How to calculate internal/external temperatures

[Guiseppe]

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?

[Tiny]

Thermometer data - there is enough buildings in existence with known insulation value & tested internal/external temps recorded to give calculated values.

[beer4life]

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.

[Tiny]

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.

[Guiseppe]

... 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.

[beer4life]

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

[Guiseppe]

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.

[beer4life]

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 .

[Guiseppe]

..
~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.