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CHAPTER 8
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CONTENTS
8.1 Natural Convection
8.2 Equation of Motion & Grashof Number
8.3 Natural Convection over Surfaces8.4 Natural Convection from Finned Surfaces
8.5 Combined Convection
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LESSON OUTCOMES
At the end of the lesson, students should be able
to:
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Understand the physical mechanism of natural convection
Derive the governing equations of natural convection, and obtainthe dimensionless Grashof number by nondimensionalizing them
Evaluate the Nusselt number for natural convection associated
with vertical, horizontal, and inclined plates as well as cylinders
and spheres
Examine natural convection from finned surfaces, and determine
the optimum fin spacing
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8.1 Natural Convection
Buoyancy force: The upward force exerted by a fluid on a body completely or
partially immersed in it in a gravitational field. The magnitude of the buoyancy
force is equal to the weight of the fluid displacedby the body.
The net vertical force acting on a body
It is the buoyancy force that keeps the ships
afloat in water (W = Fbuoyancy for floating objects).Faiza M Nasir, Jan 2011
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8.1 Natural
Convection
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The thickness of the boundary layer increases
in the flow direction.
Unlike forced convection, the fluid velocity is
zero at the outer edge of the velocity
boundary layer as well as at the surface of the
plate. At the surface, the fluid temperature is equal
to the plate temperature, and gradually
decreases to the temperature of the
surrounding fluid at a distance sufficiently far
from the surface.
In the case ofcold surfaces, the shape of thevelocity and temperature profiles remains the
same but their direction is reversed.
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The flow regime in natural convection is governed by anotherdimensionless number, Grashof Number (Gr)
The Grashof number provides the main criterion in determiningwhether the fluid flow is laminar or turbulent in natural convection.
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8.2 Grashof Number
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8.2 Grashof Number
For vertical plates, the critical Grashof Number is observed to be 109. the flow is turbulent for higher than 109 Gr number
The coefficient of volume expansion is a measure of
the change in volume of a substance with
temperature at constant pressure.
ideal gas
Tis referred to average temperature
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8.3 Natural Convection
over SurfacesNatural convection heat transfer on a surface depends on the geometry of the
surface as well as its orientation. It also depends on the variation of temperature
on the surface and the thermophysical properties of the fluid involved.
where
The constants Cand n depend on the geometryofthe surface and the flow regime, which is
characterized by the range of the Rayleigh number.
The value ofn is1/4 usually for laminar flow and 1/3
for turbulent flow.
All fluid properties are to be evaluated at the film
temperature Tf= (T
s+ T
g)/2.
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1. Find the fluid properties based on filmtemperature (Tf) where Tf= (Ts+Tg) /2
2. Calculate the Rayleigh Number (Ra)
3. Identify the characteristic length, H (from table)
4. Determine/find from table, the right correlationof Nu based on range of Ra obtained.
5. Calculate the heat transfer/heat loss
Usually radiation analysis should accompany natural convectionanalysis unless the emissivity of surface is low.
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Methodology for Solving
Problem
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A 6 m long section of an 8 cm diameter horizontal
hot water pipe passes through a larger room
whose temperature is 20rC. If the outer surfacetemperature of the pipe is 74 rC, determine the
rate of heat loss from the pipe by natural
convection. (Ans: 443 W)
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Problem 8.1
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Consider a 0.8 m x 0.8 m square plate in a room at28rC. One side of the plate is maintained at atemperature of 106rC, while the other side isinsulated. Determine the rate of heat transfer from
the plate by natural convection if the plate is :
a) Vertical position
b) Hot surface facing up
c) Hot surface facing down
(Ans : 115 W, 128 W, 64.2 W)
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Problem 8.2
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8.4 Natural Convection
over Finned Surfaces
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Natural convection flow through a channel
formed by two parallel plates are commonly
encountered in practice
When the plates are hot, the ambient fluid
enters the channel from the lower end, rises
as it is heated under the effect of buoyancy And the heated fluid leaves the channel from
the upper end
The plates could be the fins of a finned heat
sink, or the PCBs of an electronic device.
The plates can be approximated as being
isothermal (Ts = constant) in the first case,
and isoflux (qs = constant) in the second case.
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8.4 Natural Convection
over Finned Surfaces
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Characteristic lengths
(Sfin spacing orL fin height)
for vertical
isothermal
parallel
plates
The Rayleigh Number:
The average Nusselt Number:
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8.4 Natural Convection
over Finned Surfaces
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where
The rate of heat transfer:
When the fins are essentially isothermal and the fin thickness tis small relative
to the fin spacing S, the optimum fin spacing for a vertical heat sink is
All fluid properties are to be evaluated at
the average temperature Tavg = (Ts + Tg)/2.
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8.5 Combined Convection
Forced convection always accompanied by natural
convection
Error in ignoring natural convection is negligible at high
velocities but may be considerable at low velocities
Criterion to assess the relative magnitude of natural
convection in the presence of forced convection is Gr/Re2
Gr/Re2 < 0.1 Negligible natural convection
Gr/Re2 > 10 Negligible forced convection
0.1 < Gr/Re2 < 10 Both non-negligible
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Natural convection may help or give load to the forcedconvection heat transfer, depending on the relativedirections of buoyancy force and forced convectionmotions
Basically, there are three types of relative directions :
a) Assisting flow
b) Opposing flow
c) Transverse flow
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8.5 Combined Convection
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Assisting flow
the bouyant motion is in
the same direction as the
forced motion.
Heat transfer increases.
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8.5 Combined Convection
Opposing flow
the bouyant motion is in
the opposite direction
as the forced motion.
Heat transfer
decreases.
Transverse flow
the bouyant motion isperpendicular direction asthe forced motion.
enhances fluid mixing andfinally increases heat
transfer.
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When both convections cannot be ignored, use the
following correlation
nnnaturalnforcedcombined NuNuNu/1
s!
+ for assisting and transverse flow
- for opposing flow
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Problem 8.3
A 12-cm-wide and 18-cm-high vertical hot surface in 30oC air
is to be cooled by a heat sink with equally spaced fins of
rectangular profile. The fins are 0.1 cm thick and 18 cm long
in the vertical direction and have a height of 2.4 cm from the
base. Determine the optimum fin spacing and the rate of heattransfer by natural convection from the heat sink if the base
temperature is 80oC.
(Ans: 7.45 mm, 1.30 W)
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