Analytical Solution to a Transient Conduction Problem

Organized by textbook: learncheme.com/ Uses an analytical approximation to solve a transient conduction problem. Compares the solution to that calculated by the lumped capacitance method. Lumped Capacitance: Temperature of a Sphere: • Lumped Capacitance: Te... Made by faculty at the University of Colorado Boulder Department of Chemical and Biological Engineering.
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[@Magnus8909]

Thank you so much for the explanation! :)

[@praew5646]

thank you for the video

[@brianafigueroa2003]

what tables give you the eigenvalue and the C1?

[@mikew7799]

I could be mistaken but Biot # = hLc/k = h(volume/area)/k = 1500(R/3)/420 = 1500(0.025/3)/420 = 0.029. Why are you not using characteristic length?

[@LearnChemE]

Good question! You are correct, the characteristic length for a sphere is R/3, and this is typically the value used in the Biot number. However, using R as the length scale rather than R/3 corresponds to the maximum spatial temperature difference (that is, the longest distance over which heat must be transferred). This gives the most conservative estimate of time, so it is good to use R instead of R/3 if you want to know the maximum time it could take to reach the final temperature. Likewise, you could get a conservative estimate for a cylinder by using R instead of R/2, which would normally be the characteristic length in that case. Hopefully this helps!

[@JeRRY-xw6xj]

Isn't bi =.089?

[@LearnChemE]

+Gerardo Munoz Thank you! Yes, you are correct. Bi = 0.089. Luckily, the constants were found using the correct Bi of 0.089. We will fix this.

[@anilverman7002]

isnt this a convection problem, not conduction?

[@niranjanwagh5767]

it was 0.089 that's why it was lumped. Now you took 0.89. Video is helpful but misleading.

[@AJ75640]

Yeah, of course,I was also surprised! fortunately I take notes of every lecture that's why I was able to find unintentional human error, anyway the way of explanation is awesome👍👍. I am very happy to learn heat transfer concepts