight, Δ, (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∞, ρ, kf , μ, Cp, Δ , S)

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• It is impossible to achieve a correlation equation for convection heat transfer in terms of 10 variables. A better way 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 Sk k T c T

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1. Nusselt number : = 2. Eckert number : = 3. Reynods number : =

4. Temperature ratio : θs =

5. Grashof number : =

6. S : shape of the surface

7. Prandtl number : =

hLk

uL

3

2

g L

pck

2

p

uc T

sTT

LNu

ReL

LGr

Pr

kE

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The Governing Parameters of Convection Heat Transfer

• The convection heat transfer coefficient can be written as:

Nu = f( Ek , ReL, θs , GrL , Pr, S)

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• To find Reynolds number Choosing density (ρ), dimension (L), surface temperature (Ts), and dynamic

viscosity (μ) as the 4 basic parameters, and velocity (u) as the input parameter. The dimensionless number is obtained by solving the 4 constants, a, b, c, & d.

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0

( ) ( ) ( ) ( )

3 1 00

01 0

1, 0, 1, 1

Re

a b c ds

a b o c d

o

L

L T ukg kg LL CL sL s

L a b dkg a d

C cs 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 dimensionless groups.

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, θs , GrL , Pr, S)

After neglecting the two unimportant dimensionless groups, the general convection equation is

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

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

• Natural Convection: there is no bulk fluid motion induced by external 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 Number It 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 lower and upper surfaces are T1 & T2, respectively.

The convection heat transfer rate is

The conduction heat transfer rate is

The ratio

&Qcov hA(T1 T2 )

&Qcond

kAL

(T1 T2 )

NuL &Qcov&Qcond

hAkAL

hLk

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 22 ( )i

L LF ma L L L us s

2 2v

u uF A L L uLy 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 and it

controls the rate of diffusion of momentum in a fluid medium.

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

The ratio of the two is called Prandtl number.

Pr p

p

ck kc

p

kc

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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 ( ) pT

0p RT dp RdT RTd ( ) pddT T

1T

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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. For ideal gas, GrL is

( ) ( )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 LGrT

Ts

T∞

T∞

Buoyant force

Viscous force

Chapter 1 Chee 318 37

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

CT 20

q”

CTS300

Air

The convective heat flux is proportional to

TTq Sx"

Chapter 1 Chee 318 38

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

)(" TThq Sx Newton’s 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 heat is transferred from the surface to the fluid

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

The EndThe End

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