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Thermal Time Constant - TTC

The term “Time Constant” is well defined in Academic Dictionaries and Encyclopedias [6] as “the time it takes the system's step response to reach approximately 63.2% of its final (asymptotic) value”. More sophisticated explanation regarding the “63.2%” value can be found in Wikipedia [4]. Wikipedia also describes the “Thermal Time Constant” term [5]. Detailed explanation regarding “63.2%” value in context of the building thermal mass may be found in publication “Thermal Response of Buildings” of London South Bank University [3]. According to this publication the exact value of “63.2%” is as follows:

Formula – Time Constant Value 1 – 1/e = 0.632 e - Euler’s Number

Considering approximately value of "e" as 2.71828182845904, the “63.2%” value can be calculated more precisely as 63.2120558828557%. Euler's Number can be generated in MS-Excel applying the following formula: =EXP(1) and the Time Constant Value: =1-1/EXP(1)

In most cases the term is related to electronic components rather then to building element. The best definition of this term can be found on the U.S.Sensor Corp. Internet site [7], even the definition is related to electronic component: The Thermal Time Constant is a measurement of the time required for the thermistor to respond to a change in the ambient temperature. The technical definition of Thermal Time Constant is, "The time required for a thermistor to change 63.2% of the total difference between its initial and final body temperature when subjected to a step function change in temperature, under zero power conditions". By replacing the world “thermistor” by “building element”, we can define the Thermal Time Constant of the building element accordingly: The Thermal Time Constant is a measurement of the time required for the building element to respond to a change in the ambient temperature. The technical definition of Thermal Time Constant is: "The time required for a building element to change 63.2% of the total difference between its initial and final body temperature when subjected to a step function change in temperature, under zero power conditions". The unit of TTC is hour (TTC is expressed in hours).

Following example may clarify the meaning of TTC. In this example the building TTC is 40 hours. The room temperature of the building was kept as 18°C for long time. At the starting point of TTC, all internal and external energy sources were switched off, while the ambient temperature is 8°C. For the purpose of this clarification, we shall consider that the ambient temperature remains constant day and night 8°C and there is no solar radiation. The temperature of rooms in the building will start to go down. This is not linear process. Theoretically, the room temperature will reach 8°C at endless time (never), but will get close to it slower and slower. The difference between 18°C room temperature of the building and 8°C ambient temperature is 10°C. 63.2% of this difference is 6.3°C. TTC of 40 hours means that the room temperature of the building will drop by 6.3°C, from 18°C to 10.52°C in 40 hours, if the outside temperature remains constant 8°C and there are not internal or external energy sources and not solar radiation.

According to discussion at Physics Forum [9] “after 4 thermal time constants, the temperature is considered to have stabilized”. 4 TTC results in our case in 4x40hr=160hr, which means that the room temperature will fall almost to 8°C (will be stabilized) in 160 hours. In our example, the Room Temperature after 4 TTCs (4x40hr=160hr) will be 8.2°C, 0.2°C above the final temperature (8°C), far 1.8% to the final temperature.

Based on the above calculation, a formula may be developed to calculate proximity to the ambient temperature as function of the number of TTCs applied.

Formula – Proximity to the target applying number of TTCs Δ = (1/e)^n Δ - proximity to the target, % e - Euler’s Number n - number of TTC applied

In MS-Excel the above formula for n=4 will have the following form: =(1/EXP(1))^4

As the result, the observation “after 4 thermal time constants, the temperature is considered to have stabilized” [9] is not accurate, as the difference to the target is still 1.8%. The proximity to the target of 0.1% will be achieved in 7 TTCs (7x40hr=280hr) and 0.01% in 9 TTCs (9x40hr=360hr).

References 4 Time constant , Wikipedia 2016 https://en.wikipedia.org/wiki/Time_constant 5 Thermal time constant , Wikipedia 2016 https://en.wikipedia.org/wiki/Time_constant#Thermal_time_constant 6 Time constant , Academic Dictionaries and Encyclopedias 2016 http://en.academic.ru/dic.nsf/enwiki/295870/Time 7 Thermal Time Constant , U.S.Sensor Corp. 2016 https://www.digikey.com/Web%20Export/Supplier%20Content/USSensor_615/PDF/USsensor_Thermal_Time_Constant.pdf?redirected=1 9 Thermal Cycling Frequency , Physics Forum 2016 https://www.physicsforums.com/threads/calculating-time-for-object-to-reach-ambient-temperature-in-an-oven.531664/

Nowarski (talk) 20:19, 2 July 2016 (UTC)[reply]

September 2016[edit]

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A tag has been placed on your user page, User:Nowarski, requesting that it be speedily deleted from Wikipedia. This has been done under section G11 of the criteria for speedy deletion, because the page appears to be blatant advertising which only promotes or publicises a company, product, group or service, and which is a violation of our policies regarding acceptable use of user pages; user pages are intended for active editors of Wikipedia to communicate with one another as part of the process of creating encyclopedic content, and should not be mistaken for free webhosting resources. Please read the guidelines on spam, the guidelines on user pages, and, especially, our FAQ for Organizations.

If you think this page should not be deleted for this reason, you may contest the nomination by visiting the page and clicking the button labelled "Contest this speedy deletion". This will give you the opportunity to explain why you believe the page should not be deleted. However, be aware that once a page is tagged for speedy deletion, it may be removed without delay. Please do not remove the speedy deletion tag from the page yourself, but do not hesitate to add information in line with Wikipedia's policies and guidelines. If the page is deleted, and you wish to retrieve the deleted material for future reference or improvement, then please contact the deleting administrator. Melcous (talk) 06:37, 9 September 2016 (UTC)[reply]

Contested deletion[edit]

I was not aware of this policy. Sorry, please remove the tag, and if possible, keep my talk regarding the TTC in buildings.