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Thread: How to calculate internal/external temperatures

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    Default How to calculate internal/external temperatures

    I have been reading a book about solar houses. One of the Figures in the book "Differing resistances of construction elements" shows, as an example, an uninsulated timber frame wall having an exterior temperature of 2 C and the internal temperature of 10 C.

    With insulation the temperatures are 2 C and 14 C respectively. No calculations, no R values, no U values, etc.

    Assuming a known outside temperature and knowing the construction materials of the wall how is the internal temperature calculated?



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    Thermometer data - there is enough buildings in existence with known insulation value & tested internal/external temps recorded to give calculated values.
    Cheers, Tiny
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    Talking An over simplification.

    Quote Originally Posted by Guiseppe View Post
    I have been reading a book about solar houses. One of the Figures in the book "Differing resistances of construction elements" shows, as an example, an uninsulated timber frame wall having an exterior temperature of 2 C and the internal temperature of 10 C.

    With insulation the temperatures are 2 C and 14 C respectively. No calculations, no R values, no U values, etc.

    Assuming a known outside temperature and knowing the construction materials of the wall how is the internal temperature calculated?
    "There are three kinds of lies: lies, damned lies, and statistics".
    You can use the same statistics to prove whatever you wish to prove, either for or against.
    In your example, very many other factors would need to be considered.
    Too numerous to list.
    Last edited by beer4life; 01-07-12 at 08:59 PM.

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    Quote Originally Posted by beer4life View Post
    You can use the same statistics to prove whatever you wish to prove, either for or against.
    In your example, very many other factors would need to be considered.
    Too numerous to list.
    I absolutely agree with you here, the stats can only be used as a guide & only if there from a reputable source.

    The variables are endless.
    Cheers, Tiny
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    Quote Originally Posted by Tiny View Post
    ... The variables are endless.
    No they are not.

    I have been thinking about this over night and have come to the conclusion that the problem is analogous to a simple electrical circuit:

    a resistor (R) with a voltage drop (E) due to current flow (I).

    Knowing the values of either two the third can be calculated. E = I x R

    In the temperature case (R) is the thermal resistance, (E) is the temperature difference and (I) is the heat loss.

    Once again knowing the values of either two the third can be calculated.

    In my original post there are, in fact, two unknowns that are inter-related as discussed in this post - heat loss and the temperature difference.

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    Wink Exponential Functions: Introduction

    Quote Originally Posted by Guiseppe View Post
    No they are not.

    I have been thinking about this over night and have come to the conclusion that the problem is analogous to a simple electrical circuit:

    a resistor (R) with a voltage drop (E) due to current flow (I).

    Knowing the values of either two the third can be calculated. E = I x R

    In the temperature case (R) is the thermal resistance, (E) is the temperature difference and (I) is the heat loss.

    Once again knowing the values of either two the third can be calculated.

    In my original post there are, in fact, two unknowns that are inter-related as discussed in this post - heat loss and the temperature difference.
    Incorrect. It is not a linear function.
    The rate of change is a function of the difference.
    To clarify:-
    Exponential Functions: Introduction (page 1 of 5) Sections: Introduction, , , ,
    Exponential functions look somewhat similar to functions you have seen before, in that they involve exponents, but there is a big difference, in that the variable is now the power, rather than the base. Previously, you have dealt with such functions as f(x) = x2, where the variable x was the base and the number 2 was the power. In the case of exponentials, however, you will be dealing with functions such as g(x) = 2x, where the base is the fixed number, and the power is the variable.
    Let's look more closely at the function g(x) = 2x. To evaluate this function, we operate as usual, picking values of x, plugging them in, and simplifying for the answers. But to evaluate 2x, we need to remember how exponents work. In particular, we need to remember that mean "put the base on the other side of the fraction line".

    So, while positive x-values give us values like these:




    ...negative x-values give us values like these:
    Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved




    Putting together the "reasonable" (nicely graphable) points, this is our T-chart:




    ...and this is our graph:


    And a lot more here:-
    http://www.purplemath.com/modules/expofcns.htm



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    Quote Originally Posted by beer4life View Post
    Incorrect. It is not a linear function.
    The rate of change is a function of the difference. ...
    I know that in the real world both internal and external temperatures would be changing but I am not talking about that or the rate of change.

    I am looking at a simple, instantaneous, calculation.

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    Quote Originally Posted by Guiseppe View Post
    I know that in the real world both internal and external temperatures would be changing but I am not talking about that or the rate of change.

