Veriﬁcation and Improving the Heat Transfer Model in Radiators in the Wide Change Operating Parameters

: Laboratory measurements and analyses conducted in a wide range of changes of water temperature and mass ﬂow rate for different types of radiators allowed to provides limitations and assessment of the current radiators heat transfer model according to EN 442. The inaccuracy to determinate the radiator heat output according to EN 442, in case of low water mass ﬂow rates may achieve up to 22.3% A revised New Extended Heat Transfer Model in Radiators NEHTMiR md is general and suitable for different types of radiators both new radiators and radiators existing after a certain period of operation is presented. The NEHTMiR md with very high accuracy describes the heat transfer processes not only in the nominal conditions—in which the radiators are designed, but what is particularly important also in operating conditions when the radiators water mass ﬂow differ signiﬁcantly from the nominal value and at the same time the supply temperature changes in the whole range radiators operating during the heating season. In order to prove that the presented new model NEHTMiR md is general, the article presents numerous calculation examples for various types of radiators currently used. Achieved the high compatibility of the results of the simulation calculations with the measurement results for different types of radiators: iron elements (not ribbed), plate radiators (medium degree ribbed), convectors (high degree ribbed) in a very wide range of changes in the water mass flow rates and the supply temperature indicates that a veriﬁed NEHTMiR md can also be used in designing and simulating calculations of the central heating installations, for the rational conversion of existing installations and district heating systems into low temperature energy ef ficient systems as well as to directly determine the actual energy ef ficiency , also to improve the indications of the heat cost allocators . In addition, it may form the basis for the future modiﬁcation of the European Standards for radiator testing.


Introduction
Studies and analyses have shown that obtaining up to a good operating thermal characteristics of the radiators currently tested according to the "EN442-2 Radiators. Thermal power and test methods" is not possible. Analyses of the conducted measurement results have shown that the current description of the heat transfer process in convection radiator according to EN 442 [1,2] equation is practically correct only for radiators with a low degree of ribbings and mass flow rate close to the nominal value. In the case of smaller radiators mass flows, according to conducted analysis, the discrepancies are up to a dozen percent depending on the type of radiators and the water mass flow rate. The need to correctly determine the influence of the water mass flow on the heat output of the radiators was felt and signalled in some way, and various attempts were made to solve this problem. For example, Calisir et al. [3], for various connection configurations of the tested radiators, provided formulas determining the radiator heat output depending on the mass flow rate and the temperature difference of the supply and return water the form of exponential where: K T , m-radiator constants based on the test results. ∆T w -water temperature drop in the radiator For example, for the TBSE (Top-Bottom-Same-Ends) radiator connection system Φ I = 4064.9 · ∆T 1.033 for the TBOE (Top-Bottom-Opposite-Ends) radiator connection system When it is well known from the "Physics Laws" that if the water temperature drops in the radiator ∆T w and the radiator mass flow rate q m are known-the radiator heat output is determined only by the equation: The comparison of the radiator heat output in the TBSE system obtained from the formula above and according to the "Laws of Physics" in this case is shown in Figure 1. Some researchers try to attribute the influence of heat transfer conditions in the radiator from the water side only to the phenomenon of convection from the heated room side-which leads to mathematically correct relationships to a very limited extent, but at the same time contradicting the source research of this phenomenon carried out by Nusselt [4].
According to pioneering research performed by Nusselt on the of the heat transfer process in the free convection conditions the exponent of the power taking into account the influence of the temperature difference between the wall and the surrounding air in the case of laminar air flows does not exceed the value 0.25 while in the conditions of turbulent air flows it does not exceed the value 0.33.
For example, A. B. Erdogamus [5] in order to obtain acceptable accuracy for the various types of radiators tested with different water mass flow rate, suggested the following dependence for the radiator 1-row type: Φ I = 2.795 · ∆T 1.4115 (5) for the radiator 3-row type : Φ I = 7.908 · ∆T 1.3846 (6) Ássessing the results from the "mathematical" point of view, they may seem correct, but looking from the physical side of the convection phenomenon, we cannot forget about the pioneering source studies by Nusselt [4]-that in convection conditions the exponent "m" must not exceed the value of 1.33.
