So I have faced a problem dealing with transient conduction and I need a little help with the problem solving concepts. I need to determine how long it would take to reach the final temperature but I need to know the convection coefficient for that.

I have done steady state and calculation of Reynolds'/Nusselt's Numbers and everything but that was when the film temperature, $\frac{T_{s}+T_{\infty}}{2}$ was constant throughout the process. In a transient problem, the surface temperature is constantly changing, causing the film temperature to constantly change and also the Reynolds'/Nusselt numbers to both constantly change with time because the film properties are changing.

How can I combat all of these changes? I could either:

  1. Calculate the convection coefficient using either the initial temperature or the final temperature when calculating the film temperature

  2. Average the two temperatures in the beginning and then calculate the convection coefficient for that averaged temperature

  3. Calculate the convection coefficients at the initial and final temperatures and then just average those numbers

  4. Make a spreadsheet of the properties in the back of the book and then somehow write code on MATLAB that would continuously calculate the coefficient between different boundaries and then just add up the heat transfer, I would have to do that on MATLAB and it would take a long time to do.

I am very open to any suggestions. I am having a lot of trouble on this because we did not do this in my class and my professor did not really give me an answer when I talked to him

  • $\begingroup$ I suspect that your question is just too engineering specific, so you are not going to find the answer here. I would never heard of those numbers myself hadn't I prepare lectures for civil engineers... You could eventually dismantle your problem into simpler mathematical-physical entities and re-post it. $\endgroup$
    – Pygmalion
    Apr 22, 2012 at 16:01
  • $\begingroup$ Have been struggling with exactly the same issue. I see that this is from some time ago, please let me know if this got resolved. $\endgroup$ Aug 8, 2022 at 6:11

1 Answer 1


Calculate everything at the bulk temperature, which in simple words is the average temperature of your system.

  • $\begingroup$ This seems like a comment at best. It doesn't really address any of the nuance of the question. $\endgroup$ Oct 1, 2015 at 0:05

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