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.

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.

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.

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.