lecture slide 06

IUBAT- International University of Business Agriculture and Technology

Founded 1991 by Md. Alimullah Miyan

COLLEGE OF ENGINEERING AND TECHNOLOGY(CEAT)

Course Title: Heat and Mass Transfer

Course Code : MEC 313

Course Instructor: Engr. Md. Irteza Hossain

Engr. Md. Irteza Hossain

Faculty, BSME

PHYSICAL MECHANISM OF CONVECTION

Conduction and convection both

require the presence of a

material medium but convection

requires fluid motion.

Heat transfer through a solid is

always by conduction.

Heat transfer through a fluid is

by convection in the presence of

bulk fluid motion and by

conduction in the absence of it.

Therefore, conduction in a fluid

can be viewed as the limiting

case of convection,

corresponding to the case of

quiescent fluid.Engr. Md. Irteza Hossain

Faculty, BSME

• We turn on the fan on

hot summer days to help

our body cool more

effectively. The higher

the fan speed, the better

we feel.

• We stir our soup and

blow on a hot slice of

pizza to make them cool

faster.

• The air on windy winter

days feels much colder

than it actually is.

convection in daily life


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Principles of Convection

• Physical Mechanism of Convection:

• Heat transfer through a solid is always by conduction, since the

molecules of a solid remain at relatively fixed position.

• Heat transfer through a liquid or gas however can be by

conduction or convection depending the presence of any bulk

fluid motion.

• Heat transfer through a fluid is by convection in presence of

bulk fluid motion and by conduction in the absence of it.

Therefore conduction in a fluid can be viewed as the limiting

case of convection.


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Dimensionless Parameters of Heat Transfer

• For the calculation of heat transfer coefficient, a large

number of parameters needed

• This can make the equations difficult to comprehend

and hard to remember

• However both theoretical consideration and

experimental investigations have that in a lot of

cases the parameters may be grouped together to

form a small number of dimensionless similarity

parameters, which can be used for building simple

equations by which heat transfer coefficient may be

calculated.

• The most important of these dimensional less

parameters are presented herewith


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Some important Dimensionless parameters

• Reynolds number:

The Reynolds number is defined as

Where = Velocity of Fluid ( m/sec)

= Characteristic length( m), for a tube x=d

= Kinematic viscosity of fluid ( m2/sec)

• The size of Renold’s number determines whether fluid flow is

laminar or turbulent.

• It thus is said to characteristic the flow. A low Renolds number

indicate laminar flow, while a high Renolds number a turbulent

flow.

• Renolds number determines the ratio of the inertia and viscous

forces in flow.

v

uxRe

ux


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• Nusselt Number:

The Nusselt Number is defined as

h = Surface heat transfer coefficient (W/m2oC)

x = Characteristic length ( m)

k= Thermal conductivity (W/moC)

The Nusselt number can be described as a dimension less

temperature gradient at the surface.

• It is the Nusselt number that is determined by the equations

correlating the dimensionless number.

• When Nu is found, the heat transfer coefficient can easily be

calculated from the definition

k

xhNu

.


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• Prandtl number :

The definition of the Prandtl number is

• The prandtl number contains only thermodynamic data of the

fluid and is thus in itself a thermodynamic property of the fluid

• It is also interpreted as the ratio between the momentum

diffusivity and the thermal diffusivity according to the

definition

• For laminar flow it Pr gives an indication of the relative

thickness of the thermal and velocity boundary layer

Pr

)./(

)/(cos

)/(

)/(

)/(cos

.Pr

2

2

2

CmWtyconductivithermalk

mSNityDynamicVis

CkgJheatSpecificC

smydiffusivitThermal

smuidityoftheflVisKinematic

k

C

o

op

p


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• Graetz Number:

The Graetez Number is defined as:

Gz=Re.Pr. d/x

Where d = ( hydraulic ) diameter of Channel(m)

x = distance from entrance of Channel(m)

This number is used when calculating heat transfer in

Laminar flow in tube.


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Principles of Convection

• Velocity Boundary Layer:

Consider the parallel flow of a fluid over a flat plate

as shown in the figure. Surfaces that are contoured

such as turbine blades can also be approximated as

flat plate with reasonable accuracy.

• The x- co ordinate is measured along the plate

surface from the leading edge of the plate in the

direction of flow and y is measured from the surface

in the normal direction.

• The fluid approaches the plate in the x- direction

with an uniform velocity V, which is practically

identical to the free stream velocity over the plate

away from the surface


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Velocity Boundary Layer:

• Velocity Boundary Layer:

• The fluid of the adjacent layers piled up on top each other

• The velocity of the particles in the first fluid layer adjacent to

the plate becomes zero because of the no slip condition.

