Of Cakes and Boundary Conditions

As it turns out the first post will be food-related; though it’s actually with a scientific twist!  My field of science has to do with how atoms and molecules can be arranged to form large structures or materials, hence the term “Materials Science”.  Almost all Materials Scientists have one thing in common: they hate unwanted differential heating gradients!  I’ll explain what this is and why it became a problem for me recently.

Many times, when you want to heat up a material to make it into something else, you want it to heat evenly.  This way you can be sure that the material is the same inside and outside.  As you may know from talking to me, I love to bake.  I bake pies mostly, but cakes and hopefully sometime in the future a suffle.  Bakers too take issue with differential heating gradients in their cookery.  The sides of a cake can cook or “set” very fast, creating a nice dense cake area, but the inside can sometimes remain a gooey uncooked mess!  This comes from the fact that when we heat up a material, a cake for instance, the boundaries of our containers affect how heat is distributed.  There are few topics in physics that have well defined solutions.  As it turns out (for the most part) heat flow is one of them!  Think of this picture below:

C2

Here are cross-sectional views of two cases of a cake baking.  In the first case we have a magical cake on a metal pan that can be heated only from the bottom and that will form a cake shape want without running all over the place. In the second case, we have a cake baking in a metal pan with two walls.  We can think of the bottom and walls as sources of heat since the metal walls will get hot faster than the cake itself.  If we imagine the heat moving into the cake as a wave in time, we would move onto the beach you can see how the wave has a certain height when only coming from the bottom.   If waves come from the sides as well they interact to provide more heat to certain areas of the cake. We could describe this as the heat (u) at some part of our cake, x at some point in time t as u(x,t).  As I mentioned, we could model our cake problem using mathematics, in this case differential equations.  How well the cake is cooked, the heat gradient ∇u is dependent on whether or not we have boundaries on the side  Even without breaking out our Calculus textbooks we can see visually how our boundary conditions would suggest that the outside edges of our cake would heat up and cook faster than the middle.  Now we know why our cakes end up gooey on the inside instead of the outside!

What can we do to get around our boundary issues?  We can, in fact, create something close to our first picture without the walls of the plate.  We could add a material that would prevent those parts from heating up: an “insulator”

C3

In this case, instead of losing heat, no heat moves at all through the walls.  You may have used these before, they are called baking strips.  They help to allow the heat to be more evenly distributed in the cake.  Additionally, a wet rag wrapped around the walls can also serve this same purpose as well as using a pan made of insulating ceramic instead of metal.  I am beginning to think about using these more often in my cooking and wanted to share my thoughts on why, from a scientific standpoint, they are useful.

We’ll talk more about heat and free energy in the future (with and without further baking analogies).  Thanks for reading!

GRW

Baking Strips

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