IsoCalc 5.0 is a calculation program which allows the scaling of materials for thermal insulation in order to obtain the performance required by the end user e.g. heat loss, the prevention of condensation, temperature drop, surface temperature and freezing times. It is also possible to make energy saving calculation.

IsoCalc 5.0 is easy to use and therefore addressed to everyone who works in the thermal insulation sector that has a basic knowledge of the meaning of the data required by the program.

The end user should only have to insert the correct data required, based on the system to be insulated, in order to obtain the correct insulation thickness necessary and the desired performance. This manual describes how to use the program, which data is required to make the various calculations, how to insert them and how to interpret the results.

Before using the results obtained to complete the insulated system it is advisable to verify them first with our K-FLEX Technical Department.

IsoCalc 5.0 bases its calculation on the International Standard EN ISO 12241.

This version substitutes the previous one, 3.3, and includes the following modifications:

- Calculations are based on EN ISO 12241 and no longer on VDI 2055

- A more “user friendly” lay-out permits you to reduce the windows dimension and to always have access to the bar menu options

- A wider range of temperatures including cryogenic applications.

- Now available in other languages, (Italian, English, Spanish, German, Polish, Russian, French).

- Full compatibility with Windows XP^® , also without administrator privilege.

- Internal and external calculations for K-Flex cladding systems

- Greater information on “heat loss” and “freezing time” calculations.

- Ability to copy onto the clipboard for an easier spreadsheet use (e.g. Microsoft Excel^®)

- Update of K-FLEX products and their specifications.

- A wider database of fluids which help to calculate temperature variations without having to actually recuperate the physical-chemical data

- Energy saving is expressed in €/KWh instead of lire/KWh

All in all, the flexibility of the program has not been altered, and you can still use data as you please (like insulating material specifications or the properties of fluids) to make comparative calculations, to examine random cases, etc...

1.1 Functionality of IsoCalc

Fluids Type of calculation	Liquid				Gas*
Fluids Type of calculation	Tube	Sheet	Tanks^§	Ducts^#	Tube	Sheets	Tanks^§	Ducts^#
Heat loss	√	√	√	√	√	√	√	√
Thermal transmittance	√	√	√	√	√	√	√	√
Energy Saving	√	√	√	√	√	√	√	√
Dew-point Temperature	√	√	√	√	√	√	√	√
Anticondensation Thickness	√	√	√	√	√	√	√	√
Safety thickness limits	√	√	√	√	√	√	√	√
Surface temperature	√	√	√	√	√	√	√	√
Temperature changes for running fluids	√	n.a.	L	$	√	n.a.	L	$
Freezing time for static fluids	√	n.a.	$	$	n.a.	n.a.	n.a.	n.a.
Cooling time for static fluids	√	n.a.	$	$	$	n.a.	$	$
Temperature changes for static fluids	$	n.a.	$	$	$	n.a.	$	$

n.a.: not applicable

L The software does not allow this type of calculation

* For applications with Gas, see chapter 4

§ For tank calculations, see chapter 5

# For duct calculations, see chapter 6

$ calculation can be made by referring to the indications in chapter. 9. In this software version the calculation is not automatic.

2 Calculation Forms

2.1 Heat loss

By Heat loss we mean the amount of heat that flows through an insulated system (tube, walls) in a specified time and is expressed in W (= J/s). This amount has a sign which indicates whether heat is actually lost from the fluid to insulate (minus sign) or whether it receives heat (plus sign). The first situation arises when the external temperature is lower than that of the fluid to insulate (liquid or gas) and in the second, when the conditions are reversed. When the fluid is heated, its temperature rises, whilst during heat loss the temperature drops.

This calculation is based on a static state, and it refers to a stable condition between the fluid and the external temperature. Therefore calculations made when a system is turned on or closed down are not valid.

To find out how much heat is transferred (“heat loss”), one needs the following data:

Ø Temperature of the fluid to insulate (see remark 1) and the external temperature

Ø Dimensions of the duct to insulate: diameter (see remark 2) and the length of the tubes; surface and width for sheets

Ø Thickness and type of insulation

Ø Surface heat transfer coefficient “h”

It is useful to know which insulation thickness can keep fluid heat loss below a desired amount, so by experimenting one can calculate the necessary insulation thickness to guarantee an acceptable amount of heat loss.

