# Chapter 10

Mechanics

Oct 27, 2013 (4 years and 6 months ago)

135 views

CHAPTER 10

Page 10.
1

ME 352: Thermodynamics & Heat Transfer

CHAPTER 10

Forced Convection

CHAPTER 10

Page 10.
2

ME 352: Thermodynamics & Heat Transfer

The
limiting
case

of
convection

CHAPTER 10

Page 10.
3

ME 352: Thermodynamics & Heat Transfer

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

CHAPTER 10

Page 10.
4

ME 352: Thermodynamics & Heat Transfer

Despite complexity, we can simplify as follows:

conduction

no
-

slip

conditio
n

Hence HT from
layer is
pure
conduction

Can vary along x direction

use
mean or average value

CHAPTER 10

Page 10.
5

ME 352: Thermodynamics & Heat Transfer

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

CHAPTER 10

Page 10.
6

ME 352: Thermodynamics & Heat Transfer

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

CHAPTER 10

Page 10.
7

ME 352: Thermodynamics & Heat Transfer

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

CHAPTER 10

Page 10.
8

ME 352: Thermodynamics & Heat Transfer

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

CHAPTER 10

Page 10.
9

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
)

CHAPTER 10

Page 10.
10

ME 352: Thermodynamics & Heat Transfer

CHAPTER 10

Page 10.
11

ME 352: Thermodynamics & Heat Transfer

FLOW OVER A SURFACE
(of uniform temperature)

FILM TEMPERATURE (T
f
)

Average Nusselt number

Properties of the fluid are used at this temperature

CHAPTER 10

Page 10.
12

ME 352: Thermodynamics & Heat Transfer

Average friction Coefficient

CHAPTER 10

Page 10.
13

ME 352: Thermodynamics & Heat Transfer

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?

CHAPTER 10

Page 10.
14

ME 352: Thermodynamics & Heat Transfer

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

CHAPTER 10

Page 10.
15

ME 352: Thermodynamics & Heat Transfer

3. Combined Laminar and Turbulent Flow

Included transition region into turbulent region

Average friction coefficient and Nusselt number

CHAPTER 10

Page 10.
16

ME 352: Thermodynamics & Heat Transfer

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

CHAPTER 10

Page 10.
17

ME 352: Thermodynamics & Heat Transfer

Table A
-
17

CHAPTER 10

Page 10.
18

ME 352: Thermodynamics & Heat Transfer

CHAPTER 10

Page 10.
19

ME 352: Thermodynamics & Heat Transfer

CHAPTER 10

Page 10.
20

ME 352: Thermodynamics & Heat Transfer

Table A
-
19

CHAPTER 10

Page 10.
21

ME 352: Thermodynamics & Heat Transfer

CHAPTER 10

Page 10.
22

ME 352: Thermodynamics & Heat Transfer

CHAPTER 10

Page 10.
23

ME 352: Thermodynamics & Heat Transfer