How does heat loss through conduction occur?

[burashka5719]

Usually it is said that loss of heat through a chunk of material because of conduction is proportional to difference in temperature and inversely proportional to thickness of material.
E.g. if I got a wall to ΔQ = K*S*ΔT/D.
where ΔQ - is energy flow through material. K - constant characteristic to material , S - area through which energy flow happens, ΔT difference in temperature on both sides of material ( in direction of flow) and D - material thickness in direction of the flow.

What I don't understand, is why in case when the process has stabilised ( temperatures are constant on both side of material for a long time) D works to diminish the flow. I know that it is common sense, but I don't understand physics of this process. Can someone explain what happens it terms of atomic or molecular model?
Also, let's say we got a bar of homogenise material which is heated on one side. how looks distribution of temperature through a bar of material as function of time and distance from the point where heat is applied.

 

[256bits]

Also, let's say we got a bar of homogenise material which is heated on one side. how looks distribution of temperature through a bar of material as function of time and distance from the point where heat is applied.

At steady state, the graph of temperature from T1 to T2 through distance D is a straight line of constant slope.

 

[burashka5719]

At steady state, the graph of temperature from T1 to T2 through distance D is a straight line of constant slope.

Yes, but before the system stabilised? During this period distribution of temperature as function of time and distance from 0 can be different.

 

[Nidum]

Think of the block as a series of layers stacked together . First layer has to heat up before it can heat next layer etc sequentially through the total thickness .

The layers don't just conduct heat they store it as well so it takes time for their temperatures to rise .

May be better to put this in mathematical form rather than descriptive . The mathematics for one dimensional heat conduction is relatively easy to understand .

 

[sophiecentaur]

Yes, but before the system stabilised? During this period distribution of temperature as function of time and distance from 0 can be different.

Have a look at this Excel Animation. It shows the way the temperature varies in time over a 2D area when a hot object appears in it. It's a diffusion model.

 

[burashka5719]

Hello,
There are two questions in my original e-mail:
The second one - about temperature distribution as function of time and distance from heat source is more or less clear, but if someone can recommend where I can read about relevant math it would be great.
The first question actually is more of a problem: on one hand common sense tells that thicker insulation diminishes heat flow from high temperature area to cool area,
on the other hand, once the system reaches equilibrium ( constant temperature difference on both sides of insulator) it seams to me that insulator thickness shouldn't have any effect on amount of energy loss.
I try a very simplified model - a long bar of homogeneous material with constant cross section ( 1 dimensional problem) with constant temperature difference on both sides . Once equilibrium is reached insulator doesn't store heat anymore. So taking as example the above model - series of layers stacked together, why 10 or 1000 of layers will conduct less heat then a single one.
My feeling is that there is something that plays a role of resistance in electrical current transfer of flued transfer through a pipe, but in those cases there is energy loss through heat, which doesn't haven here,

 

[Nidum]

This explains the basics :

http://www.me.umn.edu/courses/old_me_course_pages/me3333/essays/essay 5.pdf

More detail :

http://ocw.mit.edu/courses/aeronaut...l-energy-fall-2002/lecture-notes/10_part3.pdf

Something practical :

http://www.foundationcoalition.org/resources/en/engr214/Chapter7/node13.html