I was wondering about this today, mainly for baking a cylindrical cake.
Say you have a solid cylinder which is at temperature
Say you then move the cylinder to a warm location (like an oven) which is at temperature
Is it possible to achieve a rate equation for
T is the temperature exactly in the centre of the cylinder and
t is time?
And therefore work out the time it would take this location to reach a temperature
T2 somewhere between
To keep it as general as possible I would prefer to assume the cylinder is height
h and radius
I've been trying to use the thermal diffusivity equation:
But my working gets messy quickly, I figured as this is quite a simple shape it should be less complicated than some similar examples I've found.
So using my notes from a differential equations course a few years back I managed to do the following:
But I'm stuck here..