• Natural convection – currents are the result of buoyancy forces generated by differences in density and differences in density are in caused by temperature gradients in fluid mass

NATURAL CONVECTION

NGr L32gT

2

b

(T Tb )

1

Tfor gases

Grashof Number:

Volumetric coefficient of expansion

For liquid

NNU a(NGr .NPr )m

a and m are constant from table 4.7-1

General equation

All the physical properties are evaluated at film temperature, Tf

NATURAL CONVECTION

NATURAL CONVECTION

Cold Plate

(Ts < T)

Hot Plate (Ts > T)

Upper surface of heated or lower surface of cooled plates

Upper surface of Cooled or lower surface of heated plates

Horizontal cylinders

NATURAL CONVECTION

NATURAL CONVECTION

Natural convection in enclosed system

NGr, 32gT

2

T2T1

NNU , hk

Verticle plate

Gases

NNU , hk

1.0

NGr, .NPr 2x103

NNU , 0.20NGr, .NPr

14

L

19

6x103 NGr, .NPr 2x105

NNU , 0.073NGr, .NPr

13

L

19

2x105 NGr, .NPr 2x107

Q

NATURAL CONVECTION

Liquid

NNU , hk

1.0

NGr, .NPr 1x103

NNU , 0.28NGr, .NPr

14

L

14

1x103 NGr, .NPr 1x107

NNU , 0.21 NGr, .NPr 1

4

7x103 NGr, .NPr 3x105

NNU , 0.061 NGr, .NPr 1

3

NGr, .NPr 3x105

NNU , 0.069 NGr, .NPr 1

3NPr0.074

1.5x105 NGr, .NPr 1x109

Horizontal plate

Gases

Liquid

The lower plate hotter than the upper plate

NATURAL CONVECTION

NATURAL CONVECTION

Water at an average temperature of 17 oC and a mass rate of 0.012 kg/s is to be used for maintaining a small plate (on which a special sensor is to be mounted) at a fixed temperature. The plate is situated within a hot air environment at a temperature of 235 C. The tube is horizontal and 1 m long. Fabricated from a plastic with a thermal conductivity of 0.05 W/m.K, the tube has a inner diameter Di = 1.4 mm, and outer diameter Do=3.2 mm.

a. Assuming that the average outer surface temperature of the tube is 120 C, estimate the heat transfer coefficient between the tube and the ambient air.

b. Assuming that the flow and thermal conditions within the tube are fully developed, estimate the heat transfer coefficient between the tube and the water.

c. Determine the overall heat transfer coefficient based on the outer tube area.

NATURAL CONVECTION

WaterTbavg = 17 oCV=0.012 kg/s

Do=3.2 mmDi=1.4 mm

T∞=235 oC

Tw=120 oC

kt=0.05 W/m.K

1. Calculate ho

2. Calculate hi

3. Calculate Uo

Natural convection - horizontal tube

Forced convection inside pipe

Boiling

Boiling experiment by Nukiyama

+/-IV

Tw

V I Tw

V1

V2

I1

I2

T1

T2

Heat released from tangstant wire

qI.V

Boiling

Boiling

h 1043(T)13

qA W/m2 16

h 5.56(T)3

16 q A W/m2 240

h 537(T)17

qA W/m2 3

h 7.95(T)3

3 q A W/m2 63

Pendidihan perolakan bebas

Nucleate boiling

Horizontal surface

Vertical surface

Penentuan h menggunakan persamaan perolakan bebas

Boiling

h 0.62kv

3V l V g h fg 0.4c pvT DvT

14

Film boiling - for horizontal cylinder

CONDENSATION

Condensation on the vertical surface

y

y

dx

v g(l v )

l

(y y 2

2)

( y)(dx)(l v )gl

dv

dy

(dx)

Force balance through eliment dx:

Gravitational force - buoyancy force = viscous-shear force

( y)(l v )g dy0

y l dv0

v

V - velocity

- thickness of liquid film at x

l and v- liquid and vapor density

l - liquid viscousity

Integrate ,

CONDENSATION

dmdgl (l v )

3

3l

gl (l v )x

2dl

qx kl (dx.1)dT

dyy0

kldxTsat Tw

x

mx gl (l v )x

3

3l

m lvdy 0

l

g(l v )

l

(y y 2

2)dy

0

Mass flowrate at point x;

The increase in mass from condensation ;

Heat transfer across liquid film, surface area (dx.1)

Cross section area of liquid film

Ac 1.dy

Volume V .(1.dy)

CONDENSATION

h fggl (l v )

2dl

kldxTsat Tw

Heat of condensation = heat flow through element dx

h fgdmkldxTsat Tw

x 4lx Tsat Tw gh fgl (l v )

14

h fggl (l v )

l

3d0

x kl Tsat Tw dx0

x

Film thickness at x:

Heat balance for dx distance,

CONDENSATION

hx l (l v )gh fgkl

3

4lx Tsat Tw

14

hx klx

hx (dx.1) Tsat Tw kl (dx.1)Tsat Tw

Imbangan tenaga juga dalam bentuk berikut

Heat transfer through convection

=Conduction through liquid film

Local heat transfer coefficient

CONDENSATION

h 0.943l (l v )gh fgkl

3

4lx Tsat Tw

14

h 1

Lhx0

L dx 4

3hxL

hL l (l v )gh fgkl

3

4lL Tsat Tw

14

Heat transfer coefficient at x=L

Average heat transfer coefficient

CONDENSATION

NNU 1.13l (l v )gh fgL

3

4lkl Tsat Tw

14

NRE 1800

NRE 4m

Dl

NRE 4m

Wl

For

Vertical tube Vertical plate, width of W

CONDENSATION

NNU 0.0077gl

2L3

l

13

(NRE )0.4

NRE 1800untuk

Condensation outside N horizontal tube

NNU hD

k0.725

l l v gh fgD3

NlklT

CONDENSATION

CONDENSATION

The outer surface of a vertical tube, which is 1 m long and has an outer diameter of 80 mm, is exposed to saturated steam at atmospheric pressure and is maintained at 50 C by flow the cooling water through the tube. What is the rate of heat transfer to the coolant, and what is the rate at which steam is condense at the surface?

CONDENSATION

CONDUCTION: Extended Surface

CONDUCTION: Extended Surface

CONDUCTION: Extended Surface

CONDUCTION: Extended Surface

CONDUCTION: Extended Surface

CONDUCTION: Extended Surface

CONDUCTION: Extended Surface