In situations where K-Flex insulation is not used, the user can insert the lambda value of the chosen material, taking care to use the value which refers to the mean working temperature of the insulation (that means the average between the internal and external fluid temperatures; see remark 3). This is made possible by choosing “K-factor” and inserting the correct value under the option “Insulation material” (see fig.1).

Figure 1

The term “h” is the sum of the convective surface heat transfer and for radiation of the insulation surface. This can be inserted by the user or can be calculated by the software.

The software does not take into consideration values of h>50, because normally they do not apply for typical insulations: in the case of strong winds, it is more economical to install a windbreak barrier, to also avoid erosion, instead of excessively increasing the insulation thickness.

Calculation “h” for tubes

The parameters to insert in order to calculate “h” are:

Ø Place of insulation (external or internal)

Ø Emission coefficient “e” which is intrinsic of the material, found on the external surface of the insulation (see remark 4). This determines radiation heat transfer between the external surface of the tube and the environment.

Ø For calculations made in internal environments (fig. 2) the user will be asked how the tube is placed (horizontal or vertical)

Figure 2

Ø For external installations (fig. 3), the user will be asked the following information:

§ Wind speed

§ Type of covering (“cladding”, determines e; see remark 4)

Figure 3

Calculation “h” for sheets

The calculation and the parameters required for sheets are the same as those for tubes. However for sheets it is not necessary to indicate whether they are placed horizontally or vertically, but the user will need to indicate the height of the sheet (fig. 4), in order to make calculations for internal and external installations.

Figure 4

For internal insulations the software takes into consideration convective laminar air flows, and laminar or turbulent flows for external insulations depending on wind speed.

Calculations regarding internal insulations protected by a cladding are possible, by using the module for external calculations and inserting “wind speed = 0.01”

Apart from heat loss Q, the program also supplies you with the following data:

ü The average thermal conductivity lambda: the lambda value, intrinsic of the chosen insulation material (eg. K-Flex ST, ECO, ...), relating to mean application temperature (T_m) (T_m= [T_int+ T_est]/2; see remark 3).

ü Thermal transmittance K: is the heat transferred by degree and for surface unit (sheet) or of the length (tubes) between the insulated system and the environment. It is therefore the ratio between the heat transferred and the difference in temperature between the fluid and the environment, expressed in [W/m²K] for sheets and in [W/mK] for tubes

ü Energy saving: this is the percentage of heat that is not lost thanks to the insulation, compared to the same system without insulation.

2.2 Anticondensation thickness

This calculation is used for cooling systems, or for those where the fluid temperature is lower than that of the environment. In this case it is important to know the minimum thickness of the insulation that ensures a sufficiently high surface temperature to avoid the formation of condensation of water vapour on the insulation (see remark 5).

In order to make this calculation the following data is required:

Ø Both fluid (see remark 1) and external temperature (see remark 6)

Ø Relative humidity of the environment (see remark 6)

Ø Dimensions of the duct to insulate: diameters for tubes (see remark 2); height for sheets

Ø Type of insulation

Ø Surface heat transfer coefficient “h”

The result of the calculation is:

ü The temperature of the formation of condensation relating to the inserted degree of humidity and ambient temperature

ü The theoretic minimum thickness to prevent the formation of condensation

ü The dimensions of the K-Flex insulation suitable for the situation, the thickness of which is the next one greater than the theoretic one.

2.3 Surface temperature

This function allows the user to calculate what the temperature will be on the external surface of an insulation material, applied with a given thickness on a duct. In reality the surface temperature is calculated by all the IsoCalc calculation modules, but the user is only able to discover it with this function. To make this calculation, the following is needed:

Ø Temperature of the fluid to insulate (see remark 1) and that of the external environment

Ø Dimensions of the duct to insulate: diameters for tubes (see remark 2); height for sheets

Ø Type and thickness of the insulation

Ø Surface heat transfer coefficient “h”

2.4 Temperature variations for tubes

However efficiently a fluid may be thermally insulated, the heat transfer with the outside will never be completely stopped. This means that the temperature of the fluid to insulate will differ along the duct in which it flows according to the heat transferred and to the intrinsic characteristics of the fluid. The calculation “variations in temperature” allows the user to discover the variation in temperature of the fluid after having passed through an insulated pipe at a given speed. To make this calculation the following is needed:

Ø Both the temperature of the fluid on entry into the pipe (see remark 1) and that of the external environment.