In the publication [6] by Marchesi, R., at al., it was emphasized that the actual operating conditions of the radiators differ significantly from the conditions in the chamber test according to EN 442, among others-curtains, water mass flow rate,supply temperature and the connection method of the radiator. After the tests, it was found that the radiators heat output decreased to 15% due to hydraulic connections and due to changes in the water mass flow from 10% to 20%. It should be clearly stated that according to the regulations of the currently binding [2] EN 442 standard, it is not possible to determine in accordance with the "Physics Laws", neither the actual thermal performance nor the energy efficiency of radiators. In principle, according to current practice, only the thermal heat output obtained by the radiator is tested in the assumed nominal and reconstructed design parameters in the radiator test chamber: water temperature drop in the radiator ∆T r = 20 K or 10 K air temperature in the room t i = +20 • C and the difference between the average water temperature and the air temperature in the room ∆T m = 50 K. Even if at the request of the Manu f acturers, tests were carried out on the heat output of radiators with a variable water mass flow q m -the equations predicted for this case in the currently valid EN442-2 standard [2] led to results that are inconsistent with the "Physics Laws". According to the proposed Equations (7)-(9) with a constant value of the exponent "c" it follows, that there is a continuous increase in the radiators heat output only due to the increasing of the water mass flow rate through the radiator q c m . In addition, it is very difficult to measure accurately the actual average temperature of the radiator-while measuring the temperature difference between the water supplying the radiator and the air temperature in the room-is indisputable and simple.
It is also known that the radiators will not work in heated rooms at the design air temperature equal to t i = +20 • C, but at the operating air temperature which in case of using Individual billing for heating costs, may be for example t i = +18 • C, while in case of oversized radiators and dysregulated central heating system or because of the individual thermal comfort requirements of the inhabitants may achieved t i = +24 • C.
There is also a fundamental question about the physical and economic sense of obtaining and maintaining during the currently conducted approval tests of radiators-air temperature exactly equal to t i = +20 • C with acceptable small deviations while cooling the walls of the chamber and looking for such a radiator water mass flow rate with a yet unknown radiator thermal power to obtain the nominal radiator return water temperaturewaiting for the stabilization of the heat transfer conditions, depending on the type of the tested radiator several dozen hours-when we know that obtained test results are useless in terms of the operation?
In addition at present a lot of emphasis is placed on activities related to the reduction of the air pollutant emissions e.g., by introducing high efficiency, low-temperature heating installations and low-temperature district heating systems-without changing the current standard EN 442 it will be very difficult to achieve.
Tests for the actual thermal characteristics of different types of radiators were carried out: iron 10-elements radiator, plate radiator, convectors in different connection configurations and operating conditions-temperature and water mass flow rates generally changes from 20% to 200% of the nominal value. The iron elements T1-type radiator constitute the vast majority of the existing central heating installations in Poland. Of course, in currently designed central heating installations, plate radiators and convector radiators are most often used.
On the basis of the studies and analyses carried out the New Extended Heat Trans f er Model in Radiators has been developed and verified. The NEHTMiR md properly describes the heat transfer processes taking place in radiators used in heating systems over a wide range of operating conditions and not only under conditions close to the nominal. This issue is particularly important in the case of existing buildings after their refurbished, where central heating installations with substantial oversized radiators and with too high supply temperature operate during the heating season practically at a mass flow rate of 2 times to 4 times smaller than the nominal value [7,8].
Conducted analyses of the actual heat consumption in more than 600 refurbished buildings showed that the vast majority did not achieve the expected reduction in actual heat consumption (and in some cases actual consumption increased) [7], due to unproperly operating conditions of radiators with very high supply temperature, low mass flow rate and the associated low energy efficiency of the heating systems (Most of which use the Iron Element Radiator T1-type).
In such facilities there is an urgent need to develop "Individual projects" for the thermal and hydraulic adaptation of existing oversized central heating systems to new actual heat demand of the rooms, which is not possible without knowledge of a good model describing the heat transfer in radiators under these conditions.
In addition in such buildings the individual heat cost allocator is commonly used and the current heat transfer model in radiators according to EN 442 [2] is used for their so f tware. As the measurements and analyses carried out have shown, errors due to differing significantly from the nominal of the radiators and the incorrect installation point the heat allocators reach up to 40%.
The developed NEHTMiR md model is essential for: directly assessing the actual energy efficiency of the heating system in the heating season and in the Individual Heating Costs Allocation System, while established the suitable conditions for operational regulation of the Central heating installations and district heating systems.
In addition it will also allow for an appropriate modification of the EU Standards regarding the scope and test conditions of the radiators.

