MkamalHeat Transfer II (Introduction) (1)

8/12/2019 MkamalHeat Transfer II (Introduction) (1)

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Convection Heat Transfer

Heat transfer:Heat transfer (or heat) is thermal energy in transit due to a temperature difference. According

to the 2nd law of thermodynamics heat is transferred from a higher temperature body to a

lower temperature body.

Modes of heat transfer:

(i) Conduction: Mechanism of heat transfer through a solid or fluid in the absence of any

fluid motion.

(ii) Convection: Mechanism of heat transfer through a fluid in the presence of bul fluid

motion.

(iii) !adiation: "he energy of the radiation field is transported by electromagnetic waves

#or alternatively$ photons%. !adiation heat transfer does not re&uire material medium.

Types of convection heat transfer:Convection heat transfer depends on how the fluid motion is initiated.

(i) 'atural or free convection

(ii) orced convection

Natural or free convection:

*n natural convection$ any fluid motion is caused by natural means such as the buoyancy

effect$ which manifests itself as the rise of warmer fluid and the fall of cooler fluid.

Forced convection:*n forced convection$ the fluid is forced to flow over a surface or in a tube by e+ternal means

such as a pump$ blower$ or a fan.

Newtons law of cooling:*t states that the rate of heat flow, heat transfer from a solid surface of area A$ at a

temperature "wto a fluid at a temperature "sis

Qconvection = hA (Ts-T).

Convection heat transfer coefficient (h): "he rate of heat transfer between a solid surface and

a fluid per unit surface area and per unit temperature difference is called convection heat

transfer coefficient (h).

Qconvection = hA (Ts-T)

-here$ h convection heat transfer coefficient$ -,m2.%C

Convection heat transfer coefficient strongly deends on the follo!ing fluid roerties:

(i) /y decreasing dynamic viscosity$ convection heat transfer coefficient can be

increased.

(ii) /y increasing thermal conduction$ 0 convection heat transfer coefficient can be

increased.

(iii) /y increasing specific heat$ Cp convection heat transfer coefficient can be increased.

(iv) /y increasing fluid velocity$ 1 convection heat transfer coefficient can be increased.

Convection heat transfer coefficient also deends on:


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(v) urface geometry

(vi) urface roughness

(vii) "ype of fluid flow.

Laminar and Turbulent flows:

An essential first step in the treatment of any convection problem is to determine whether theboundary layer is laminar or turbulent. urface friction and the convection transfer rates

depend strongly on which of these conditions e+ists.

"a#inar flo!:

*n the laminar flow$ fluid motion is highly ordered and it is possible to identify streamlines

along which particles move.

luid motion along a streamline is characteri3ed by velocity components in both the + and y

directions.

Tur$ulent flo!: luid motion in the turbulent flow is highly irregular and is characteri3ed by

velocity fluctuations. "hese fluctuations enhance the transfer of momentum$ energy and

species$ and hence increase surface friction as well as convection transfer rates.

luid mi+ing resulting from the fluctuations maes turbulent boundary layer thicness larger

and boundary layer profiles (velocity$ temperature) flatter than in laminar flow.

Transition flo!:"ransition flow occurs between laminar and turbulent flow. "he transition

from laminar to turbulent flow does not occur suddenly rather$ it occurs over some region in

which the flow hesitates between laminar and turbulent flows before it becomes fully

turbulent.

Transition fro# la#inar to tur$ulent deends on:(i) urface geometry

(ii) urface roughness

(iii) ree stream velocity

(iv) urface temperature

(v) "ype of fluid.

"he velocity profile is appro+imately parabolic in laminar flow and becomes flatter in the

turbulent flow with a sharp drop near the surface.

Effect of turbulence:(i) *ntense mi+ing of the fluid.

(ii) 4nhance heat and momentum transfer between fluid particles.(iii) *ncrease conduction heat transfer rate.

Types of flow:(i) *nternal flow: "he fluid is completely confined by the inner surfaces of the tube

and there is limit on how much the boundary layer grows.

(ii) 4+ternal flow: "he fluid has a free surface and thus the boundary layer over the

surface is free to grow indefinitely.

