So, I'm a Chemical Engineering student.

That means I know a lot about physics, especially heat and fluid transfer. I thought, to improve my studies and to make it more personal, I would make a site to discuss any and all things engineering! I might make it like a journal entry format to showcase what I've learned so far. You know what, that's a good idea!

October 9th, 2025

I'm almost halfway through my fall semester of my third year. I have a heat transfer quiz tomorrow on mainly "transient problems"

Which, from my understanding, is when your condidtions (like heat, temperature) change over time. General procedure is calculating Fourier # to see if you can use more simple assumptions and go from there. The homework was lowkey light, but I definitely have to review :( 90% of the time they want you to calculate how much time a system takes to reduce/increase to a certain temperature, but to calculate Fourier's number, you usually do need the time? that's my main worry.

Okay, I think that calls for the Biot number. It's the h times the characteristic length (Volume/Area) over the thermal conductivity.

• If Bi is less than 0.1, you can used lumped capacitance (can assume that the body is one uniform temperature)
• If Bi is greater than 0.1, you can use approximate solution with tables (huge temperature difference within material, cannot just use lumped capacitance). OR if the outside temperature has not fully penetrated into the material, that's when the semi-infinite solid comes in!!
• If it is 0.1, it's straight up transient, use Heisler charts (not on quiz)

OK, I think I've figured it out:

• calculate Biot #. If less than 1, use lumped capacitance:


I know these pictures kinda suck, but stay with me!!

• If greater than 1, use the approximate solution (you can find the unknown values using the table that'll be provided:

• In special cases (which he'll msot likely make obvious) we have to use the semi-infinite solid method, whose values can also just be values in tables: