Chapter 10

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27 Οκτ 2013 (πριν από 3 χρόνια και 7 μήνες)

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CHAPTER 10


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ME 352: Thermodynamics & Heat Transfer







CHAPTER 10



Forced Convection


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The
limiting
case

of
convection


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Convection heat transfer strongly depends on:

-
Dynamic viscosity

-
Thermal conductivity

-
Density

-
Specific heat

-
Fluid velocity

-
Geometry and roughness of solid surface

-
Type of flow : stream lined vs. turbulent.


Therefore expect

complicated relations

Fluid motion enhances
heat transfer

Since brings colder &
hotter regions together


Hence: higher
conduction rates at
larger no. of sites in
fluid

The higher the fluid velocity,

the higher the heat transfer rate


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Despite complexity, we can simplify as follows:

conduction

no
-

slip

conditio
n

Hence HT from
surface to adjacent
layer is
pure
conduction

Can vary along x direction


use
mean or average value


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Nusselt Number

It is common practice to

Nondimensionalise governing

Equation and combine variables

Dimensionless heat transfer coefficient

The larger the Nu the more effective is convection

Nu=1


heat transfer 批 灵re c潮摵cti潮

Thermal
conductivity of
fluid

Characteristic
length


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Velocity Boundary Layer

Consider fluid flow over a flat plate. Assume adjacent layers of fluid piled up on each other.

INVISCID

FLOW REGION

DRAG FORCE OR FRICTION FORCE


SHEAR STRESS

Dynamic viscosity
, units: N.s/m2


measure of resistance to flow &
function of temperature


Velocity

Distance from surface at
which V
=0.99
V


Consider 2 adjacent layers in the boundary layer.

Faster layer will try to drag slower one

thus exerting a:

Smooth stream lines

Highly ordered motion

Velocity fluctuations

Highly disordered motion


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Previous equation to determine shear stress

is not practical since assumes prior

knowledge of velocity profile.

Important parameter
directly related to heat
transfer coefficient and
power requirements of
pump or fan


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Critical Reynolds number

Reynolds number,
Re

Transition from laminar to turbulent flow is dependant on:

-
Surface geometry

-
Surface roughness

-
Free stream velocity

-
Surface temperature and type of fluid…etc


Re

critical, flat plate ~ 5x10
5

Laminar and Turbulent flow


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ME 352: Thermodynamics & Heat Transfer

Thermal Boundary Layer

Prandtl number,Pr

Distance from the surface at which

temperature difference T
-
T
s

is 0.99(T



T
s
)


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FLOW OVER A SURFACE
(of uniform temperature)

FILM TEMPERATURE (T
f
)

Average Nusselt number

Properties of the fluid are used at this temperature


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Average friction Coefficient


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1. Laminar Flow

And

Local friction and heat transfer coefficients

Integration over the length of the plate gives average friction and heat transfer coefficients

For Pr (
>

0.6)

What is the critical distance above which no longer laminar?


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2. Turbulent Flow

(5x10
5
<
Re
x
<

10
7
)

Local friction and heat transfer coefficients

and


and 5x10
5
<
Re
x
<

10
7

For 0.6
<

Pr
<

60

Integration over the length of the plate gives average friction and heat transfer coefficients


and 5x10
5
<
Re
x
<

10
7

For 0.6
<

Pr
<

60

for 5x10
5
<
Re
x
<

10
7


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3. Combined Laminar and Turbulent Flow

Included transition region into turbulent region

Average friction coefficient and Nusselt number


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If flat plate subjected to uniform flux and not temperature

(laminar flow)

(turbulent flow)

Gives 36% and 4% higher for laminar and turbulent flow compared to isothermal case


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Table A
-
17


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Table A
-
19


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ME 352: Thermodynamics & Heat Transfer