• This motionless layer slows down the particles of the

neighboring layer as a result of friction between the particles of

these two adjoining fluid layers at different velocities.Engr. Md. Irteza Hossain

Faculty, BSME


• The Fluid layer then slows down the molecules of the next

layer and So on.

• Thus the presence of the plate is felt up to some normal

distance from the plate beyond which the free stream

velocity remains essentially unchanged.

• As a result the x- component of the fluid velocity , u varies from

0 at y=0 nearly V at y=

The region of the flow above

the plate bounded by in which

the effects of the viscous

shearing forces caused by fluid

viscosity are felt is called the Velocity

Boundary layer.


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Wall Shear Stress Shear stress: Friction force per unit area.

The shear stress for most fluids is

proportional to the velocity gradient, and

the shear stress at the wall surface is

expressed as

The fluids that obey the linear

relationship above are called Newtonian

Fluids.

Most common fluids such as water, air,

gasoline, and oils are Newtonian fluids.

Blood and liquid plastics are examples

of non-Newtonian fluids. In this text we

consider Newtonian fluids only.

dynamic viscosity

kg/m s or N s/m2 or Pa s

1 poise = 0.1 Pa s


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• Near the front edge of the plate the thickness of the boundary

layer is thin and it then grows successively thicker

• As long as the boundary layer is thin, there is no mixing

between layers at different distances from the plate, the flow is

said to be laminar.

• In the laminar layer region, the velocity profile is approximately

parabolic

• At some distances from the leading edge, the laminar layer will

become unstable, and eddies will develop, mixing in the

different layers. The flow is then becoming Turbulent.

• Because of the mixing, the difference in velocity between layers

is much smaller in turbulent flow than in Laminar flow. Thus

the velocity profile is much flatter in turbulent flow


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•Even in the turbulent region there is a laminar sub layer

closet to the surface

• For the flow across a Flat plate, the type of flow , laminar or

turbulent, can be determined from the Renolds number

•For the flow across a Flat plate, The transition from laminar to

turbulent occurs when Re > 5 x 105


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Flow Across Tubes

• Consider the flow in a tube as shown in the figure.

• A boundary layer fills the entire tube and the flow is said to be

fully developed.

• If the flow is laminar, a parabolic velocity profile is experienced

as shown in figure 5.3 a

• When the flow is turbulent, a some what blunter profile is

observed as shown in figure 5.3 b

• Transition from laminar flow to turbulent takes place at

Re>2300Engr. Md. Irteza Hossain

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Thermal Boundary Layer

• The velocity boundary layer is developed because of the

viscous action in the fluid close to a wall.

• If the wall is heated or cooled there will also developed a

thermal boundary layer in which the temperature change from

the wall temperature to the temperature of the undisturbed fluid

• Consider the flow of a fluid at a uniform temperature T∞ over

an isothermal flat plate at Temperature Ts

• The fluid particles in the layer adjacent to the surface reach

thermal equilibrium with the plate and assume the surface

temperature Ts .

• These fluid particles then exchange energy with the particles

in the adjoining fluid layer and so on

• As a result , a temperature profile develops in the flow field

that ranges from Ts at the surface to T∞sufficiently far from

the surface


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• The flow region over the surface in which the temperature

variation in the direction normal to the surface is significant is

the thermal boundary layer

• The thickness of the thermal boundary

layer at any location of the surface

is defined as the distance from the surface

at which the temperature difference

T- Ts = 0.99( T∞ - Ts )

• Special case: Ts = 0, Then T=0.99 T∞ at

the outer edge of the thermal boundary

layer, which is analogous to u=0.99V for

velocity boundary layer

• The convection heat transfer rate anywhere along the surface

is directly related to the temperature gradient at that location.

t


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• The thickness of the thermal boundary layer

increases in the flow direction, since the effects of

heat transfer are felt at greater distances from the

surface further down stream.

• The shape of the temperature profile in the thermal

boundary layer dictates the convection heat transfer

between a solid surface and the fluid flowing over it.


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Thermal Boundary Layer• The velocity boundary layer formed because of the viscous

action of the fluid close to wall.

• If the wall is heated ( or cooled) there will also develop a

Thermal boundary layer in which the temperature change from

the wall temperature to the temperature of the undisturbed

fluid.

• The shape of the thermal and velocity boundary layer in laminar

flow will be similar but the thickness will not necessarily be the

same

• The relative thickness of the two layers is related to prandal

number by ≈

• Gases: The prandal number is 0.7 - 1 and in laminar flow the

thermal and velocity boundary layer thicknesses are thus

approximately equal

)3/1exp(Pr onentpositiveaisnWhereth

vn


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• Liquid metals: ( Pr<<1) The thermal boundary layer ( in laminar

flow) is considerably thicker than the velocity boundary layer

• For oils : ( Pr>>1)The velocity boundary layer is the thickest

• For turbulent boundary layers, the mixing with in the layer will

result in more or less equal thicknesses of the velocity and

thermal boundary layers.