%elocity &oundary layer:


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"he region of flow that develops from the leading edge of the plate in which the effects of

viscosity are observed is called the boundary layer. ome arbitrary point is used to designate

the y position where the boundary layer ends this point is usually chosen as the y coordinate

where the velocity becomes ## percent of the free stream velocity.

luid velocity at the surface of the plate is 3ero (because of no5slip condition)$ and gradually

increases with distance from the plate. At a sufficiently large distance from the plate$ the fluid

velocity becomes e&ual to the 6free stream velocity7 1. "he region above the plate surface

within which this change of velocity from 3ero to the free stream value occurs is called the

boundary layer (velocity boundary layer) also called the hydrodynamic boundary layer. "he

thicness of this region is called the boundary layer thicness and is denoted by . "he

boundary layer thicness increases with the distance + from the leading edge of the plate$ i.e.

(+).


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*nitially$ the boundary5layer development is laminar$ but at some critical distance from the

leading edge$ depending on the flow field and fluid properties$ small disturbances in the flowbegin to become amplified$ and a transition process taes place until the flow becomes

turbulent. "he turbulent5flow region may be pictured as a random churning action with

chuns of fluid moving to and fro in all directions.

"he transition from laminar to turbulent flow occurs when

89%8>=

xuxu-here$ =u free stream velocity$ m , sec

x distance from leading edge$ m

==

0inematic viscosity$ m2,sec

'roerty variation !ith ti#e in a tur$ulent $oundary layer:


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The ther#al $oundary layer:


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A velocity boundary layer develops when there is fluid flow over a surface a thermal

boundary layer must develop if the fluid free stream and surface temperatures differ.

Consider flow over an isothermal flat plate. At the leading edge the temperature profile isuniform$ with "(y) ". However$ fluid particles that come into contact with the plate

achieve thermal e&uilibrium at the plate7s surface temperature. *n turn$ these particles

e+change energy with those in the ad;oining fluid layer$ and temperature gradients develop in

the fluid. "he region of the fluid in which these temperature gradients e+ist is the thermal

boundary layer$ and its thicness is defined as t. -ith increasing distance from the leading

edge$ the effects of heat transfer penetrate further into the free stream and the thermal

boundary layer grows.

ignificance of the $oundary layers:


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"he velocity boundary layer is of e+tent ( )x and is characteri3ed by the presence of

velocity gradient and shear stresses. "he thermal boundary is of e+tent t(+) and is

characteri3ed by temperature gradients and heat transfer. "he principle manifestations of the

two boundary layers are$ respectively$ surface friction$ convection heat transfer. "he ey

boundary layer parameters are then the friction coefficient C fand the heat transfer convection

coefficient h$ respectively.

or flow over any surface$ there will always e+ist a velocity boundary layer$ and hencesurface friction. However$ a thermal boundary$ and hence convection heat transfer$ e+ists

only if the surface and free stream temperatures differ.

The #ean velocity:

"he velocity various over the cross section and there is no well5defined free stream$ it is

necessary to wor with a mean velocity mu when dealing with internal flows. "his velocity

is defined such that$ when multiplied by the fluid density and the cross sectional area of

the tube Ac$ it provides the rate of mass flow through the tube. Hence cm Aum = .

Flow in tubes:"he fluid velocity in a tube changes from 3ero at the surface to a ma+imum velocity at the

tube centre. A boundary layer develops at the entrance. 4ventually the boundary layer fills

the entire tube$ and the flow is said to be fully developed. *f the flow is laminar$ a parabolic

velocity profile is e+perienced. -hen the flow is turbulent$ a blunter profile is observed. *n a

tube$ the !eynolds number is again used as a criterion for laminar and turbulent flow.

or


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.2=

dumd "he flow is usually observed to be turbulent and where d is the tube

diameter.

Again$ a range of !eynolds numbers for transition may be observed$ depending on the

surface roughness and smoothness of the flow. "he generally accepted range for transition is

.=%%%!e2%%%


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m

8%>a

wor with the Moody (or ?arcy) friction factor$ which is a dimensionless parameter defined

as

2

2

mu

Ddx

dp

f

= . -here f is the friction factor.

