How does heat loss through conduction occur?

Click For Summary

Discussion Overview

The discussion revolves around the mechanisms of heat loss through conduction, particularly focusing on the effects of material thickness and temperature distribution in a heated bar of homogeneous material. Participants explore the theoretical and mathematical aspects of heat conduction, including steady-state conditions and transient behaviors.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that heat loss through a material is proportional to the temperature difference and inversely proportional to the thickness of the material, as expressed in the equation ΔQ = K*S*ΔT/D.
  • There is a question regarding the physics behind why increased thickness diminishes heat flow even when the system reaches equilibrium, where temperatures are constant on both sides.
  • Participants discuss the temperature distribution in a bar heated on one side, noting that at steady state, the temperature profile is a straight line with a constant slope.
  • Others highlight that before reaching steady state, the temperature distribution changes over time and distance, suggesting a sequential heating of layers within the material.
  • One participant mentions the analogy of layers storing heat and the time it takes for each layer to heat up before transferring heat to the next layer.
  • There is a suggestion to express the concepts in mathematical terms, as the mathematics of one-dimensional heat conduction is considered relatively straightforward.
  • A participant shares a reference to an Excel animation demonstrating temperature variation over time in a 2D area when a hot object is introduced, relating to diffusion models.
  • Another participant seeks further reading on the relevant mathematics of temperature distribution and expresses confusion about the role of thickness in heat conduction at equilibrium.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the impact of material thickness on heat conduction, particularly at equilibrium. While some agree on the basic principles of heat conduction, there remains uncertainty and differing interpretations of how thickness affects energy loss in steady-state conditions.

Contextual Notes

Participants note that the discussion involves assumptions about the homogeneity of materials and the simplifications made in modeling heat conduction. The relationship between thickness and heat flow is not fully resolved, and the discussion reflects ongoing exploration of these concepts.

Who May Find This Useful

This discussion may be of interest to students and professionals in physics, engineering, and materials science, particularly those exploring heat transfer, thermal dynamics, and mathematical modeling of physical processes.

burashka5719
Messages
5
Reaction score
0
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.
 
Science news on Phys.org
burashka5719 said:
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.
 
256bits said:
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.
 
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 .
 
Last edited:
burashka5719 said:
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.
 
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,
 

Similar threads

Undergrad How to measure average thermal conductivity of a metallic material?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Generate heat conduction curves at different time steps
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Estimate thickness of an object based on radiative heat flux decay curve
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Temperature change due to mixing liquids, heating and heat losses
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Warm-up time for a hollow cylinder
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Heat Flow Rate: Dependence on Conductivity & Temp Diff
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad How to understand experiment to measure heat capacity of solid?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Extremely strange consequence of the speed of heat value
  • · Replies 19 ·
Replies
19
Views
2K
Undergrad Determining heat loss and required insulation
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Possible error sources in thermal conductivity experiment?
  • · Replies 16 ·
Replies
16
Views
14K