Table Of ContentStudies in Systems, Decision and Control 101
Damian Piotr Muniak
Radiators
in Hydronic
Heating
Installations
Structure, Selection and Thermal
Characteristics
Studies in Systems, Decision and Control
Volume 101
Series editor
Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland
e-mail: [email protected]
About this Series
The series “Studies in Systems, Decision and Control” (SSDC) covers both new
developments and advances, as well as the state of the art, in the various areas of
broadly perceived systems, decision making and control- quickly, up to date and
withahighquality.Theintentistocoverthetheory,applications,andperspectives
on the state of the art and future developments relevant to systems, decision
making,control,complexprocessesandrelatedareas, asembeddedinthefieldsof
engineering,computerscience,physics,economics,socialandlifesciences,aswell
astheparadigmsandmethodologiesbehindthem.Theseriescontainsmonographs,
textbooks, lecture notes and edited volumes in systems, decision making and
control spanning the areas of Cyber-Physical Systems, Autonomous Systems,
Sensor Networks, Control Systems, Energy Systems, Automotive Systems,
Biological Systems, Vehicular Networking and Connected Vehicles, Aerospace
Systems, Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power
Systems, Robotics, Social Systems, Economic Systems and other. Of particular
valuetoboththecontributorsandthereadershiparetheshortpublicationtimeframe
and the world-wide distribution and exposure which enable both a wide and rapid
dissemination of research output.
More information about this series at http://www.springer.com/series/13304
Damian Piotr Muniak
Radiators in Hydronic
Heating Installations
Structure, Selection and Thermal
Characteristics
123
Damian PiotrMuniak
Institute of Thermal Power Engineering
CracowUniversity of Technology
Kraków
Poland
ISSN 2198-4182 ISSN 2198-4190 (electronic)
Studies in Systems,DecisionandControl
ISBN978-3-319-55241-5 ISBN978-3-319-55242-2 (eBook)
DOI 10.1007/978-3-319-55242-2
LibraryofCongressControlNumber:2017934310
©SpringerInternationalPublishingAG2017
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart
of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission
or information storage and retrieval, electronic adaptation, computer software, or by similar or
dissimilarmethodologynowknownorhereafterdeveloped.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publication does not imply, even in the absence of a specific statement, that such names are exempt
fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.
The publisher, the authors and the editors are safe to assume that the advice and information in this
book are believed to be true and accurate at the date of publication. Neither the publisher nor the
authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor
for any errors or omissions that may have been made. The publisher remains neutral with regard to
jurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations.
Printedonacid-freepaper
ThisSpringerimprintispublishedbySpringerNature
TheregisteredcompanyisSpringerInternationalPublishingAG
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
Contents
1 Introduction.... .... .... ..... .... .... .... .... .... ..... .... 1
1.1 Thermal Comfort .... ..... .... .... .... .... .... ..... .... 2
References.. .... .... .... ..... .... .... .... .... .... ..... .... 12
2 Radiators in Hydronic Heating Installations. Historical Outline,
Types and Structure. .... ..... .... .... .... .... .... ..... .... 15
2.1 Historical Outline.... ..... .... .... .... .... .... ..... .... 15
2.2 Current Realizations of the Concept of a Radiator Intended for a
Hydronic Heating Installation.... .... .... .... .... ..... .... 19
2.2.1 Segment (Column) Radiators .. .... .... .... ..... .... 19
2.2.2 Panel Radiators..... .... .... .... .... .... ..... .... 21
2.2.3 Convector Radiators . .... .... .... .... .... ..... .... 24
2.2.4 Canal Radiators..... .... .... .... .... .... ..... .... 26
2.2.5 Tube Radiators ..... .... .... .... .... .... ..... .... 27
2.2.6 Surface Radiators ... .... .... .... .... .... ..... .... 29
References.. .... .... .... ..... .... .... .... .... .... ..... .... 45
3 Radiator Thermal Characteristic.... .... .... .... .... ..... .... 49
3.1 Introduction .... .... ..... .... .... .... .... .... ..... .... 49