*esistance to fluid flo!+ the ressure dro in the flo! direction:

a

The fanning

frictionfactor:

"he fanning

friction factor

is called the

friction

coefficient$

which is

defined as

2

2

m

s

f

u

C

=

-here fC is

the friction

coefficient or drag coefficient$ whose value in most cases is determined e+perimentally$ and is the density of the fluid. "he friction coefficient$ in general$ will vary with location

along the surface.

The #ean or &ul, Fluid te#erature:

"he mean or bul temperature of the fluid at a given cross section is defined in terms of the

thermal energy transported by the fluid as it moves past the cross section. "he rate at whichthis transport occurs$ $tE may be obtained by integrating the product of the mass flu+

( )u and the internal energy per unit mass Tc p over the cross section. "hat is$

=c

c

A

cpt AdTcuE

Hence if a mean temperature is defined such that mpt TcmE = . -here pC is the specific

heat of the fluid and m is the mass flow rate. "he product mp TCm A" any cross section

along the tube represents the energy flow with the fluid at that cross section. *n the absence of

any wor interactions (such as electric resistance heating) $ "he conservation of energy

e&uation for the steady flow of a fluid in a tube can be e+pressed as ( )iep TTCmQ =

.-here iT and eT are the mean fluid temperature at the inlet and e+it of the tube$respectively$ and Q is the rate of heat transfer to or from the fluid.


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@""s5"m&s,h "i

"e

"m

"s4ntry region

ully developed region

After all$ the bul temperature is the representative of the total energy of the flow at any

particular location. "he bul temperature is used for overall energy balances on systems.

The ther#al conditions:

"he thermal conditions at the surface of a tube can usually be appro+imated with reasonable

accuracy to be constant surface temperature ("s constant) or constant surface heat flu+( ).tan tconsqs= or e+ample$ the constant surface temperature condition is reali3ed when a

phase change process such as boiling or condensation occurs at the outer surface of a tube.

"he constant surface heat flu+ condition is reali3ed when the tube is sub;ected to radiation or

electric resistance heating uniformly from all directions. "he convection heat flu+ at any

location on the tube can be e+pressed as ( )ms TThq = $ where h is the local heat transfercoefficient and sT and mT are the surface and the mean fluid temperatures at that location."herefore$ where h constant$ the surface temperature " smust change when =sq constant$

and the surface heat flu+ sq must change when sT constant. "hus we may have either sT

constant or =sq constant at the surface of a tube$ but not both.

Constant surface heat flu ( =sq constant):

*n the case of =sq constant$ the rate of heat transfer can also be e+pressed as( )

ieps TTCmAqQ ==

"hen the mean fluid temperature at the tube e+it becomesp

s

ieCm

AqTT

+= .

%ariation of the tu$e surface and the #ean fluid te#erature along the tu$e for the case of

constant surface heat flu:

Constant surface te#erature (Ts = constant):

*n the case of"s constant$ the rate of heat transfer is e+pressed as


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&

"

@""s5"m

"i

"scostant

"scostant

"i

"s

lnThAQ = where

i

e

ie

is

es

ie

T

TLn

TT

TT

TTLn

TTT

=

=

ln

is the logarithmic mean

temperature difference. Here isi TTT =

and ese TTT = are the temperature differences between the surface and the fluid at theinlet and the e+it of the tube$ respectively. "hen the mean fluid temperature at the tube e+it in

this case can be determined from ( ) pCmAh

isse eTTTT

= .

The variation of the #ean fluid te#erature along the tu$e for the case of constant surface

Te#erature:


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%elocity rofile in the fully develoed region:


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Ther#al entry region+ length and ther#ally develoed region:

"he region of flow over which the thermal boundary layer develops and reaches the tube

centre is called the thermal entry region and the length of this region is called the thermal

entry length. "he region beyond the thermal entry region in which the dimensionless

temperature profile remains unchanged is called thermally developed region.

"he region in which the flow is both hydrodynamically and thermally developed is called the

fully developed flow.

Ther#al entry lengthst%.%8 re. >r d laminar flow

t9% d "urbulent flow

or >r BB 9 and h taminar flow.


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!"ial #ariation of the convection heat transfer coefficient for flow in atube:

#iscous$energy dissipation function:"he energy e&uation in the rectangular co5ordinate system for a elemental control volume for

steady$ two dimensional (+$ y) flow of an incompressible$ constant5property fluid when

consider for convection energy$ conduction energy and viscous energy is determined as

+

+

=

+

2

2

2

2

y

T

x

TK

y

Tv

x

TuCp

-here is the viscous5energy dissipation function and is defined as

222

2

+

+

+

=

y

u

x

v

y

v

x

u

"he left hand side represents the net energy transfer due to mass transfer on the right hand

side the first term represent the conductive heat transfer$ and the last term on the right hand

side is the viscous5energy dissipation in the fluid due to internal fluid friction.

%hysical significance of the dimensionless parameters:"he dimensionless parameters such as the !eynolds number$ 'usselt number and >randtl

numbers are introduced and the physical significance of these dimensionless parameters in

the interpretation of the conditions associated with fluid flow or heat transfer is discussed.

The *eynolds nu#$er:


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"he !eynolds number represents the ratio of the inertia to viscous force. "his result implies

that viscous forces are dominant for small !eynolds numbers and inertia forces are dominant

for large !eynolds numbers. "he !eynolds number is used as the criterion to determine

whether the flow is laminar or turbulent. As the !eynolds number is increased$ the inertia

forces become dominant and small disturbances in the fluid may be amplified to cause the

transition from laminar to turbulent.

where:

vs5 mean fluid velocity$

L5 characteristic length (e&ual to diameter (2r) if a cross5section is circular)$

D 5 (absolute) dynamic fluidviscosity$ E 5 inematic fluid viscosity: E D , F$

F 5 fluid density.

Nusselt nu#$er:

"he 'usselt number is a dimensionless number that measures the enhancement of heat

transfer from a surface that occurs in a real situation$ compared to the heat transferred if ;ust

conduction occurred. "ypically it is used to measure the enhancement of heat transfer when

convection taes place.

where

L characteristic length$ which is simply 1olume of the body divided by the Area of

the body (useful for more comple+ shapes)

kf thermal conductivityof the GfluidG

h convectionheat transfer coefficient

"hus the 'usselt number may be interpreted as the ratio of heat transfer by convection to

conduction across the fluid layer of thicness . /ased on this interpretation$ the value of the

'usselt number e&ual to unity implies that there is no convection5the heat transfer is by pure

conduction. A large value of the 'usselt number implies enhanced heat transfer by

convection.

The 'randtl nu#$er:

"he >randtl number is a dimensionless number appro+imating the ratio of momentum

diffusivity and thermal diffusivity. "he >randtl number provides a measure of the relative


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effectiveness of momentum and energy transport by diffusion in the velocity and thermal

boundary layers$ respectively.

where:

E is the inematic viscosity$ ,.

is the thermal diffusivity$ ! , (cp).

*n heat transfer problems$ the >randtl number controls the relative thicness of the

momentum and thermal boundary layers.

The tanton nu#$er:

"he &tanton numberis adimensionless numberwhich measures the ratio of heat transferredinto a fluid to the thermal capacity of fluid. *t is used to characteri3e heat transfer in forced

convectionflows.

where'

h convectionheat transfer coefficient

F densityof the fluid

cpspecific heatof the fluid

" velocityof the fluid

*t can also be represented in terms of the fluidIs'usselt$ !eynolds$ and >randtlnumbers:

where

#uis the 'usselt number

$eis the !eynolds number %ris the >randtl number

Heat transfer enhancement:everal options are available for enhancing heat transfer associated with internal flows.

4nhancement may be achieved by increasing the convection coefficient and,or by increasing

the convection surface area. or e+ample$ h may be increased by introducing surface

roughness to enhance turbulence$ as$ for e+ample$ through machining or insertion of a coil5

spring wire. "he wire insert provides a helical roughness element in contact with the tube

inner surface. Alternatively$ the convection coefficient may be increased by inducing swirl

through insertion of a twisted tape. "he insert consists of a thin strip that is periodicallytwisted through


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MkamalHeat Transfer II (Introduction) (1)

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