Description of the Existing State
Currently to determine the thermal characteristics of a convector and radiators of different types the EN 442 [2] is commonly used. The general equation describing the radiators heat output according to the EN 442 [2] standard is in the form of: where: On the other hand, when conducting tests on radiators of varying height and fixed length with a variable water mass fluxequations in the form of: It should be emphasized that at present there is practically nothing tested on the dependence of the radiator's heat power output on the variable water mass flux. However. all the above models do not properly describe the heat transfer process in the area of the radiators mass flows rates much smaller than the nominal values.
The problem of determining the actual radiators thermal characteristics under a wide changes of the water mass flow rate conditions is not a new issue. Pioneering research was carried out in the 1969 [9], 1970 [10] by W. Wasilewski and in the 1974 [11], 1981 [12] by R. Rabjasz in which he proposed an equation describing the radiators thermal output in the form of: where c w is the specific heat of the water, m, K M -the constant thermal characteristics of the radiator, ∆t 1 -temperature difference between the supply water and the air temperature in the room.

NEHTMiR-New Extended Model of the Heat Transfer in Radiators
Studies and analyses have shown that the best current model of description of the heat trans f er process in the radiators proposed by by W. Wasilewski [9,10] and by R. Rabjasz [11,12] described by the Equation (10) is correct for water flows through the radiators not less than around 40% of the nominal value. Below these mass water flow values differences between actual and calculated radiator heat outpu are unacceptable and the problem is bigger in the case of ribbed radiators with larger quotient of the outer surface transmitting heat to the air in the room and the surface contacting the water.
The main assumption in the verified New Extended Heat Trans f er Model in Radiators NEHTMiR md is the variability of the radiator heat transfer coefficient depending on the water mass flow rate and temperature difference described in the equation: In operating conditions the heat transfer process in radiators takes place at a variable value of the heat transfer coefficient due to temperature and water mass flow rate changes described by Equation (11). The New Extended Heat Trans f er Model in Radiators, NEHTMiR md is presented in Figure 2. For the elementary surface of the radiator dAx the heat flux transferring to the air in the room describes the equation: Taking into account Equation (11) we will get: An elementary change in the temperature difference between water and air along element dAx describes the equation: On the basis of the above relationship substitute the Equation (13) we will receive: After conversion Equation (15) we will get: Integrating in the boundaries for: Ax = 0, ∆t x = ∆t 1 and for Ax = Ar, ∆t x = ∆t 2 after the transformation we will get the equation describing the energy efficiency of the radiators in the form of: and radiator heat output: Equation describing the temperature of the return water from the radiator: The exponent dm is variable and its value depends on the radiator water mass flow rate and the radiator type. In the case of the plate, multi-row radiator with a ribbing level up to φ = 8.0 good result can be achieved using Equation (21): For the convectors with a higher degree of ribbing, especially in forced airflow conditions, a better result can be achieved by describing the exponent dm as a power function in the form of Equation (22): Generally, in the case of radiators optimalization of the temperature distribution on the surface of the heater in terms of obtaining the greatest possible radiator heat output -it is important but solved only once at the stage of construction (design) of the radiator. However, during the operation-only the actual thermal characteristics of the radiator used are important. That means, how the actual radiator heat output is changing at the set temperature of the air in the heated room-when changing the parameters over which we are influenced i.e., the supply temperature t s and the radiator water mass flow qm. And also whether the radiator heat output corresponds to the actual thermal needs of the room.
During the radiators thermal characteristics tests the actual energy e f f iciency can be directly determined in a very wide range of parameter changes by measuring for the specified ater mass flow rates q m and the set supply temperature t s and air in room t i -two standard radiator response parameters: the heat output Q r and return water temperature t r .

Purpuse and Scope of the Studies Carried Out
The primary purpose of the studies was to verify the developed New Extended Heat Trans f er Model in Radiators NEHTMiR md and also experimentally verify the relationship between the indications of heat cost allocators located at different heights on the radiator and the measured actual amount of heat transferred by the radiator to the environment.

Test Methodology
The research used a closed-type chamber located in the Accredited C.O. Armature Laboratory of the Institute of Heating and Sanitary Technology in Radom and the open-type chamber located in the Heating and Air Conditioning Institute of the Warsaw University of Technology.
