Conduction
![[url=https://pixabay.com/en/teacup-cup-of-tea-tea-drink-1121646/]"Tea"[/url] by andergrin is in the [url=http://creativecommons.org/publicdomain/zero/1.0/]Public Domain, CC0[/url]](https://www.geogebra.org/resource/zvBPUcWg/vIPT35P3IJ5srZjS/material-zvBPUcWg.png)
Conduction is the transfer of energy from one object or location to another via direct contact between or through materials. This is fundamentally different than convection in which the hot material itself moves. In this case, the materials don't move, but rather energy flows through them. How the heat is transferred is actually via photons (light). Books often describe molecules "bumping into" one another to transfer the heat. While that's a nice picture, from what we know of nature, those molecules don't quite do that. They are waves, and waves emit energy quanta in the form of photons among one another. If the "bumping" picture helps, then use it. Just be careful about taking it too far.
Conductivity depends on the surface area through which the heat will be conducted, the length of the path over which it will be conducted, and the properties of the material through which the heat is conducted. In the picture of hot tea above, the handle end of the spoon outside the liquid will become warm. The length and cross-sectional area of the handle, as well as the type of metal used, are all related to the rate that heat arrives at, or conducts to the spoon's end. Also, the hotter the handle end of the spoon becomes, the slower heat (energy) will flow. This must be true since heat flow ceases if the handle ever matches the hot tea in temperature. The closer the two are in temperature the slower the flow.
This conduction process is often called Newton's Law of Cooling even though it applies equally to heating as in the tea spoon above. The energy is being conducted as kinetic energy of molecules in a fashion rather similar to passing of a baton during a race. One molecule with lots of energy transfers (as a photon) some energy to its neighbor, and the process continues. The equation to describe the rate of heat (Q) transfer in Newton's law of cooling from a hotter region at temperature TH to a cooler one at temperature TC is:
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The constant , where A is the cross sectional area, L is the length of the path along which the heat is conducted and (greek lower case kappa) is the thermal conductivity of the material along which heat is being conducted. A table of thermal conductivity values is listed below. To find the rate of temperature change, or dT/dt, we need to consider the mass and heat capacity of the material. The rate of change of temperature is related to the rate of heat being transferred by. Here, m is the mass of the material or object that is undergoing the temperature change due to heat transfer, and c is its specific heat capacity, or the amount of heat in joules needed to raise the temperature of a unit mass of the material (a kilogram) by one degree kelvin. This allows us to express the rate of change of temperature as: Below is a short list of materials and their corresponding thermal conductivities. Many more can be found via web search.| Material | Conductivity (W/m/K) |
| Air | 0.026 |
| Aluminum | 1500 |
| Concrete | 1 |
| Glass | 0.58 to 1.89 |
| Cast Iron | 55 |
| Paper | 0.05 |
| Redwood Bark | 0.03 |
| Rubber | 0.16 |
| Water | 0.6 |
Solution of Newton's Law of Cooling Differential Equation for Object and Environment
Layered Materials
In the event that materials are layered together in an attempt to slow heat transfer as in a double pane window, we must not add the conductivities together. Doing this would lead to an absurdity anyway. For instance, if we compare a single pane window with a double pane which is made up of two thicknesses of glass as well as an air gap between them, if we were to add the conductivities to find the total conductivity of the double pane window, we'd get a bigger conductivity. This would imply that heat would conduct faster! That can't be true. There are lots of cases in nature where adding things like layers in the present case or circuit elements in electronics studies requires that we add differently.
While conductivity is a measure of how well something conducts heat, the inverse of conductivity which is called thermal resistivity or resistance, is a measure of how much it resists the conduction or flow of heat through itself. It is the resistivities that are additive in the usual sense when materials are layered. For multiple layers of different thicknesses, the thermal resistance R along with its corresponding thickness L can be written as where each of the resistance terms is just the inverse of the conductivity of the material. We may equate and then plug it into the heat transfer equation to find the rate of heat loss through such a layered material.
EXAMPLE: A single pane window in which the pane is 3mm thick is used in a house. The area of the glass outer surface is 1.5m2. The outside air is 5 degrees Celsius at night while the inside of the house is maintained at 25 Celsius. What is the rate of heat loss through the window by conduction. Assume the glass has a conductivity of
ANSWER: Given all these values the heat loss is 14kW, or joules per second lost.
EXAMPLE: A double pane window in which each pane is 3mm thick and are separated by a layer of trapped gas (assume air) of thickness 1cm is used in a house. The area of the glass outer surface is 1.5m2. The outside air is 5 degrees Celsius at night while the inside of the house is maintained at 25 Celsius. What is the rate of heat loss through the window by conduction? Assume the glass has a conductivity of
ANSWER: Here we have to find the thermal resistance of the composite system of three layers by using the expression In this case, we have two layers of glass and one of air, so we get Next we substitute that in as and solve for Using the provided constants gives a rate of heat loss of 77W.
I should note that the actual rates are lower than this because of the air inside the room not being at 25C right against the window. Also, the heat loss means that the outside air right against the window will be warmer than the ambient outdoor air. So the delta temperature term would actually be lower than the one used. How much depends on a lot of factors... on convection. For instance, having curtains that to some extent trap cold air near the window inside the home, you'd slow the heat loss at night. If the night is windy, the outside air against the window will almost certainly match the ambient temperature quite well as compared to a still night.