    I am looking at a simple, instantaneous, calculation.

    A good start here would be to understand how "R" values are calculated.

    "The R-value is a measure of used in the building and industry. Under uniform conditions it is the ratio of the temperature difference across an insulator and the (heat transfer per unit area, ) through it or .The R-value being discussed is the unit thermal resistance. This is used for a unit value of any particular material. It is expressed as the thickness of the material divided by the . For the thermal resistance of an entire section of material, instead of the unit resistance, divide the unit thermal resistance by the area of the material. For example, if you have the unit thermal resistance of a wall, divide by the cross-sectional area of the depth of the wall to compute the thermal resistance. The unit thermal conductance of a material is denoted as C and is the reciprocal of the unit thermal resistance. This can also be called the unit surface conductance and denoted by h. The higher the number, the better the 's effectiveness. (R value is 1/h.) R-value is the of U-value.


    Factors=

    There are many factors that come into play when using R-values to compute heat loss for a particular wall. Manufacturer R values apply only to properly installed insulation. Squashing two layers of batting into the thickness intended for one layer will increase but not double the R-value. Another important factor to consider is that studs and windows provide a parallel heat conduction path that is unaffected by the insulation's R-value. The practical implication of this is that one could double the R value used to insulate a home and realize substantially less than a 50% reduction in heat loss. Even perfect wall insulation only eliminates conduction through the insulation but leaves unaffected the conductive heat loss through such materials as glass windows and studs as well as heat losses from air exchange.


    Thermal conductivity versus apparent thermal conductivity

    is conventionally defined as the rate of thermal conduction through a material per unit area per unit thickness per unit temperature differential (delta-T). The inverse of conductivity is resistivity (or R per unit thickness). is the rate of heat flux through a unit area at the installed thickness and any given delta-T.
    Experimentally, thermal conduction is measured by placing the material in contact between two conducting plates and measuring the energy flux required to maintain a certain temperature gradient.
    For the most part, testing the R-value of insulation is done at a steady temperature, usually about 70°F with no surrounding air movement. Since these are ideal conditions, the listed R-value for insulation could be higher than it really is, because most situations with insulation are under different conditions
    A definition of R-value based on apparent thermal conductivity has been proposed in document C168 published by the American Society for Testing and Materials. This describes heat being transferred by all three mechanisms—conduction, radiation, and convection.
    Debate remains among representatives from different segments of the U.S. insulation industry during revision of the U.S. FTC's regulations about advertising R-values illustrating the complexity of the issues."


    As you can see, its not that simple.
    Hope that helps.


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    Cheers, Tiny
    "You can lead a person to knowledge, but you can't make them think? If you're not part of the solution, you're part of the problem.
    The information is out there; you just have to let it in."

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    Wink Varistor.

    Quote Originally Posted by Guiseppe View Post
    No they are not.

    I have been thinking about this over night and have come to the conclusion that the problem is analogous to a simple electrical circuit:

    a resistor (R) with a voltage drop (E) due to current flow (I).

    Knowing the values of either two the third can be calculated. E = I x R

    In the temperature case (R) is the thermal resistance, (E) is the temperature difference and (I) is the heat loss.

    Once again knowing the values of either two the third can be calculated.

    In my original post there are, in fact, two unknowns that are inter-related as discussed in this post - heat loss and the temperature difference.
    The problem with your analogy, is that you are considering the walls as a resistor and liken the solution as using a constant value for R.
    ~R varies with temperature differential.
    Therefor it behaves like a VARISTOR, and cannot be simply calculated with Ohm's Law.

    Another point to raise is that all Thermodynamic calculations use Absolute Zero as the reference. ( Minus 273 degrees Centigrade.)
    A varistor is an electronic component with a "-like" . The name is a of . Varistors are often used to protect against excessive transient by incorporating them into the circuit in such a way that, when triggered, they will shunt the current created by the high voltage away from the sensitive components. A varistor is also known as Voltage Dependent Resistor or VDR. A varistor’s function is to conduct significantly increased current when voltage is excessive.
    Note: only non-ohmic variable resistors are usually called varistors. Other, ohmic types of variable resistor include the and the .

    Last edited by beer4life; 02-07-12 at 06:00 PM.

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    Quote Originally Posted by beer4life View Post
    ..
    ~R varies with temperature differential.
    Sorry mate but the R value cannot change - it is the heat loss that changes with differing temperatures either side of the material.

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