The temperature and water mass flow rate measurements were automatically taken every 10 s and recorded using the AL 154 DAO system. Temperature measurements were made using a multi-channel temperature measurement system. The system ensures the accuracy of the temperature measurement at 0.1 K and the automatic recording of measurement values. And the thermographic camera AGA 750 and AGEMA 470 Pro with digital thermographic image recording system for recording and processing thermal images was used to determine the actual temperature distribution on the surface of the radiator and chamber walls and determine the emissivity of the surface of walls and radiator on the basis of a known measured temperature. The instruments and measuring systems used were checked and periodically checked prior to the start of the tests.
During the tests it was measured: the temperature of the water supply t s , return t r , air temperature in room t i at the reference point at height of (0.75 m from the floor at a distance of 1.5 m from the heater), the temperature on the surface of the radiator at 8 points, the temperature on the mounting plate of the heat cost allocators and the water mass flow rates q m .
In order to ensure high accuracy of the measurement water mass flow rates q m , especially at the lowest flows, it was carried out from time to time the check measurements by weight method. An additionally three programmed heat cost allocators located at a height of 0.5 h, 0.52 h and at the height currently commonly used by Heat Cost Allocation Companies 0.75 h have been installed on radiator.
According to thermography measurements, an example of a temperature distribution on the surface of heater T1 is shown on Figure 3.
The location of the heat cost allocators and the arrangement of the radiator temperature measuring points are shown in the Figure 4.       An additional range of quantitatively managed tests to determine the actual operational thermal characteristics of the T1 10-elements iron radiator is shown graphically in Figure 10.

Result and Analysis
The comparison between the measurement and simulation calculations result of radiator heat output, radiator e f f iciency and return water temperature according to the NEHTMiR md for 10-elements iron radiator T1 with no extended external surface (ribbed degree around 1.0) at t s = 70.0 • C is presented in the Tables 1 and 2. Across a wide range of tests and measurements carried out, the discrepancy between the results obtained from simulation calculations based on the NEHTMiR md and the actual values obtain from measurement's had not exceed 2.5%.
On the other hand, using the EN 442 model, discrepancies in the radiator heat output under low water mass flow conditions reach up to −22.3%.
On Figures 11 and 12 for example a comparison between the result of the simulation calculations based on developed NEHTMiR md and measurements the temperature distribution of the water flowing through the radiator and radiator surface temperature distribution along its height obtain from thermography measurements are provided (measurement 1 and 4).   Profile of the radiator T1 surface temperature change, at t s = 70.2 • C, and mass flow rate qmx from 39% to 356% nominal flow rate is presented in Figure 14. As it can be seen in Figure 13 under the high radiator water mass flow rate conditions, the pro f ile of temperature changes and changes in radiator heat output along the heat transfer surface is close to linear. However, in the case of a mall mass water flow rate ( Figure 13-measurement 4)-the profile of the temperature distribution and radiator heat output changes are clearly different from the linear. In addition Figure 14 shows, that for a small water mass flow in the upper zone of the radiator there is the largest difference between the temperature of the water and the radiator wall of about 6.0 K. From the level less than half of the heater in this case, the temperature difference between the flowing water and the radiator wall T f − T s does not exceed 0.9 K.
Along the entire heat transfer area of the radiator the difference between the surface temperature determined from the thermography measurements and simulation calculations according to NEHTMiR md for Elements Iron Radiator T1-type does not exceed 2%.
The developed NEHTMiR md with high accuracy describes heat transfer processes under significant changes of the radiator water mass flow rate and temperature supply. It is highly recommended and useful for determination of seasonal operating conditions and actual energy e f f iciency of the radiators and the whole central heating installations.
On Figures 15 and 16 for example,the radiator T-1 surface temperature distribution according the thermography measurements at t s = 89.7 • C and mass flow rate q mx = 0.0307 kg/s and q mx = 0.0051 kg/s are presented.     Across a wide range of tests and measurements carried out for ribbed radiator Delonghi type 22, the discrepancy between the results obtained from simulation calculations based on the NEHTMiR md and the actual values obtain from measurement's had not exceed 2.0%.
On the other hand, using the EN 442 model, discrepancies in the radiator heat output under low water mass flow conditions reach up to −9.2%.
On Figures 19 and 20 for example,the radiator Delonghi type 22, surface temperature distribution according the thermography measurements at t s = 89.6 • C and mass flow rate q mx = 0.0247 kg/s, (measurement 2) and q mx = 0.0012 kg/s, (measurement 3) are presented.  The comparison radiator Delonghi type 22 effectiveness according the tests and simulation calculations based on the NEHTMiR md (measurements from 1 to 4) for radiator water mass flow rate from 22% to 100% of the nominal value are presented are presented on Figure 21.
