solar water heating theory r t dobson foru… · 24.10.2008 · 1 sahpa ® south african heat pipe...

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SAHPA®

South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch

Solar Water Heating TheorySolar Water Heating Theory

R T DobsonR T DobsonSenior LecturerSenior [email protected]@sun.ac.za

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TheObjective

of this talk is to present thebasic theory

on which solar water heaters work.

We will considerflat plate solar water heaters

(both thermosyphon and pumped)as well as

evacuated tube solar water heaters

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Contents

How do we?:

•Collect the heat•Transport the heat •Store the transferred heat

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A little about myself

1970-1980 Nuclear Energy1980-1985 Solar Energy

1985-1988 Missile Manufacture Management1988-2008 Heat Transfer Lecturer

My research philosophy is:

Adaptive engineeringwere we try and engineer our heat transfer systems to make

exclusive use ofnatural forces

such as gravity, surface tension density gradients and buoyancyto do the job for us

without the use of any mechanically moving parts such as pumps and mechanical activators and active electronic and mechanical

controls and switches

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We used the roof and the car park as our solar water heater test laboratory at Kwikot LTD, Edinburg Road, Benoni

Solar panels

Integral Solar water heaters

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Thelma (Kwikot Factory Personal manager) cooking pap along side Benoni Lake in 1983

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Front and back-page of our “Frost Resistance” Panel

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Solar water heater Solar water heater configurationsconfigurations

• Integral

• Thermosyphon

• Pumped

• Close-coupled

• Swimming pool

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Integral solar water heaterIntegral solar water heater

Solar collector and Water Storage all in one unitColl

ecto

r

Wate

r stor

age

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ThermosyphonThermosyphonsolar water solar water heaterheater

Collec

tor

Water storage

Solar collector below water Storage and water flows by thermosyphonic action

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Pumped solar water heaterPumped solar water heater

Solar collector below water storage. Water is pumped

Collec

tor Water

storage

Water Pump

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CloseClose--coupled coupled ThermosyponThermosyponsolar water heatersolar water heater

Solar collector and water storage separated but on a common integrated support platform to look like a single unit

Water storage

Collec

tor Roo

f

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Water storage

tank

Tank-in-tank heat exchanger

Solar collector

Thermosyphon (or natural circulation indirect solar water heating system

Circulation loop containing anti-freeze

and water solution

CloseClose--coupled Indirect Tankcoupled Indirect Tank--inin--Tank Tank ThermosyphonThermosyphon solar water heatersolar water heater

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Swimming pool solar water Swimming pool solar water heaterheater

Water pumped from pool up to solar collectors on roof

Open water tank

“High-pressure” pump

Solar collector

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Swimming Swimming pool solar pool solar

water heating water heating systemsystem

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Thermosyphon solar water heating systemHow does it work?

HFhot = ρhotgH Fcold = ρcoldgH

The density of the hot fluid is less than the density of the cold fluid. The force of attraction to the earth of the hot fluid is less than for the cold fluid. As a result of this force imbalance cold fluid sinks and the hot fluid rises and the fluid circulates around the loop. The denser or heavier fluid package will sinks and pushes the less-dense or lighter fluid up

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Hot

Cold

Coldwatersinks

Hot water rises

Insulation

Glass cover

Thermosyphon solar water heating system

Cold water sinks

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Basic theory: Divide the system into control volumes and apply the conservation of mass, momentum and energy

inm&

outm&

invm&

outvm&

mg

outP

inP inhm&

outhm&

x∆℘τ

x∆

R

TT

Q

coldhot

ferheat trans

−=

&

outin mmt

m&& −=

∆∆

APPxmgvmvm

t

mv)( inoutoutin −−∆℘−−−=

∆∆ τ&&

Conservation of mass:

Conservation of momentum:

Conservation of energy and heat transfer: ferheat transoutin Qhmhmt

U&&& +−=

∆∆

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Heat transfer equation: [W] coldhot

R

TTQ

−=&

Conduction: C/W][ °∆=kA

xR

Convection: C/W][ 1 °=

hAR

Radiation: ( )( )[

)273()273()273()273(

1

212

22

1 ++++++=

TTTTAR

σε

Q&

Cold Hot

∆x

Q&

Cold Hot

Fluid

Q& Hot

Cold vacuum

Basic heat transfer theory:

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convectionQ& reflectedQ&

Insulation

Absorber

Glass

longwaveradiationQ&

shortwave

incidentsolarQ &

conductionQ& longwaveradiationQ&

shortwave

incidentsolarQ &

longwaveradiationQ&

Insulation

Absorber

reflectedQ&

convectionQ&

0≈conductionQ& 0≈conductionQ& (a) No glass cover plate

(b) With glass cover plate

Basic theory: Effect of glazing (glass)

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EvacuatedEvacuated--tube solar water tube solar water heatersheaters