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Forced and Free convection

• Forced convection:

The fluid flow is by forecd( by fan or a pump, or any

other means external to the fluid itself)

For forced convection the type of flow( turbulent or

laminar) is determined from Reynolds number

• Free convection:

The fluid flow is caused by temperature induced density

differences in the fluid.

• For free convection the type of flow is determined by the

Grashof number.

• The dimensionless equations by which heat transfer

coefficient can be calculated are as follows:

In forced convection Nu= f( Re, Pr)

In Free convection Nu=f(Gr.Pr) Engr. Md. Irteza Hossain

Faculty, BSME

FORCED CONVECTION

• The Bulk Temperature:

The bulk temperature is important in all heat transfer involving

the flow inside the closed channel

• The total energy added can be expr

essed in terms of bulk – temperature

difference by

• Considering some differential length dx the heat addition dq

can be calculated either bulk temp difference or in terms of

heat transfer coefficient

• Where Tw and Tb are the wall and bulk temperature at the

particular x location

)( 12 TbTbcmq p

)()2( bwbp TTdxrhdTcmdq


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FORCED CONVECTION

• The total heat transfer can be expressed as

• A is the total heat transfer area. Because Tw and Tb can vary

along the length of the tube, a suitable averaging process must

be adopted for use with the above equation.

• In this respect we recall the concept of log mean average

temperature( LMTD)\

• The LMTD will be discussed in HE chapter

avbw TTAhq )(.


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Flow Across a Flat Plate (Laminar flow)

• The local Nusselt number at a location x for Laminar Flow over

a Flat plate is as follows:

• The Average Nusselt number over a distance L for Laminar

Flow is determined by the following( The flow is laminar whole

of the Plate):

53/1 105Re6.0PrPrRe332.0 5.0 XxK

xhNu x

x

x

53/1 105Re6.0PrPrRe664.0 5.0 XK

hLNu LL

The Fluid properties are evaluated at film temperature


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Flow Across a Flat Plate ( Turbulent Flow)

• The local Nusselt number at a location x for Turbulent Flow

over a Flat plate is as follows:

• The Average Nusselt number over a distance L for Turbulent

Flow is determined by the following ( The Flow is Turbulent

whole of the plate and laminar flow region is very shall):

• The Fluid properties are evaluated at film temperature

75

3/1

10Re105

60Pr6.0PrRe0296.0 8.0

x

x

x

x

X

K

xhNu

75

3/1

10Re105

60Pr6.0PrRe037.0 8.0

L

L

X

K

hLNu


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Forced convection – Turbulent flow in Tubes and Channels

• Fully developed Turbulent Flow in smooth tubes is

recommended by Dittus and Boelter

• Where n=0.4 for heating of the fluid

n=0.3 for cooling of the fluid

The above equation is valid developed turbulent flow in smooth

tubes with Prandtl numbers varies from 0.6 to 100 and

Re>10,000 and with moderate temperature difference between

wall and fluid conditions

• Despite of limitation to Re>10,000 it may for fluids with low

viscosity ( μ< 2. μH2

0) be used when Re>2300 i.e for whole

turbulent region

nNu Pr.Re023.0 8.0


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• Fully developed Turbulent Flow in smooth tubes is

recommended Petukhov

• Where n=0.11 for Tw>Tb

n= 0.25 for Tw <Tb

n=0 for constant heat flux or for gases

All properties are evaluated at Tf= (Tw + Tb) /2 except Viscosity

The equation is applicable for the following ranges

0.5 <Pr <200 for 6 percent accuracy

0.5 < Pr < 2000 for 10 percent accuracy

10 4< Re < 5 x 106

0.8 < <40

n

w

b

f

fNu )(

1Pr)8/(7.1207.1

PrRe)8/(3/22/1

w

b

210 )64.1Relog82.1( df


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• Entrance Region

In the entrance region the flow is not fully developed . For the

entrance region and for shot tubes( 1o<L/d<100) Nusselt

recommended the following relation

Nu=0.036 . Re 0.8. Pr1/3 . (d/L)0.055

Where L is the length of the tube and d is the diameter of the

tube

The properties are evaluated at mean bulk temperature


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Forced convection –Laminar flow in Tubes and Channels

• A some what simpler empirical relation is proposed by Sieder

and Tate for laminar flow in TUBES:

• The Average Nusselt number:

• The equation is valid for

etemperaturbulkmeantheofityvisdynamicthe

etemperaturbulkmeantheofityvisdynamicthe

L

dNu

GzNu

w

w

w

cos

cos

))(.(Pr).(Re86.1

).()(86.1

14.03

1

14.03

1

10...ReL

dGz

L

dpr


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Forced convection –Laminar flow in Tubes and

Channels

• Local and Average Nusselt numbers for circular tube thermal

entrance regions in fully developed flow

Kays,sellers have calculated the local and average Nusselt

numbers for Laminar entrance regions of circular tubes for the case

of a fully developed velocity profile.