3.2 The Radiator Static Thermal Characteristic Assuming Constant
Surface Film Conductance from the Radiator Wall External
Surface.... .... .... ..... .... .... .... .... .... ..... .... 50
3.3 The Radiator Static Thermal Characteristic Taking Account of
Variable Surface Film Conductance from the Radiator Wall
External Surface. .... ..... .... .... .... .... .... ..... .... 53
3.4 The Radiator Static Thermal Characteristic Taking Account
of the Variability in Surface Film Conductance to the Radiator
Wall Internal Surface . ..... .... .... .... .... .... ..... .... 65
3.5 The Radiator Dynamic Thermal Characteristic... .... ..... .... 88
3.5.1 The Convector Radiator Dynamic Thermal
Characteristic.. ..... .... .... .... .... .... ..... .... 89
v
vi Contents
3.5.2 The Surface Radiator Dynamic Thermal Characteristic.... 94
References.. .... .... .... ..... .... .... .... .... .... ..... .... 104
4 Methods of the Radiator Heat Output Control. .... .... ..... .... 109
4.1 The Convector Radiator Heat Output Control.... .... ..... .... 116
4.2 The Surface Radiator Heat Output Control.. .... .... ..... .... 116
4.2.1 The Underfloor Radiator Temperature Control System
with a One-Way Thermostatic Valve .... .... ..... .... 117
4.2.2 The Underfloor Radiator Temperature Control System
with a Two-Way Thermostatic Valve
on the Return Pipe .. .... .... .... .... .... ..... .... 121
4.2.3 The Underfloor Radiator Temperature Control System
with a Two-Way Thermostatic Valve on the
Supply Pipe... ..... .... .... .... .... .... ..... .... 124
4.2.4 The Underfloor Radiator Temperature and the Room
TemperatureControlSystemwithaThermostaticControl
Valve ... .... ..... .... .... .... .... .... ..... .... 126
4.2.5 The Underfloor Radiator and the Room Temperature
Control System with an Electric Regulator.... ..... .... 128
4.2.6 The Underfloor Radiator and the Room Temperature
Control System with an Electronic Regulator .. ..... .... 130
4.2.7 Control System of a Surface Heating Installation with
Numerous Heating Loops. .... .... .... .... ..... .... 132
4.2.8 The Underfloor Radiator Temperature Control System
Using the Return Water Temperature Limiter.. ..... .... 135
4.3 The Impact of the Radiator Connection Method on the Heat
Output .... .... .... ..... .... .... .... .... .... ..... .... 137
References.. .... .... .... ..... .... .... .... .... .... ..... .... 142
5 The Sizing of Surface Radiators. .... .... .... .... .... ..... .... 145
5.1 The Underfloor Radiator Thermal Calculations and Sizing... .... 145
5.1.1 Equivalent Resistance Method (Trapezoidal Rule) ... .... 153
5.1.2 The Method According to Standard EN 1264.. ..... .... 162
References.. .... .... .... ..... .... .... .... .... .... ..... .... 178
6 Selection of Radiators for Heating Installations Computational
Examples .. .... .... .... ..... .... .... .... .... .... ..... .... 181
References.. .... .... .... ..... .... .... .... .... .... ..... .... 251
Symbols
a Coefficient of temperature levelling (thermal diffusion), m2/s, or a
correction factor taking account of the variability in surface heat
conductance to the radiator wall internal surface depending on the
working medium mass flow (–)
’ ’
a, b Lengths of the elementary trapezium bases (m)
a Floor covering factor (–)
B
a Pipe spacing factor (–)
b
a Theradiatorcoveringfactor,takingaccountofthedensityofthefloor
u
covering by pipes (–)
a Pipe external diameter factor (–)
dz
A Radiator surface area—air side (m2)
A Skin surface area (m2)
s
A Surface area of a single element of a column radiator on the air side
el
(m2)
A Nominal surface area of a column radiator (air side) for which the
el,o
thermal characteristic parameters are determined (m2)
a , a Lengths of the trapezium heating plates (bases) upwards and
g d
downwards, respectively (m)
b Thermal absorption coefficient, J/(m2·s0.5·K) or pipe spacing (m)
B Factor of conversion to the underfloor radiator overall heat transfer
coefficient (–)
B Nominal (reference) factor of conversion to the underfloor radiator
0
overall heat transfer coefficient (–)
B Boundary value of the factor of conversion to the underfloor radiator
gr
overall heat transfer coefficient (–)
c, c Specific heat (of the substance/material or water, respectively) (J/
w
(kg∙K))
c’ , c’ Distancebetweenthepipeaxisandthetrapeziumupperorlowerside,
g d
respectively (m)
vii