Evacuated double walled

glass tube

Vacuum

Black paint

glass

Hot water

Cold water

Vapour

Condensate

Hot water

Evacuated double walled

glass tube +

heat pipe

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Typical domestic evacuatedTypical domestic evacuated--tube tube solar water heater installationsolar water heater installation

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Waterstorage

tank

Pump Expansion tank

Heat exchanger

Typical pumped indirect solar Typical pumped indirect solar water heating systemwater heating system

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solarQ&

( ) ( )inwater outwater air gsurroundincollector

by water

TTcmTTU-

−=−

=−

&&

&&&

solar

absorbedlost

Q

QQQin

ατ

( )air gsurroundincollector TTU −=lostQ&

inwaterinwater cTmQ −− = &&

outwater

outwater

cTm

Q

−

−

= &

&

wateroQ int&

( ) solarreflected QQ && ατ−= 1

solarin QQ && ατ=

( )air gsurroundincollector int TTU −−= solarcollectoro QQ && ατ

inwater

kowater

cTm

Q

−

−

= &

&tan int

inwaterinwater cTmQ −− = &&

Water storage

tank

Basic theory: Heat collection

Heat storage

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Co

llect

or

eff

icie

ncy

, η (

%)

0

100

100 300 200 Temperature difference, Tc – Ta (°C)

where2

TTT outwater inwater

c+≈

80

60

40

20 Black paint Black paint

+ Glass Selective coating + Glass

Evacuated glass tube

Typical solar water heater collector characteristics

( )

( )

( )solar

inwater outwater

solar

solar

air gsurroundincollector

solar

solar

solar

solar

input

input

collected

ac

Q

TTcm

Q

waterintoheat

Q

TTU-

Q

collectedheat factor lossheat

and ,Q

Q

Q

Q factor input heat

Q

Q efficiency colloectorsolar where

:is sticcharacteri eperfofmanc thermalcollector Solar

&

&

&

&&

&

&

&

&

&

&

−==

−==

=⋅==

=

−+=

ατ

ατατ

η

η

b

a

TTba

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ThanksThanks

Corrosion?? Freezing??

Overheating??

Air bubbles??

Pressure??

Reverse thermosyphoning??

Automatic air relief??

Expansion relief??

Gas loaded heat pipe temperature control??

My rules!@#$%^&*()?:Up to 40% electricity savings50 % efficient 500 W/m2 over an 8 hour period

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Waterstorage

tank

Pump Expansion tank

Heat exchanger

Typical pumped indirect solar Typical pumped indirect solar water heating systemwater heating system

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Consider a hollow pipe with a variable diameter and fashioned into a closed loop and also containing a working fluid

Divide the loop up into a number of smaller control volumes, apply the equations of change to each control volume, and integrate around the loop!

∆z

z

g

Expansiontank

Theoretical modeling

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Theoretical modeling (cont.)

Assumptions:* One-dimensional flow* Both liquid and vapour phases are incompressible* Density (pressure) waves occur instantaneously, ie speed of

sound >>

outin0 mmt

m&& −==

∆∆

m&

VAm ρ=&

Single phase flow

outin0 mmt

m&& −=≠

∆∆

Two-phase flow but mass enters the

expansion tank instantaneously

Conservation of Mass

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Conservation of Energy

Single phase flowfor the ith control volume with the temperature T expressed explicitly:

( )tt

ttt imimQcm

tTT outinoutin,

i

ii &&& −+∆+=∆+

i = enthalpym = ρ A∆z

c = specific heat

Heat transfer rate

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Conservation of Energy

( )outinoutin,i

ii imimQcm

tuu

tttt

&&& −+∆+=∆+

If ut+∆t < uf then vtttt cuT ∆+∆+ =hp and 0=∆+ ttx

If u t+∆t > uf then sattt TT =∆+

hp and tt

fgtt

ftttt uuux ∆+∆+∆+∆+ −= , where fgfhp xuuu += ,

fgf xiii += , hpvf Tcu = and hppf Tci = .

Two-phase flowfor the ith control volume with the temperature T expressed explicitly:

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Conservation of Momentum applied to heat pipe control volumes to determine the mass flow rate

Assumptions:* Quasi-eqilibrium* Both liquid and vapour phases are incompressible* Homogeneous two-phase flow model* Hydrostatic pressure at a point (Archimedes and

Boussinesq ‘s approximation)

Buoyancy driving term Frictional-resistance term


∑

∑

∑

∑

=

=

=

=

+

−−=k

k

k

k

N

k

N

k

N

k

N

k

A

L

mA

LL

r

C

A

L

L

t

m

1 kx,

k

1

22

kx,

kequiv,f,k

hpi,k

ko,ko,,f

1 kx,

k

1kkk sing

dd

&

&

ll

ρφ

φρ

solar water heating theory r t dobson foru… · 24.10.2008 · 1 sahpa ® south african heat pipe...

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