Ø The dimensions of the pipe to insulate: diameter (see remark 2) and length

Ø The specific heat and the density of the fluid (the default data refer to water).

Ø The flow speed of the fluid

Ø Type and thickness of the insulation

Ø Surface heat transfer coefficient “h”

The result is:

ü the temperature variation of the internal fluid after having passed through a given length of tube.

ü Heat loss Q re-calculated to the mean temperature of the fluid, that is to say Tm = (T_entry-T_exit)/2

2.5 Freezing time for tubes with static fluid

In the case of static fluid in a cold environment, over a certain period of time the loss of heat from the fluid will lower the temperature. If the environmental temperature is lower than the freezing point of the fluid in question, (eg. 0°C for water) it is possible that the fluid will reach freezing temperature.

The time required for the freezing process depends on the efficiency of the insulation: the more the fluid is insulated, the slower will be the heat and temperature. The program allows you to calculate freezing time as function of:

Ø Both the initial temperature of the fluid (see remark 1) and the ambient temperature

Ø The dimensions of the pipe to insulate

Ø Specific heat, latent melting heat and freezing temperature of the fluid (the default data refer to water)

Ø The formation of ice (the percentage of the mass of water that will solidify)

Ø The type and thickness of insulation

Ø Surface heat transfer coefficient “h””

If the user only needs to know the time to reach freezing temperature, the value “0%” should be inserted in the “formation of ice” field (see remark 7).

2.5.1 Cooling time

With the module “freezing time” it is also possible to calculate the cooling time required for a liquid to arrive at a final required temperature. It is necessary to modify the following fields, by inserting the following data (see note 8):

Ø Freezing temperature = final temperature

Ø Formation of ice = 0 %

3 Calculations relating to liquids not included in the IsoCalc database

To calculate the variation in temperature and the liquid freezing time, the program makes the data of the following liquids available: water, milk, beer, ammonia, heavy and light crude, ethylene glycol and glycerin. Should it be necessary to make calculations based on liquids not included in this list, the operations are possible if the user already knows the physical-chemical data relevant to the liquid in question, inserting them in the requested fields (overwriting the default values):

- density: this is the ratio between the weight and the volume occupied by the liquid. This is dependent on the temperature, therefore to make precise calculations it is advisable to use the data which refers to the internal temperature. IsoCalc requires the following units of measure: [Kg/m³] = 1000 [g/ml] = 1000 [Kg/l]

- freezing temperature: this is the solid<>liquid transition temperature, i.e. at which a liquid solidifies or a solid melts. IsoCalc requires the data as [°C], therefore the eventual conversion from Kelvin degrees [K] is: °C = K-273

- specific heat: indicated as Cp, this describes how much heat is necessary to increase the fluid temperature by 1°C. This is usually expressed as [cal/g°C] while IsoCalc requires it to be expressed as [J/Kg K]. For the conversion of units of measure: 1 cal/g°C = 4180 J/Kg K. (for conversions of other units of measure see for example www.themeter.net). The specific heat depends on the temperature, therefore to make accurate calculations it is advisable to use the data which refers to the working temperature.

- latent melting heat: indicated as DH_fus, this is the heat required to melt a solid (or the heat to be extracted from a liquid to solidify it). This is expressed as [J/g], numerically the same as [KJ/Kg] which is the format required by IsoCalc.

An interesting database for this data can be found for example at www.engineeringtoolbox.com

4 The use of IsoCalc for gas containing systems

The IsoCalc calculation formulas which are valid for liquids give results which are in some cases also valid (approximately) for gas containing systems.

An important value which helps the user to verify whether results are reliable in the case of tubes or ducts is the speed of gas: the higher it is (very turbulent), the more its behaviour resembles that of a liquid. Therefore the higher the speed of the gas, the more negligible is the difference between the IsoCalc result and that calculated for gases.

