Thermal Conductivity

In keeping with the theme of material properties from the last post, today we’ll talk about thermal conductivity which is a material property that relates to the conduction of heat.

Fundamentals of Thermal Resistance

The Thermal Resistance Analogy
Thermal resistance is a convenient way of analyzing some heat transfer problems using an electrical analogy in order to make complicated systems easier to visualize and analyze.  It is based on an analogy with Ohm’s law which is:

In Ohm’s law for electricity, “V” is the voltage which drives a current of magnitude “I”.  The amount of current that flows for a given voltage is proportional to the resistance (R_elec).  For an electrical conductor, the resistance depends on the material properties (copper tends to have a lower resistance than wood, for example) and the physical configuration (thick short wires have less resistance than long thin wires).

Refrigerators and Cryotherapy

What does a common household refrigerator have in common with a home medical treatment? One answer might be that you get ice cubes out of your freezer to put on your black eye or sprained ankle. There might be other answers surrounding your treatment when the refrigerator tips over on top of you, but in this post we are going to talk about refrigerator operation and cryotherapy.

Quenching in a Finite Bath

In an earlier post we looked at the transient 1 dimensional temperature profiles and

temperature gradients across a piece of metal being quenched in a tank large enough that the temperature of the quench fluid never changed.  In this post, we’ll look at a different case: a piece of steel small enough that the temperature is uniform across the piece which is being quenched in a bath small enough that the temperature of the quench fluid goes up as the steel cools down.  We’ll assume that the quench fluid is well-stirred so that it can also be characterized by single temperature.

Thermal Gradients from Quenching

Many heat treating operations involve a quench—that is, an immersion in a fluid at a lower temperature in order to achieve a rapid cooling rate. It is commonly used for hardening in ferrous metals. Quench fluids include air, water, oils, and many others. From a heat transfer standpoint, quenching of a hot metal has a lot of interesting aspects: determining the heat transfer coefficient (possibly with phase change) at the surface, calculating transient temperature profiles inside the material (with implications for thermal stresses and metallurgical properties), effects of thermal transport properties (possibly time-dependent, or spatially non-uniform) on the heat transfer, and others. In this post, we’ll discuss transient temperature profiles and temperature gradients induced by quenching a one-dimensional (wide enough and long enough that the main effects are controlled by the thickness) piece of tool steel. 

More Useful Lumps

All beginning heat transfer classes cover the topic of lumped capacitance calculations: the case where heat conduction within a body is fast enough that the entire body can be considered to be at a single temperature. 

This is a very useful tool for estimating heat transfer in some situations.   However, with just a little work, we can extend the tool to a broader application.

How big is the heat flow?

Sometimes it is useful to have a ballpark idea of the size of a heat flow before even starting a more detailed heat transfer analysis.  It is also kind of fun to have a rough idea of the magnitude of different heat flows. To those ends, we present this figure: