chap8 natural convection

8/6/2019 Chap8 Natural Convection

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CHAPTER 8

1Faiza M Nasir, Jan 2011


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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

Faiza M Nasir, Jan 2011 2


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LESSON OUTCOMES

At the end of the lesson, students should be able

to:


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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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.

Faiza M Nasir, Jan 2011


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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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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)


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)


Problem 8.2


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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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Characteristic lengths

(Sfin spacing orL fin height)

for vertical

isothermal

parallel

plates

The Rayleigh Number:

The average Nusselt Number:



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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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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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Assisting flow

the bouyant motion is in

the same direction as the

forced motion.

Heat transfer increases.



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)


chap8 natural convection

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