The radiator Delonghi type 22, effectiveness according simulation calculations based on the NEHTMiR md as a function of the radiator surface area for radiator water mass flow rate from 22% to 100% of the nominal value are presented on Figure 22.
The developed "New Extended Heat Transfer Model in Radiators" describes very well heat transfer processes under wide changes of the seasonal operating conditions also in the ribbed types of radiators.   Along the entire heat transfer area of the radiator Delonghi-22 , the differences between the ctual temperature determined from the thermal measurements on the radiator Delonghi-22 surface and the results of the simulation calculations based on developed NEHTMiR md does not exceed 2.0%.  As can be seen on Figure 26, under conditions of high water mass flowing through the Delonghi-22 (ribbed degree 4.76), the profile of radiator temperature and heat output changes along the heat transfer surface is practically linear. In the case of a small mass water flow rate q min = 0.0059 kg/s, 24% nominal q mo , see Figure 24-measurement 4-the profile of temperature and radiator heat output changes are more non-linear compared to the non-ribbed radiator T1-type. In order to carry out a complete verification of the New Extended Heat Trans f er Model in Radiators, NEHTMiR md an additional test cycle of convector type radiators with a very high degree of ribbing (from 22.1 to 36.9) also with forced airflow was carried out using a 3-steped drum fan .
The radiators were made up of 8 copper tubes dimeter 18 × 0.5 mm , on which aluminum ribs of 0.15 mm thickness, diameter 125 × 200 mm, and spacing 5 mm were mounted. Tubes arranged in two rows in a combination 2 tubes of parallel or in a serial connection. The convector radiator housing is made of steel sheet. The view of the convector radiators are showed on Figures 27 and 28.  A number of measuring series were carried out over a wide range of changes in the water mass flow rate through the convector radiators from approximately from 26% to 216% of the nominal mas flow rate.
The comparison between the measurement and simulation calculations result of radiator heat output, radiator efficiency and return water temperature according to the NEHTMiR md for Convector Radiator type-8RR and type-8RS with extended external surface (ribbed degree around 22.1) at t s = 51.1 + −0.1 • C and radiator water mass flow rate from 0.0047 kg/s (34% nominal) value to 0.0303 kg/s (216% nominal) value are presented in the Table 5. The comparison between the measurement and simulation calculations result of radiator heat output, radiator e f f iciency and return water temperature according to the NEHTMiR md for Convector Radiator type-8RS with extended external surface (ribbed degree around 22.1) at t s = 58.8 + −0.2 • C and radiator water mass flow rate from 0.0047 kg/s, 26% (nominal) value to 0.0303 kg/s 168% (nominal) value are presented in the Tables 6 and 7. The comparison between the measurement and simulation calculations result of the Convector Radiator type-8RR heat output, with extended external surface (ribbed degree around 22.1) according to the NEHTMiR md at t s = 51.1 • C and radiator water mass flow rate from 0.0047 kg/s, 34% (nominal) value to 0.0303 kg/s, 216% (nominal) value are presented on the Figure 29. The comparison between the measurement and simulation calculations result of the convector radiator type-8RS heat output, with extended external surface (ribbed degree around 22.1) according to the NEHTMiR md at t s = 58.8 + −0.2 • C and radiator water mass flow rate from 0.0035 kg/s, 26% (nominal) value to 0.0226 kg/s, 168% (nominal) value are presented on the Figure 30 .
The difference between the actual heat output of the convector radiators with extended external surface (ribbed degree around 22.1) and calculated according to the NEHTMiR md do not exceed 4.3%.  Actual radiator heat output: Qrac = 924 W Heat output according to radiator effectiveness: Qr = (70.6 − 21.1) × 4186 × 0.143 = 911 W, Q rac = 924 W Actual radiator return temperature t rac = 63.4 • C The return water temperature according to radiator effectiveness: The Discrepancy The discrepancy in the results of measurements and simulation calculations of the radiator efficiency, radiator heat output and return temperature in terms of mass flow rate changes from 39% to 179% of the radiator nominal mass flow rate does not exceed 2.5%.  The discrepancy in the results of measurements and simulation calculations of the Radiator Delonghi-22 efficiency, radiator heatoutput and return temperature in terms of mass flow changes from 23% to 151% of the radiator nominal mass flow rate does not exceed 1.5%.  Actual radiator heat output according to "NEHTMiR md ": Qrac = 388 W Heat output according to radiator effectiveness: Qr = (58.6.0 − 20.8) × 4186 × 0.720 = 399 W, Q rac = 388 W, dQr = −2.8% Actual radiator return temperature: t rac = 32.1 • C The radiator return temperature according the "NEHTMiR md " radiator effectiveness: t rmd = 58.6 − 37.8 × 0.720 = 31.4 • C, dtr = 2.2% The Discrepancy The discrepancy in the results of measurements and simulation calculations of the high ribbed convective Radiator-8RR efficiency , radiator heat output and return temperature in terms of mass flow changes from 26% to 202% of the radiator nominal mass flow rate does not exceed 4.3%.