viii Symbols
c , c Correction factors for the radiator thermal characteristic exponent
0 1
n (–)
c Correction factor dependent on the fluid flow character, the Gr∙Pr
k
product and the radiator plate heating/cooling method (–)
C Factor of conversion to the radiator wall overall heat transfer
coefficient, related to the heating surface area A (–)
C Factor of conversion to the radiator wall overall heat transfer
1
coefficient,relatedtotheradiatordimensionscharacteristicofagiven
series of types (–)
C Correction factor takingaccountofthemutual screeningeffect ofthe
2
radiator elements giving up heat or of the heat flux non-linear rise
resulting from an increasein theradiator characteristic dimension (–)
C Correction factor taking account of the temperature field hetero-
3
geneity in the floor (–)
C Nominal (reference) factor of conversion to the radiator wall overall
o
heat transfer coefficient for which thermal characteristic parameters
are determined (–)
d Pipe internal diameter, m
w
d Internal diameter of sheathing or insulation, m
w,iz
d Pipe external diameter, m
z
d External diameter of sheathing or insulation, m
z,iz
e Radiator wall thickness, m
e Reference pipe wall thickness, m
0
e Pipe wall thickness, m
R
f Clothing surface area factor (–)
cl
f Factor of conversion to the boundary density of the underfloor
gr
radiator heat flux (–)
g Gravitational field acceleration, m/s2
Gr Grashof number (–)
h Height of the elementary trapezium or the valve plug lift, m
h Person’s height, m
cz
h‘ , h‘ Vertical distance between the pipe axis and the underfloor radiator
g d
upper and lower heating surface, respectively, m
h Trapezium height, m
o
h , h trapezium height upwards (above the pipes) and downwards (under
og od
the pipes), respectively, m
h , h Trapezium height upwards (above the pipes) and downwards (under
ug ud
the pipes) converted to the reference layer equivalent thickness,
respectively, m
H Radiator height (in the case of panel radiators), m
k System amplification factor (–)
k Thermostatic head amplification factor, mm/K
m
l Net length of the pipe, m
l Characteristic linear dimension related to heat absorption from the
0
radiator surface, m
Symbols ix
L Indicative value of the underfloor radiator coil length, m
w,or
L Parameterdeterminingtheradiatorsize,e.g.lengthinmetres,number
of elements, modules, etc.,
m Element mass, kg
m Radiator mass, related to 1 m2 of outer surface, kg/m2
A,g
m Mass of the water in radiator, related to 1 m2 of outer surface, kg/m2
A
m Person’s weight, kg
cz
m_ Water mass flow in the radiator, related to 1 m2 of outer surface,
A
kg/(s∙m2)
m , m , m Exponents for coefficient a in floor heating (–)
b u dz i
m_ Working medium mass flow, kg/s, kg/h
M_ Unit heat output generated due to metabolism, W/m2
n Exponent of the radiator thermal characteristic that takes account
of the impact of the mean temperature difference on the value of
surface film conductance from the radiator external surface (–)
n Number of elements in a column radiator (–)
el
n Nominal(reference)numberofthecolumnradiatorelementstowhich
el,o
the thermal characteristic parameters are related (–)
n Boundary value of the radiator thermal characteristic exponent (–)
gr
n Exponentoftheconvectiontermofthesurfacefilmconductancefrom
k
the radiator external surface, dependent on the flow character (–)
n Exponent of the radiator thermal characteristic that takes account
p
of the impact of ambient pressure on the radiator heat output (–)
N Nusselt number
u
p Water vapour partial pressure, Pa
a
p’ Pressure other than standard ambient pressure of the radiator
ot
operation, Pa
p Standard ambient pressure for which theradiator nominal power was
ot
measured, Pa
Pr Prandtl number (–)
Pr Prandtl number for the fluid flow core (–)
f
Pr Prandtl number for the fluid at the pipe wall (–)
w
r , r Radii of the wall cylindrical sector, m
1 2
Ra Heat resistance of conductance from the radiator external surface,
(m2∙K)/W
’
Rc Heat resistance related to the external surface of a cylindrical wall
with unit length l = 1m, (m∙K)/W
R’ Heatresistancerelatedto1m2oftheexternalsurfaceofacylindrical
j
wall, (m2∙K)/W
’ ’
R , R Unit resistance of the trapezium overall heat transfer upwards and
kg kd
downwards, respectively, related to 1 linear metre of the pipe,
(m∙K)/W
R The trapezium overallheatresistancerelated tounit length,(m∙K)/W
c