Moreover, the results supplied by IsoCalc are always conservative, both in the case of tubes, ducts and tanks, which means that heat losses and temperature differences are overestimated, so calculated insulation thicknesses in reality will give higher performances, as can shown in the table below:

Case

IsoCalc results

(referring to a liquid)

Suitability for systems containing gas (conservative approximation)

T_ambient > T_internal

1) Heat loss

2) T-surface (for anticondensation thickness)

3) variation T

1) yes, since Q_liq > Q_gas,losses will be slightly overestimated

2) yes: since T_liq < T_gas the thickness will be slightly oversized

3) the software calculates variations of T always greater that actual ones

T_internal > T_ambient

1) Heat loss

2) T-surface (for safety limits)

3) variation T

1) yes, since Q_liq > Q_gas

2) yes: since T_liq > T_gas the scaling for safety limits is based on a worse situation

3) the software calculates variations of T always greater that actual ones

We advise you to consult the K-FLEX technical support when interpreting results.

5 Tanks

IsoCalc 5 is not equipped with a calculation formula for tanks. However it is possible to make certain calculations by carefully comparing the tank to a cylindrical tube or a sheet, depending on the cases, as described below.

In the case of tanks there is not a stable condition since the temperature of the fluid held within changes continuously, becoming closer to that of the environment; the time depends on the type of fluid, the dimensions of the tank, the characteristics of the insulation and environmental conditions. Results obtained with IsoCalc, which we repeat are based on a stable condition, are therefore approximate because they take into account the initial fluid temperature.

However this approximation represents a conservative situation and is therefore extremely valid for practical purposes (see also chapter 7). In any case, an indepth examination of tanks, which also takes into consideration the internal heating and agitating systems, is beyond the capacity of this software.

5.1 Rectangular tanks

If a fluid is contained in a rectangular tank, it is possible to make the following calculations:

- Heat loss

- Surface temperature

- Anticondensation thickness

by using the module relating to sheets.

To calculate heat loss, it is necessary to calculate the average heat transfer area by using the following formula

A = (2a + 2b + 4s)L + 2(a+s)(b+s); s = insulation thickness

5.2 Cylindrical tanks

If the tank is cylindrical, it is possible to use the module relating to tubes to make the following calculations:

- Heat loss

- Surface temperature

- Anticondensation thickness

To calculate heat loss, it is necessary to treat the tank as a tube of the same length, in such a way that the 2 transfer surfaces represented by the bases of the tank are included in the calculation. The equivalent length of such a tube represents the height of the tank increased by a sufficient amount so that the total heat transfer area obtained is roughly equal to the real one of the tank.

To calculate the equivalent length one can use the following formula:

where s = insulation thickness; D (diameter of the insulated tank) = d + 2s

Using this equivalent length L_eq it is possible to apply the heat loss results with an acceptable approximation (error << 1%). The other results are more or less precise because they do not depend on the total transfer surface.

6 Ducts

In order to make calculations for rectangular ducts, one must use the module for the calculations of sheets, after having calculated the average heat transfer area of the duct using the following formula:

A = (2a + 2b + 4s)L; s = insulation thickness

7 How to interpret the results

§ Approximations used

All calculations are based on the temperature of the liquid at the source of the system to be insulated.

However this temperature is not constant (for example see the “variation in temperature” module) because the longer the distribution system the closer this will resemble the environment temperature. This means that the difference between the internal and external temperatures is reduced along the distribution system: making the calculation at the source of the system, where the difference in temperature is greater, will therefore represent a conservative approach, important for the scaling based on heat loss, energy saving and hourly costs.

§ Heat loss Q

The quantity Q expressed in [W] (J/s) describes the heat lost from the system every second: lost (minus sign) or gained (plus sign). The exact definition of Q is “loss of power” since Q has the same unit of measure as power. By multiplying Q by a chosen length of time (expressed in seconds) one can calculate the amount of heat that is dispersed in [J], or how much energy (heat = energy!) is wasted by the system in that length of time (e.g. 1 month, 1 year, etc...). Usually kilowatthour [KWh] is used to measure energy which is the product of Q (expressed in KW) for time expressed in hours, since the price of energy refers to KWh.

