In advanced heat transfer courses, a technique exists for reducing a partial differential equation where the dependent variable is a function of two independent variables, to an ordinary differential equation where that same dependent variable becomes a function of only one independent variable. The key to this technique is finding out what the similarity variable to make this transformation is. The difficulty is that the form of the similarity variable is not intuitive, and many heat transfer textbooks do not reveal how this variable is found in classical problems such as viscous and thermal boundary layer theory. It turns out that one way to find this variable is by utilizing the integral technique. By employing the integral technique to boundary layer theory, it will be shown that when the approximate functional relationship for the dependent variable (temperature, velocity, etc) can be represented by an nth order polynomial, the similarity variable can be found very simply. This is seen to be a good tool especially in heat transfer education, but has applications in research as well.
- Heat Transfer Division
Utilizing the Integral Technique to Determine the Similarity Variable in Classical Heat Transfer Problems: One Dimensional Heat Conduction in a Finite or Semi-Infinite Solid
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Kobus, CJ. "Utilizing the Integral Technique to Determine the Similarity Variable in Classical Heat Transfer Problems: One Dimensional Heat Conduction in a Finite or Semi-Infinite Solid." Proceedings of the ASME 2013 Heat Transfer Summer Conference collocated with the ASME 2013 7th International Conference on Energy Sustainability and the ASME 2013 11th International Conference on Fuel Cell Science, Engineering and Technology. Volume 1: Heat Transfer in Energy Systems; Thermophysical Properties; Theory and Fundamental Research in Heat Transfer. Minneapolis, Minnesota, USA. July 14–19, 2013. V001T03A003. ASME. https://doi.org/10.1115/HT2013-17097
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