Fundamentals of Heat and Mass Transfer, 6...

1Fundamentals of Heat and Mass Transfer, 6e

Fundamentals of Heat and Mass

Transfer, 6th edition

Presented E-mail: [email protected]

Telephone: 88399000-2511

mailto:[email protected]


Chapter 6 Introduction to convection

Convection: energy transfer between a surface and a fluid moving over the surface

ObjectivesUnderstand the physical mechanism of convection;

Develop means to perform convection transfer calculation

Contents:Basic contents on convection heat transfer and convection

mass transfer

physical origin, dimensionless parameters, analogies


Chapter 6 Introduction to convection

Convection: energy transfer between a surface and a fluid moving over the surface()

the bulk fluid motion (advection)

the random motion of fluid molecules (conduction or diffusion)

The determination of convection transfer coefficient and related heat transfer

enhancement method are the central problems in the study of convection issue.


Chapter 7 External flow

Chapter 8 Internal flow

Chapter 9 Free convection

Chapter 10 Boiling and condensation

Chapter 11 Heat exchangers


6.1 the convection boundary layer

Boundary layers: velocity, thermal , concentration,

Friction coefficient

Convection heat transfer coefficient

Convection mass transfer coefficient



The velocity boundary layer Fluid velocity=0 at the surface

Velocity grow Velocity u

Shear stress (), parallel to fluid velocity

In boundary layer ( a thin layer): velocity gradients and shear stresses are large

Region outside the boundary layer: velocity gradients and shear stresses are

negligible

uu 99.0Velocity boundary layer thickness



Velocity boundary layer: developed whenever there is fluid flow over a surface

For a Newtonian fluid

dynamic viscosity

kg/m S

u velocity along the x direction

m/s

surface shear stressN/m2

Cf: the local friction coefficient,

to determine the friction drag a dimensionless parameter

sx

y

u

Cf


6.1 the thermal boundary layer

99.0)/()( TTTT sst Thermal boundary layer thickness when

Developed when the flow free stream and the surface temperatures differ

x y

T

h


6.1 the concentration boundary layer

Example: air past the surface of a pool of water evaporation a binary mixture of chemical species A and B,

Sublimation

CA: molar concentration , kmol/m3


Concentration boundary layer:

concentration gradients exist()

:thickness is defined asc 99.0)(

)(

,,

,

AsA

AsA

CCCC

Molar flux of species A , NA (kmol / s m2)A

Binary diffusion coefficient, DAB

Fick s law Diffusion mass transfer,y

CDN AABA

''

At the surface y=0,

diffusion mass transfer 0''

,

y

AABsA

y

CDN



Analogous to Newtons law of cooling


)( ,.,''

AsAmsA CChN

,,

0

AsA

AAB

mCC

yy

CD

h

hm, convection mass transfer

coefficient, m/s,

y

CDN AABA

''


6.1 significance of the boundary layer

Flow over a surface velocity boundary layer surface friction

Flow over a surface with temp difference thermal boundary

layer convection heat transfer

Flow over a surface with concentration difference concentration

boundary layer convection mass transfer

items Characteristics Key parameters

Velocity gradient,

shear stresses

Friction coefficient Cf

Temp gradient,

heat transfer

Heat transfer coefficient,

h

Concentration gradient,

species transfer

Mass transfer coefficient,

hm

t

t

c


6.2 local and average convection

coefficients

Heat transfer

The local heat flux , q

The total heat rate , q

Average convection heat transfer coefficient, h



coefficients

Mass transfer

NA: molar transfer rate kmol/s



coefficients

Molar flux mass flux

Molar transfer rate mass transfer rate

0

''

,

y

AABsA

yDn

Molecular weight (kg/kmol)

Molecular weight (kg/kmol)