→ Example: if the result of the calculation is Q = 12.124 W and one wants to know the amount of energy dispersed in one year, then:

- 1 year = 365x24 = 8760 hours. Q = 0.012124 KW => energy dispersed = 106.2 KWh

§ Energy saving / alternative

Every KWh which does not reach its destination, because it is dispersed along the duct, represents a loss in terms of cost. We could use as an example a pipe which carries hot water from a water heater to a shower. Thanks to the insulation one can reduce the amount of heat that is dispersed and therefore save money (for example by lowering the temperature of the boiler). IsoCalc 5 depicts this quantity as the percent of heat that can be saved compared to the same system without any form of insulation:

→ Example: Tube diameter = 25mm, T_int = 0°C, T_est= 25°C => Q_not _insulated = 21.1W.

Using K-Flex ST 10 mm => Q_insulated = 7.7W corresponds to a heat saving of 63.5%.

In the field below the “hourly cost” field the user can choose the thickness of a K-Flex product and see approximately what the heat savings would be (in order to obtain a more precise value the user must repeat the calculation inserting this thickness in the “insulation thickness” field; see remark 9)

§ Hourly cost

The hourly cost calculates the heat dispersed every hour as “lost money” per hour, multiplying the heat loss Q (expressed by KW) by the energy cost: the latter being indicated by the user in the correct field as cost per KWh (default value = 0.500 €/KWh)

→ Example: Q = 620 W => hourly cost = 0.31 €

§ Temperature for the formation of condensation / anticondensation minimum thickness

Condensation forms on piping with lower temperatures than those of the environment if the humidity in the air is sufficiently high. For all ambient temperatures (T_amb) and their relative humidity (UR) the software is actually able to calculate the temperature of condensation formation (see remark 6).

The temperature of condensation formation completely depends on the ambient temperature and its UR, and not on the type of insulation material chosen to make the calculation.

The calculation “surface temperature” is used to calculate the minimum insulation thickness so that the surface temperature of the insulated tube is greater than that of condensation temperature.

However, in the field “dimensions of K-Flex insulation”, IsoCalc suggests the K-Flex product which has a minimum thickness range greater than that of the anticondensation range.

→ Example: anticondensation thickness = 14.6mm (with a 25 mm diameter tube) => K-Flex product to install = 19x25. However it can be chosen, in order to be on a safer side, to install a greater thickness if the humidity value inserted is only approximate.

§ Surface temperature

Knowing the insulation surface temperature allows one to evaluate the suitability of the insulation for its chosen application: apart from heat saving it may be necessary to know whether it is compatible with other structures in the immediate vicinity, or whether being close to the insulation could cause any risks (safety limits). The possibility of the formation of condensation is a topic that has already been discussed. By increasing the thickness of the insulating layer, the surface temperature becomes closer to that of the environment.

§ Temperature variations

The variation in temperature (that is usually indicated as DT) allows the user to know the final temperature of the liquid when it exits the pipe.

The result of the temperature variation DT is subtracted from the temperature of the liquid on entering to arrive at the exit temperature.

→ Example: if with T_initial = 30°C, the result is DT = - 0.3°C => T_final = 30 – (-0.3) = 30.3 °C

Therefore the user can decide whether this final temperature is still within the limits imposed by the project or whether it could create problems for the liquid (e.g. it may reach boiling or freezing temperature).

§ Freezing time / alternatives

Freezing time t_freeze, indicated in hours, is the time required for the change in temperature of the liquid from its initial temperature to its freezing temperature. Moreover, if in the “formation of ice” field the user inserts a value grater than 0 %, for example 20%, the resulting time includes also the time for solidifying 20% of the liquid present.

→ Example: formation of ice = 0% => t_freeze = 0.23 h (= 13’48”)

formation of ice = 20% => t_freeze = 4.04 h (= 4h2’24”)

IsoCalc also shows the freezing time which relates to the K-FLEX products’ available thicknesses.

Please not: for calculations based on the two types of crude oil (light and heavy) included in the software, as the freezing temperature the “pour point” is considered, that is the temperature at which the liquid becomes so thick to make it difficult to flow through a pipe. This temperature however does not correspond to a phase-change, therefore the Cp value is used as the “latent heat” to calculate the time necessary for the formation of a given percentage of solid (or better: of viscose oil).

8 Remarks

1) IsoCalc 5.0 fixes the maximum temperature limit of liquid to insulate at 250°C. This temperature is far above the maximum tolerated temperature of elastomeric insulation (included between 115°C and 150°C, depending on the type of insulation). This choice allows the user to extend calculation possibilities to dual systems in which the insulation is made with 2 materials: the first, resistant to high temperatures (for example rock wool), directly in contact with the hot tube, and the second, a K-FLEX insulation, used to cover the first one, to ensure a not permeable barrier against water vapour.