Conclusions
A revised New Extended Heat Trans f er Model in Radiators NEHTMiR md is general and suitable for all types of radiators, both new radiators and existing radiators after a certain period of operation. It describes the heat transfer processes with very high accuracy in panel radiators (medium ribbed), iron elements radiators (not ribbed), convectors (high ribbed) not only in the nominal conditions -in which the radiators are designed, but what is particularly important also in the operating parameters when the radiators water mass flow rate changes from 10% to 200% of the nominal value and at the same time the supply temperature changes whole range of radiators operation during the heating season (in all tests range max inaccuracies are below 4.3%).
In order to prove the general nature of the NEHTMiR md the comparison of the calculations and measurements results for older iron elements radiators previously commonly used in central heating installations, new plate radiators and convectors currently designed are presented.
Across a wide range of tests and measurements carried out for ribbed radiator Delonghi type 22, the discrepancy between the results obtained from simulation calculations based on the NEHTMiR md and the actual values obtain from measurement's in terms of mass flow changes from 23% to 151% of the nominal value-do not exceed 2.0%.
The discrepancy in the results of the measurements and based on the NEHTMiR md simulation calculations for the Iron Elements Radiator T-1 in terms of mass flow changes from 39% to 179% of the radiator nominal mass flow rate-not exceed 2.5%.
In case of the tests and measurements carried out for High Ribbed Convective Radiator type-8RR across a very wide range of change: supply temperature from t s = 42.3 • C to t s = 59.0 • C and water mass flow from 29% to 258% of the nominal flow rate, maximum discrepancy between the measured and obtain from simulation calculations result according NEHTMiR md -do not exceed 4.3%.
The additional thermography measurements of the temperature distribution on the radiators surface, in the entire range fully confirmed the results obtained from the simulation calculations based on the NEHTMiR md .
This issue is particularly important in the case of the existing buildings after their refurbished , where central heating installations with substantial oversized radiators and with too high supply temperature operate during the heating season practically at a mass flow rate of 2-times to 4-times smaller than the nominal value [7,8,13].
Conducted analyses of the actual heat consumption in more than 600 refurbished buildings showed that the vast majority did not achieve the expected reduction in actual heat consumption (and in some cases actual consumption increased) [7] due to unproper operating conditions of radiators with to high supply temperature, low mass flow rate and the associated low energy efficiency of the heating systems. In such facilities there is an urgent need to develop "Individual projects" for the thermal and hydraulic adaptation of existing oversized central heating systems to new actual heat demand of the rooms, which is not possible without knowledge of the "good model" describing the heat transfer proces in radiators under these conditions.
In addition, in such building the individual heat cost allocators are commonly used and the current heat transfer model in radiators according to EN 442 is used for their so f tware. As the measurements and analyses carried out have shown, errors due to differing significantly from the nominal radiators operating conditions and the incorrect installation point of the heat cost allocators reach up to 40%, [13].
Achieved the high compatibility of the results of the simulation calculations with the measurement results for different types of radiators: Iron Elements, Plate Radiators, Convectors in a very wide range of changes in the water mass f low rates and the supply temperature indicates that the developed NEHTMiR md model is also essential for: • directly assessing the actual energy efficiency of the heating system in the heating season. • improve the indications of the heat allocator due their proper programming in the Individual Heating Costs Allocation Systems [14] . • to establish the suitable conditions for operational regulation of the Central Heating Installations especially in existing buildings after their refurbishment as well as for the District Heating Systems with substantial oversized heat exchangers.
Verified NEHTMiR md can also be used in: designing and simulating calculations of the central heating installations, for the rational conversion of the existing installations and district heating systems into low temperature energy efficient systems.
In addition, it may form the basis for an appropriate modification of the EU Standards regarding the scope and test conditions of the radiators.