convective heat transfer (natural).doc
DESCRIPTION
Convective Heat TransferTRANSCRIPT
• 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