2) The diameter to use as a reference when inserting the correct value of the insulation is the external diameter of the tube, that is the internal diameter of the tube (through which the liquid flows) increased of the double of the pipe-wall thickness..

3) The exact average working temperature is the average between the surface temperature of the tube (≈ internal fluid temperature) and that of the external surface of the insulation: for a precise calculation an additional operation is required. Using an approximate value as that of the software (as regulations prescribe), the calculated heat loss is greater than the real amount if T_ext >T_int (conservative example), and less than the actual amount if T_ext <T_int (also a conservative example for “cold” applications).

4) The default value e = 0.93 refers to the uncovered black elastomeric foam, as K-Flex ST. Using a K-Flex product of a different colour (for example K-Flex ECO, green) the e value should be modified => see remark 9.3

5) The“anti condensation” calculation is a part of the “surface temperature” calculation, in as much as the surface temperature is calculated based on the insulation thickness until it is the same as the vapour condensation temperature

6) To make a reliable anticondensation thickness calculation, one must first find out the true environmental conditions to which the insulation is subjected, or to which average temperature and humidity the insulation is placed during its working period . These values are chosen with common sense, in a conservative manner, therefore it is important to examine the following examples:

- if the relative humidity (UR) measured varies between 75% and 78%, the percentage to use for the calculation will be 80%

- if the temperature value and UR change during the working period, to make the calculation one can use the worst situation (maximum humidity and the corresponding temperature or the minimum temperature and the corresponding humidity), or the average conditions, after having calculated how long these extreme conditions persist and how sensitive the system is when tested for the formation of condensation.

- if the user does not have the temperature and UR values, use the values of the worst possible conditions to make the calculation, obtainable, for example, by consulting the weather report of the area where the insulation is situated.

It is important to note that, especially for external installations, it would be logical to use conditions that allow one to preserve the installation from condensation for a reasonable length of time (for example, 90% of the working time), in order to avoid excessively re-scaling the insulation. In the space of one day there could be high oscillations of temperature and humidity, and usually, the lowest temperature corresponds to the lowest amount of humidity. There are also moments during the day (for example at dawn) when the atmospheric humidity reaches its saturation point, which changes rapidly, as one can see by noticing the formation of dew on a field and its later disappearing.

The software accepts a maximum humidity value of 96%. Over this value, in fact, insulation thicknesses increase excessively, so it would be only logical to increase ventilation in the rooms, change the coefficient of emission or change other parameters. This is applicable for rooms such as kitchens, bathrooms, shower rooms etc, where an anticondensation thickness calculated based on average humidity would be inefficient.

It is advisable to consult the K-Flex technical division when problems occur

7) To make the calculation of the freezing time, pay attention to the value inserted in the “formation of ice” field. In fact, this field allows one to calculate the time necessary to obtain a partial or a total solidification of the liquid, indicated as a percentage of the mass of liquid in the “formation of ice” field. This value could prove useful if the user needs to know, for example, how much time passes before the piping becomes blocked (partially, 0-99% “formation of ice”, or totally, 100% “formation of ice”) caused by solidification of the liquid. In many practical situations, the formation of ice of up to 25% of the total surface is considered acceptable.

8) To make the calculation of cooling time the user should take into account the following examples, where it is necessary to calculate the time that it takes for a liquid to pass from 30°C to 10°C, with an ambient temperature of -10 °C:

→ Example: the various fields should be filled in as follows:

- Ambient temperature = -10°C

- Internal temperature = 30°C (initial temperature)

- Freezing temperature = 10°C (final desired temperature)

- Formation of ice = 0%

If the liquid in question is not included in IsoCalc, it will be necessary to also fill in the fields relative to density and specific heat (see chapter 3), while the field relative to latent heat is not necessary for this calculation.

9) The approximation of energy saving obtained by choosing one of the thicknesses in the “alternately calculated for K-Flex dimensions” field, is a result of the fact that heat loss is recalculated substituting only the new chosen thickness, without recalculating “h”.

