Applied Contact Temperature

We’ve talked before about the contact temperature and the effect that different materials have on the temperature that you feel when you first touch them.  Today we’ll look at that effect in a more applied way.

A Cold Snap, Part 2

In the last post, we talked about the ground temperature during a cold snap.  Today, we’ll look at the same situation from two different viewpoints.

A Cold Snap

Following a series of relatively warm days, we had a sudden (over a period of a few hours) drop in temperature and things then stayed very cold for several days.  This led me to wonder how fast the ground would cool under such circumstances.

For the purposes of getting a simple, quick feel for the effect of the air temperature change, we’ll look at a somewhat simplified version of the actual events.  Of course this result won’t exactly match what happened in real life, but it will provide a reasonable estimate.

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).

Tire Heating on Landing, Part 2

In the last post, we talked about the moments of sliding/rolling motion when a tire first contacts a surface with a mismatched velocity.  Using the assumptions and simplifications outlined in that post, today we will make estimates of heat generation at the tire/runway interface, and temperature profiles inside the tire material based on a hypothetical airplane landing scenario.

Tire Heating on Landing

When an airplane first touches the runway, there is an interesting moment of drama because the ground (relative to the airplane’s wheel) is moving past quite rapidly, while the wheel just at the instant of touchdown, is not moving at all.  Of course, there is a great deal of friction between the non-rotating wheel and the moving ground, so the wheel is accelerated rapidly in rotation until it “catches up” to the ground speed and rolls without sliding.  However, the wheel has some rotational inertia and so requires a little bit of time to get up to speed.  During that time, the tire is sliding across the ground and generating a lot of heat. Today we’ll talk about a rough approximation for the heat generated and transferred to the tire during an airplane landing.

Heat Transfer in the Kitchen, Part 3

This will be the third (and final, at least for now) post about heat transfer in the kitchen.

Heat Transfer in the Kitchen

When I tell people (and by 'people', I mean 'non-engineers') that my field of specialization is heat transfer, I usually get some incredulous response on the theme of, "There is a whole field where someone would study nothing but heat transfer?" with the implied sub-text of "sane someone" accompanied by lots of extra question marks.  I have to admit that in everyday experience, most people don't have to think quantitatively about heat transfer.  However, almost everybody connects (non-quantitatively) with heat transfer in the kitchen, so in this post we'll explore heat transfer in cooking.

Duhamel's Theorem, part 2

As an additional example of Duhamel’s theorem that we talked about in the last post, we’ll use the solution to a sudden change in temperature at the surface of a semi-infinite solid to examine the temperature in a thin layer in the wall of the cylinder of an internal combustion engine.

Leveraging Solutions with Duhamel's Theorem

There are many transient heat transfer problems that can be solved analytically for a simple boundary condition, but would be difficult or impossible to solve with a more complicated, time-dependent boundary condition. In many cases, if the original solution can be formulated, possibly through parameterization, as the response to a unit step change on the boundary, Duhamel’s theorem can be used to extend the simple solution to a more complex case.

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. 

Isothermal and Isoflux Boundary Conditions

In analytical conduction problems, two commonly used boundary conditions are isothermal, meaning that the temperature at the boundary is fixed, and isoflux, which means that the heat flux at the boundary is fixed. The two are mutually exclusive (you can’t specify both the heat flux and the temperature on a single boundary) and lead to very different thermal behaviors inside the body. In this post, we’ll look at the effects of these two boundary conditions.

Laser Melting of a Plastic

A high-intensity laser beam that deposits energy over a millisecond time scale into a mostly transparent plastic is an ideal candidate for analysis using the equations of thermal explosions.  

More Useful Lumps (Part 2)

In our last post, we examined the case of lumped capacitance where the free-stream temperature was a function of time and presented the equation governing that situation. This time, we’ll look at some specific examples.

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.

Freezing water on a warm night

Everybody knows that water freezes at 32 deg F. 

Then how come frost (which is just ice that has come from the water vapor in the air) can sometimes be seen in the morning on nights when the temperature never got below 32 deg F?  

 Similarly, backpackers and desert dwellers occasionally report a film of ice on a puddle or bucket of water on not-quite-freezing nights.

The answer has to do with the nature of heat transfer.  Heat can move by conduction (movement through a solid, or a fluid at rest) by convection (movement between a solid and a flowing fluid) or by radiation (direct exchange of energy via electromagnetic waves).  The temperature of a surface depends on the temperatures of the surroundings plus the effects of all three modes of heat transfer.

From the ground...down (part 3)

Some people might think that we’ve already talked about this topic enough, but we know better. 

In the last two posts, we talked about how temperature fluctuations at the surface of the ground might affect the underground temperature, and specifically, how deeply those fluctuations might penetrate.

So, now imagine that there might be an application where it wasn’t the surface temperature nor the ground temperature that mattered, but the difference between the two.   (This actually is important for certain applications that propose to use that temperature difference to generate small amounts of electricity).

From the ground...down (part 2)

Last post we talked about the idea of a “penetration depth” to describe how deeply a fluctuating surface temperature might affect the temperature of the ground below.  

 Before we go on to talk more about the ground, we should point out that that kind of calculation isn’t limited to just temperature distribution in the ground.  It can be used to approximate the penetration depth of many situations where the surface temperature fluctuates periodically.  For example, if you wanted to estimate how deeply the temperature fluctuations penetrate into the wall of an engine cylinder, you might use properties for steel (α =17.7 mm^2/s) and the frequency of the periodic temperature variation of the cylinder (if the engine was running at 2000 rpm, you’d have 1000 temperature cycles per minute, or a frequency of 105 rad/s).  With those numbers, and using our definition of 2.2% fluctuation for the penetration from the last post, you could calculate a penetration depth of 2.2 mm. 

From the ground...down

If you’ve ever lived in a house with a basement, or spent time in a cave, you are probably aware that the temperature underground remains fairly constant regardless of what the air temperature is doing.  Many times the basement is the warmest part of the house in the winter, and the coolest in the summer.  Old time root cellars took advantage of this uniform temperature before air conditioners and central heat were common. 

  

Obviously, fluctuations in the air temperature will penetrate some distance into the ground.  How deep will they go?  While this question is fascinating all by itself, it has some practical implications, too.

Thermal Explosions

While the term thermal explosion sounds very dramatic, it really just refers to a thermal event where the heat release (or absorption) occurs over a time period that is very small relative to the time scale of interest, and in a volume that is negligibly small compared to the surroundings in which the temperature distribution is to be calculated.  So, for example, the heat released by the combustion of  blasting powder in a small hole (time scale of milli-seconds) could be analyzed as a thermal explosion if the time scale of interest was on the order of seconds.  Also the decay heat generated by a pocket of radioactive rock (say, over 100 years) could be analyzed as a thermal explosion if the period of interest were, say, 10,000 years.