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Dr. Şaziye Balku 1

HEAT TRANSFER BY CONVECTION

Dr. Şaziye Balku 2

CONDUCTION

Mechanism of heat transfer through a solid or fluid in the absence any fluid motion.

CONVECTION

Mechanism of heat transfer through a fluid in the presence of bulk fluid motion

• Natural (free) Convection

• Forced Convection

(depending on how the fluid motion is initiated)

Dr. Şaziye Balku 3

• Viscous-inviscid

• Internal flow-External flow

• Open-closed channel

• Compressible-Incompressible• Laminar-Turbulent• Natural- Forced• Steady- Unsteady• One-,two-,three-dimensional

CLASSIFICATION OF FLUID FLOWS

Dr. Şaziye Balku 4

VISCOSITYWhen two fluid layers move relative to each other, a friction force develops between them and the slower layer tries to slow down the faster layer.

internal resistance to flow• cohesive forces between the molecules in liquid• molecular collisions in gases.

Viscous flows: viscous effects are significant

Inviscid flow regions: viscous forces are negligibly small compared to inertial or pressure forces.

measure of stickness or resistance to deformation1. Kinematic viscosity2. Dynamic viscosity

Dr. Şaziye Balku 5

VISCOSITY DEPENDS ON

• TEMPERATURE

• PRESSURE

For liquids dependence of pressure is negligible

For gases kinematic viscosity depends on pressure since its relation to density

µ Dynamic viscosity (kg/m.s or poise)

ν Kinematic viscosity, m2/s or stroke

ρ

µν =

Dr. Şaziye Balku 6

Convection heat transfer

- Dynamic viscosity

- Thermal conductivity

- Density

- Specific heat

- Fluid velocity

- Geometry

- Roughness

- Type of fluid flow

Dr. Şaziye Balku 7

NEWTON’S LAW OF COOLING

)( ∞

•

−= TThAQ SSconv

h

(W)

Convection heat transfer coefficient (W/m2.0C)

The rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature difference

Dr. Şaziye Balku 8

GENERAL THERMAL ANALYSIS

)(∞

•

−= TThAQSSconv

)( iep TTCmQ −=••

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FORCED CONVECTION

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• LAMINAR FLOW

Smooth streamlines

Highly- ordered motion

(highly viscous fluids in small pipes)

• TURBULENT FLOW

Velocity fluctuations

Highly-disordered motion

• TRANSITIONAL FLOW

Dr. Şaziye Balku 11

REYNOLDS NUMBER

Flow Regime:

Geometry

Surface roughness

Flow velocity

Surface temperature

type of fluid

Ratio of the inertial forces to

viscous forces in the fluid

µ

ρυυ D

v

D mm ==Re

mυ

D

ρµ /=v

Mean flow velocity

Characteristic length of

the geometry

Kinematic viscosity

Dr. Şaziye Balku 12

• Critical Reynolds number (Recr)

for flow in a round pipeRe < 2300 ⇒ laminar

2300 ≤ Re ≤ 4000 ⇒ transitional

Re > 4000 ⇒ turbulent

• Note that these values are approximate.

• For a given application, Recr depends

upon

– Pipe roughness

– Vibrations

– Upstream fluctuations, disturbances

(valves, elbows, etc. that may disturb

the flow)

Definition of Reynolds number

Dr. Şaziye Balku 13

• For non-round pipes,

• the hydraulic diameter

Dh = 4Ac/P

Ac = cross-section area

P = wetted perimeter

HYDRAULIC DIAMETER

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Velocity

No-slip condition

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THERMAL BOUNDARY LAYER

Flow region over the surface in which the temperature variation in the direction normal to the surface

Velocity profile influences temperature profile

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VELOCITY

in rectangular),,( zyxυr

),,( zr θυr

One dimensional

flow in a circular pipe

A flow field is best characterized by the velocity distribution, and velocity may vary in three dimension

in cylinderical coordinates

In which direction does the velocity change in this figure???

Dr. Şaziye Balku 17

NUSSELT NUMBER(Dimensionless number)

k

hLNu c=

Thqconv

∆=•

L

Tkq

cond

∆=

•

Nuk

hL

LTk

Th

q

q

cond

conv ==∆

∆=

•

•

/

Dr. Şaziye Balku 18

PRANDTL NUMBER

• Boundary layer theory

k

C pµ=Pr

Pr<<1 heat diffuses very quickly in liquid metals, tbl thicker

Pr>>1 heat diffuses very slowly in oils relative to momentum, tblthinner than vbl

k

C

heatofydiffusivitmolecular

momentumofydiffusivitmolecularpµ

α

ν===Pr

Dr. Şaziye Balku 19

PARALLEL FLOW OVER FLAT

PLATES

5105Re ×==µ

ρυ cr

cr

x

53/15.0 105RePrRe664.0 ×<== LLk

hLNu

75

3/18.0

10Re105

60Pr6.0PrRe037.0

≤≤×

≤≤==

L

Lk

hLNu

laminar

turbulent

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NATURAL CONVECTION

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CONVECTIVE HEAT TRANSFER

COEFFICIENT

2

3)(

υ

β CsL

LTTgGr ∞−

=

PrLL GrRa =

n

L

C CRak

hLNu ==

Grashof number

Rayleigh number

Prandtl number

Nusselt number

Table 20-1

viscosity

Coefficient of volume expansion