CONVECTION
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Transcript of CONVECTION
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CONVECTION
Convection Heat Transfer
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Why is it windy at the seaside?
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Cold air sinks
Where is the freezer
compartment put in a fridge?
Freezer compartment
It is put at the top, because cool air sinks, so it cools the food on the
way down.
It is warmer at the bottom, so this warmer air
rises and a convection
current is set up.
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Convection• Convection is the transfer
of heat by the motion of liquids and gases.– Convection in a gas occurs
because gas expands when heated.
– Convection occurs because currents flow when hot gas rises and cool gas sink.
– Convection in liquids also occurs because of differences in density.
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Free and Forced Convection
• When the flow of gas or liquid comes from differences in density and temperature, it is called free convection.
• When the flow of gas or liquid is circulated by pumps or fans it is called forced convection.
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Heat Convection Equation
qH = h A (T2 -T1)
Area contacting fluids (m2)
Heat transfer coefficient(watts/m2oC)
Heat flow (watts)
Temperaturedifference (oC)
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Heat transfer from a solid to the surrounding fluid
• In this method of heat transfer, the heat transfers from a surface to the fluid depends on the fluid flow properties as well as the thermal properties of the fluid.
• The following discussion is for a Newtonian fluids.
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CONVECTIVE HEAT TRANSFER COEFFICIENT
• The convective heat transfer coefficient depends on: 1)The fluid flow characteristics.
2)Thermal and physical properties of the fluid.
The methods which have been used to evaluate this coefficient are empirical relationships. Or a derived equations from a theoretical basis.
• Some times called film coefficient (the thin layer in contact)• h[w/m2.k] depends on : ρ, µ, v, Cp, k, L• Unitless numbers usually used to predict h.
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CONVECTION: h=?Natural or Forced in different cases
Perpendicular on cylindrical pipes
Perpendicular on cylindrical pipes
Flat horizontal plate Flat horizontal plate
Boiling Inside cylindrical tube
condensation
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Introduction and dimensionless numbers
Flow condition: 1-Laminar. 2-Transient.3- Turbulent.
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• In order to calculate the value of heat transfer coefficient (h) there are some dimensionless equations which help to find the closer h value under a variable situations.
• Prandtl number: the ratio of the shear component of diffusivity for momentum µ/ρ to the diffusivity for heat k/ρCp. and physically relates the relative thickness of the hydrodynamic layer and thermal boundary layer.
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• NUSSELT number:Relates data for the heat transfer coefficient h to
the thermal conductivity k of the fluid and a characteristic dimension D.
• REYNOLD number:
• GRSHOF number: Represent the ratio of the buoyancy forces to the
viscous forces in free convection and plays a role similar to that of Reynolds number in forced convection.
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The volumetric expansion coefficient is defined as:
-1
1
where: is the volume is the temperature
is the volumetric expansion coefficient, (deg)
dVV dT
VT
Ethyl alcohol: 112 x 10-5 /deg. C
Methyl alcohol: 120 “
Benzene: 124 “
Glycerin: 51 “
Air: 3 “
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2
For ideal gases1
1 1But and
and it follows that1
For an ideal gas, and it follows that
1g
dVV dT
dV d
ddT
PR T
T
Ideal gas only
True for any material
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Correlations for forced convection over a flat surface
In forced convection h value depends on: 1-Reynold’s Number 2- Geometry.
Re< 500,000 laminar Re>500,000 Turbulent
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• If the flow is laminar:
• ReL<500,000• If the turbulent part is longer than the laminar then:
• ReL>500,000• But if both parts is important at the stage of ReL=500,000
then:
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Flow Perpendicular to a Single Cylinder
D
Re
1/ 3Re Prm
Nu
DvN
N CN N
Use properties at the film temperature. Velocity is free field velocity of fluid.
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Flow Past a Single Sphere
Re
0.5 1/ 3Re Pr
Re Pr
2.0 0.60 1 70,000 0.6 400
Nu
DvN
N N NN N
Use properties at film temperature.
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Forced convection inside cylindrical pipes
• All properties taken at TB (Bulk temperature) the average temperature of the fluid at any section of the pipe.
• D: the internal diameter of the pipe.• ReD< 2300 Laminar flow.
• ReD>2300 Turbulent flow.
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• If the temperature at the surface of the pipe is constant and laminar flow:
• Relation (1):
• If D/L is very small then Nu =3.66• Relation (2): If the pipe is short and laminar
flow:• If :
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In heat transfer from fluid to another one of them inside a pipe and the other outside the pipe and inside the external pipe (include the internal pipe).
• The last relation can be used except the special dimension for Nu and Re
We use DH
All properties approximated at total temperature average except µs approximated at the surface
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inside cylindrical pipes Turbulent flow
• For turbulent flow there are many correlations some of the famous are:
• n=0.4 if Ts>Tfluid
• n=0.3 if Ts<TfluidFor fluids having viscosity higher than water this correlation is more precise:
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Free or Natural Convection• In this case of heat transfer Groshof number has
been suggested, which describes the fluid motion, under two conditions:
• 1- Fluid is not induced by external force.• 2- the motion within the fluid is brought about by the
influence of temperature on the fluid density and development of buoyant force.