9 Theoretical basics

9.1 Heat transfer between tubes

Heat Q [W] transferred through an insulated tube is:

Ti, Te = internal and external temperature of the tube, respectively [°C o K]

L = length of tube

d = internal diameter of tube [m]

D = external diameter of the insulated tube [m]

a = coefficient of heat transfer for convection (fluid -> internal tube) [W/m².K]

h = coefficient of superficial heat transfer (convection and radiation between the insulated surface and the environment) [W/m².K]

l = Thermal conductivity of the insulation [W/m.K]

9.2 Heat transfer between flat surfaces (sheets)

Heat Q [W] transferred through an insulated sheet is:

A = sheet surface [m²]

s = insulation thickness [m]

a = coefficient of heat transfer for convection (fluid -> internal wall) [W/m².K]

h = coefficient of superficial heat transfer (convection and radiation between the insulated surface and the environment) [W/m².K]

l = Thermal conductivity of the insulation [W/m.K]

9.3 Heat transfer for convection and radiation

Usually a is ignored in the calculation of Q, since heat transfer convection of a flowing liquid is so efficient that the term 1/a is almost zero.

The term h is the sum of the heat transferred for convection and for radiation of the external surface of the tube or sheet and the environment:

h = a_conv + a_irr

a_conv depends on the: surface temperature (T_sup), the dimensions of the insulated tube/sheet, the speed of the external air, the position of the tube/sheet. The calculations are based on semi-empirical formulas. The exact formulas are described in EN ISO 12241.

a_irr, the term referring to radiation, is only dependant on the difference in temperature between the external surface of the insulation (T_sup) and that of the environment:

a_irr = e.e₀

e₀ = coefficient emissivity of black colour = 5.67 10^-8 [W/m²K⁴]

e = coefficient emissivity of the surface material (insulation, coverings ...)

The coefficient e depends on the color of the material: as a general rule, the darker it is, the higher the e value is. One must bare in mind that material subjected to radiation, the one that e refers to, is the one on the outermost surface of the insulation; usually the covering of the insulation, the insulation itself without any covering, or the material of the tube (iron, steel, copper, etc.) for calculations without insulation.

IsoCalc 5.0 lists the e for the K-Flex ST product (default value), for the CLAD products (covered), and for an uncovered tubes.

For grey (eg. K-Flex H) or green coloured products (eg. K-Flex ECO) the e value is approximately 0.80

However the e values are tabulated in literature for every type of material (see for example VDI 2055 or www.engineeringtoolbox.com)

9.4 Temperature variation

The exit temperature of a running fluid in a tube (T_f) is given with the following formula:

T_e = external temperature [°C o K]

T_i = temperature of fluid on entering [°C o K]

k = heat transmittance [W/m.K] => see chapter 2.1

L = tube length [m]

Cp = specific fluid heat [J/Kg.K]

d = flow rate [Kg/s]

If the fluid is resting, the following is used:

T_e = external temperature [°C o K]

T_i = fluid temperature on entry [°C o K]

k = heat transmittance [W/m.K] => see chapter 2.1

t = time [s]

Cp = specific fluid heat [J/Kg.K]

m = mass of fluid [Kg]

9.5 Freezing time

Freezing time is the sum of the time necessary to bring the liquid to its freezing temperature (or fusion) plus the time needed to solidify the percentage of the liquid indicated by the user. The formula for the temperature variation time and the equation which gives one the amount of heat to subtract from a mass of liquid m to render it solid DH_fus ^.m = Q, are used respectively.

The freezing time, in hours [h], is given by:

T_e = external temperature [°C o K]

T_i = initial temperature of the fluid [°C o K]

T_cong = freezing temperature (or fusion) [°C o K]

k = heat transmittance (see chapter 2.1) for heat transfer from T_i to T_cong [W/m.K]

L = tube length [m]

m = liquid mass [Kg]

x = percentage of solid formation compared to the initial mass

DH_fus= melting latent heat (or solidification, see charter 3) [KJ/Kg]

Cp = specific fluid heat [KJ/Kg.K]

Q = heat transferred to the environment of the liquid at freezing temperature [W]

10 Disclaimer

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THE CALCULATIONS ARE PROVIDED "AS IS", WITH NO WARRANTIES WHATSOEVER. ALL EXPRESS, IMPLIED AND STATUTORY WARRANTIES.

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