,,

0

AsA

AAB

m

yy

Dh

AAA CM


Example 6.1


6.3 laminar and turbulent flow

Flow condition: laminar flow() turbulent flow


6.3 laminar and turbulent flow

Boundary layer development on a flat plat

Laminar flow: fluid flow is highly ordered, streamline

Transition zone: laminar or turbulent

Turbulent flow: flow is highly irregular, random, 3-D motion, chaotic flow

3 regions in the turbulent boundary layer: viscous sublayer ()buffer layer ()turbulent zone ()


5105Re

xux

Critical Reynolds number, ranging in 105~3X106

xucx

,Re

Determination parameter for the onset of turbulent flow :

Reynolds number =the ratio of inertia to viscous forces

= /

x, characteristic length


Laminar and turbulent thermal

boundary layer

Laminar region :streamline, temperature gradient is decreased in the streamline direction heat transfer

coefficient is decreased

Transition region:

Turbulent region: local convection heat transfer

coefficient is decreased

along the flow direction.


Thermal and species concentration

boundary layer

Laminar region :streamline, temp and concentration gradient decrease in the streamline direction heat and

mass transfer coefficient decrease

Transition region:

Turbulent region: local convection heat and mass

transfer increased


Example 6.4 p362

For concentration boundary layer


6.4 the boundary layer equation



Boundary layer equations for laminar flowComply with fundamental laws of nature:

Including conservation of mass, energy and chemical species, Newtons second law of motion

Assumption

In the Cartesian coordinate, equations for the steady, 2D flow of an incompressible fluid with constant properties are summarized in Appendix D the convection Transfer Equations.

( Appendix E gives the corresponding equations for the boundary layer in turbulent flow.)



The continuity equation



The x momentum equation x

The net pressure

force

The net rate

force due to

viscous shear

stresses

The net rate due

to fluid motion

across boundary



The energy equation,

The net

conduction rate

in the y direction

The net rate due

to fluid advection

Viscous dissipation

Neglect in some cases



The species concentration equation

The net transport

of species A due

to advection

The net transport

of species A due

to y-direction

diffusion



Laminar boundary layer equations

Right side: diffusion terms

If neglect

Left side: advection terms

44


6.5 boundary layer similarity

Nondimensionalizing the governing equations:

L: characteristic length of the surface of interest,

V: velocity of the upstream

Viscous dissipation is neglected


Nondimensional form of the

boundary layer equation



Similarity parameters (important, apply results for a surface to geometrically similar surfaces)

Reynolds number Re

Prandtl number, Pr,

If both the boundary conditions and similarity parameters

are same for two different conditions (that is geometrically

similar ), then solution of the differential equations for the

nondimensional velocity and temperature will be same.

VLRe

Dynamic viscosity, kg/s m

Kinetic viscosity, m2/s



Functional form of the solutions

Local

Nusselt Number

Average



Functional form of the solutions


6.6 physical significance of the

dimensionless parameters

Reynolds number: the ratio of inertia to viscous forces

Grashof number: the ratio of the buoyancy forces to

viscous forces

Prandtl number: the relative effectiveness of momentum

and energy transfer by diffusion in the velocity and

thermal boundary layer, the relative thickness of velocity

and thermal boundary layer.

For gas Pr=1, For liquid metal Pr1

n is a positive component


6.6 physical significance of the

dimensionless parameters


6.7 boundary layer analogies

Analogy

Analogy between momentum-energy-mass



Analogy between two convection coefficient

In general, n=1/3

OK for both

turbulent and laminar

Example 6.6 p379



The Reynolds analogy



The Chilton-Colburn analogies ()

jh: Colburn j factor for heat transfer, j

jm: Colburn j factor for mass transfer j

Valid In laminar flow when

Approximately valid in turbulent flow condition


6.8 the convection coefficients

The primary objective on the problem of

convection is to develop means to

determine the convection coefficient h.

6.9 summary


Homework Assignment

Boundary layer profiles

6.1

6.3

Heat transfer coefficients

6.5

Similarity and dimensionless parameters

6.20

Reynolds analogy

6.34

Mass transfer

6.41

Example 6.3

Fundamentals of Heat and Mass Transfer, 6...

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