X= length of the body involved in the free convectionβ= coefficient of expansion for fluid being heated .∆T= the difference in temperature between the surface and the fluid .
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Empirical Correlations
Typical correlations for heat transfer coefficient developed from experimental data are expressed as:
3 Pr LTTg GrRa sLL
nLL CRa
kLhNu
3/14/1
nn For Turbulent
For Laminar
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Nu: average convective heat transfer coefficient for the surface.K= thermal conductivity ration for heat exchangers.a, k depends on the geometry and orientation of the surface.
Surface K a ConditionVertical plate 0.59 0.25 104 <Gr Pr<109
Vertical cylinder 0.021 0.4 Gr Pr>109
Horizontal cylinder 0.525 0.25 It gives good results
especially when Pr>0.5 and 103<Gr<109
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When the medium is air natural convection
are
horizontal
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Horizontal Plate
Cold Plate (Ts < T)
Hot Plate (Ts > T)Active Upper Surface
Active Lower Surface
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Empirical Correlations : Horizontal Plate
•Define the characteristic length, L as
PAL s
•Upper surface of heated plate, or Lower surface of cooled plate :
1173/1
744/1
1010 15.0 1010 54.0
LLL
LLL
RaRaNuRaRaNu
•Lower surface of heated plate, or Upper surface of cooled plate :
1054/1 1010 27.0 LLL RaRaNu
Note: Use fluid properties at the film temperature
2
TT
T sf
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Boiling and Condensation
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Classification of Boiling
• Microscopic classification or Boiling Science basis:• Nucleated Boiling• Bulk Boiling• Film Boiling• Macroscopic Classification or Boiling Technology basis:• Flow Boiling• Pool Boiling
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Further Behavior of A Pool of Liquid
Increasing DT
Natural Convection
Onset of Boiling
Isolated Bubble Regime
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Boiling occurs when the surface temperature Tw exceeds the saturation temperature Tsat corresponding to the liquid pressure
re) temperatu(excess TTT where Th)TT(hq :ratefer Heat trans
satwe
esatws
Boiling process is characterized by formation of vapor bubbles, which grow and subsequently detach from the surface
Bubble growth and dynamics depend on several factors such as excess temp., nature of surface, thermo physical properties of fluid (e.g. surface tension, liquid density, vapor density, etc.). Hence, heat transfer coefficient also depends on those factors.
Boiling
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Pool Boiling Curve
sq
eT
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Modes of Pool Boiling
Free convection boiling
Nucleate boiling
Transition boiling
Film boiling CT
CTC
CTC
CT
e
e
e
e
120
12030
305
5
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Condensation occurs when the temperature of a vapor is reduced below its saturation temperature
Condensation heat transfer Film condensation
Heat transfer rates in drop wise condensation may be as much as 10 times higher than in film condensation
Condensation
Drop wise condensation
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Laminar Film condensation on a vertical wall (VW)
Condensate Film
g
y
y
x
Tsat
(x)
A
T
y
x
AA
y
yyu
l
yyyu
l
ygA)vl(
A
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Laminar Film condensation on a vertical wall (cont..)
4/1
lwsat
3lvlfg
4/1
vlfg
lwsatl
)TT(x4k)(gh
)x(h)(gh)TT(xk4)x(
fg
wsatL
fg
wsatL
4/1
lwsat
3lvlfg
L
h)TT(Ah
hqm :rateon Condensati
)TT(Ahq :ratefer heat trans Total
length. plate theis L where
)TT(Lk)(gh
943.0h coeff. Average
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ExampleLaminar film condensation of steamSaturated steam condenses on the outside of a 5 cm-diameter vertical tube, 50 cm high. If the saturation temperature of the steam is 302 K, and cooling water maintains the wall temperature at 299 K, determine: (i) the average heat transfer coefficient, (ii) the total condensation rate, and (iii) the film thickness at the bottom of the tube.Given: Film condensation of saturated steamRequired: (i) Average heat transfer coefficient, (ii) total condensation rate, (iii) and film thickness1. Effect of tube curvature negligible2. Effect of liquid sub cooling negligible3. Laminar
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Example (contd...)
Condensate Film
g
y
y
x
Tsat
(x)
A
T
4/1
lv)wTsatT(L
3lk)vl(g'
fgh943.0
_h
:bygiven is coefficentsfer heat trasn Average The
3m/kg03.0v kg/J610432.2fgh
:properties water of Table From
Evaluate hfg at the saturation temperature of 302 K
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Example (contd...)
kg/s 1033.7)10432.2(
)5.0)(05.0()3)(7570(
:is rate oncondensati totalThe (ii)
KW/m7570)1087.0)(3)(5.0(
)611.0(03.0996)81.9)(10432.2(943.0
943.0
/sm 100.87
kg/m 996
W/mK 611.0 for water Also,
46
2
4/1
6
36
4/13
26-
3
fgfg
lwsat
lvlfh
l
l
l
hTAh
hQm
TTLkgh
h
k
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Example (contd...)
m 1008.1)81.9)(996(
)1067.4)(103(0.87 Hence,
kg/ms 1067.4)05.0)((
)1033.7(
:is film of unit widthper rateflow mass The
3
is thicknessfilm The iii)(
43/136-
34
3/1
l
Dm
g lvl
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