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Heat Transfer and fluid friction for fully laminar flow in

ducts of various cross – sections

• Non circular cross sections:

If the cross section of the channel through which the

fluid flow is not circular, the above equations may

still be used.

• In that case the diameter should be calculated as

Hydraulic Diameter DH,

Where , A= Cross sectional area of Flow ( m2)

P= wetted perimeter

P

ADH

.4


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Heat Transfer and fluid friction for fully laminar flow in

ducts of various cross – sections

• Shah and London have complied the heat transfer and fluid friction

information for fully developed laminar flow in ducts with varieties

of cross section. Average Nusselt numbers based on Hydraulic

diameter of cross section


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Flow Across Cylinders• In forced convection across a cylinder, the Nusselt Number

will be different on the front and the back side.

• An average Nusselt number for he circumference can be

estimated from the following empirical relationship

f stands for film temperature

3/1

3/1

Pr)(Re

Pr)(

ff

nf

fn

ff

f

CNu

duC

k

hdNu

Ref C n

0.4-4 0.989 0.330

4-40 0.911 0.385

40-4000 0.683 0.466

4000-40,000 0.193 0.618

40,000-400,000 0.0266 0.805Engr. Md. Irteza Hossain

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Flow Across Cylinders


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Newton’s law of cooling

• The rate of loss of heat from an object to surroundings

is proportional to the temperature difference between the

object and it’s surroundings.

= Rate of heat transfer

h convection heat transfer coefficient, W/m2 · °C

As the surface area through which convection heat transfer takes place

Ts the surface temperature

T the temperature of the fluid sufficiently far from the surface.=

ConvectionQ


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PROBLEM AND SOLUTION

• In a certain glass making process, a square plate of glass 1 m2

area and 3 mm thick heated uniformly to 90 oC is cooled by air

at 20 oC flowing over both sides parallel to the plate at 2 m/sec.

Calculate the initial rate of cooling the plate.

Neglect temperature gradient in the glass plate and consider

only forced convection

Take for glass: ρ = 2500 kg /m3 and Cp = 0.67 KJ/kg oK

Take the following properties of air at 550C

ρ= 1.076 kg /m3 : Cp = 1008 J/kg oK, k=0.0286W/m o C and

μ=19.8 x10-6 N-S/m2


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• Air at 30 oC flows with a velocity of 2.8 m/sec over a plate 1000

mm ( Length) x600 mm( width) x25 mm ( thickness). The top

surface of the plate is maintained at 90 oC. If the thermal

conductivity of the plate material is 25 W/m oC, Calculate:

a. Heat lost by the plate

b. Bottom temperature of the plate for the steady state

condition

The thermo- physical properties of air at mean film temperature

(90+30)/2= 60 oC are:

ρ=1.06 kg/m3 , Cp= 1.005 KJ/Kg, k= 0.02894 W/moC ,

=18.97x 10-6 m2/s, Pr=0.696


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• In a straight tube of 60 mm diameter, water is flowing at a

velocity of 12 m/sec. The tube surface temperature is

maintained at 70 oC and the flowing water is heated from the

inlet temperature 15 oC to an outlet temperature of 45 oC.

Taking the physical properties of water as its mean bulk

temperature , Calculate the following :

1. The heat transfer co-efficient from the tube surface to the

water

2. The heat transferred

3. The length of the tube

The thermo – physical properties of water at 30 oC are:

ρ= 995.7 kg/m3 Cp=4.174 KJ/Kg oC , k=61.718 x10-2 W/m oC,

=0.805 x10-6 m2/sec, pr= 5.42


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• A long 10 cm diameter steam pipe whose external surface

temperature is 110 oC passes through some open area that is

not protected against the winds. Determine the rate of heat

loss from the pipe per unit length of its length when the air is at

1 atm pressure and 10 oC and wind is blowing across the pipe

at a velocity of 8 m/sec. At value of C and n at different

Renold’s no is given below:


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Ref C n

0.4-4 0.989 0.330

4-40 0.911 0.385

40-4000 0.683 0.466

4000-40,000 0.193 0.618

40,000-400,000 0.0266 0.805


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lecture slide 06

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