Interesting chemical engineering exam question – 6: If you have studied the principles of chemical engineering transport processes, take a look at this question.

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When I was in school, the TJDX Department of Chemical Engineering had 10 majors. They are: 1) Chemical Engineering, 2) Organic Synthesis (Petroleum Chemistry), 3) Chemical Engineering Machinery, 4) Chemical Catalysis, 5) Technical Ceramics, 6) Electrochemistry, 7) Polymers, 8) Dye Intermediates, 9) Nuclear Chemical Engineering, 10) Corrosion Prevention. Among these ten specialties, only the three undergraduate programs in Chemical Engineering, Petroleum Chemistry, and Chemical Catalysis include *‘Reaction Engineering’* in their curriculum ； Only the two undergraduate programs in chemical engineering and petrochemical engineering teach *‘Chemical Separation Processes’* ； Only the two undergraduate programs in chemical engineering and petrochemical engineering teach *Chemical Engineering Thermodynamics* ； There is only one undergraduate major in chemical engineering, and it requires studying *‘Principles of Chemical Engineering Transport Processes’* ； Only the undergraduate major in Chemical Engineering teaches *Mathematics for Chemical Engineering*. Therefore, only the undergraduate program in chemical engineering has produced two academicians on campus, M-2 deans, N-1=3 Changjiang Scholars, and O-2=4 Distinguished Young Scholars. Here, 5≤M, N, O≤7; the foundation in chemical engineering lies in this. From 1977 to 1985, 30 students were admitted per class, and there should have been 3–6 professors per class. \"Principles of Chemical Engineering Transport Processes\" is considered the most difficult chemical engineering course to study, and it is said that now undergraduates in every university’s chemical engineering department are taking it. I really learned something from it. Can I use it? We take this course twice in total, once during our undergraduate studies and once during our graduate studies. The above is the opening statement. Well, in the latter part of the course \"Principles of Chemical Engineering Transport Processes,\" when discussing 1) laminar flow inside a fully developed circular pipe, with a similarly fully developed concentration boundary layer (or temperature boundary layer), under conditions of constant wall temperature (or constant wall concentration), the Nusselt number (or Schmid number) equals 3.66 ； 2) In the case of fully developed laminar flow inside a circular tube, with a similarly fully developed concentration boundary layer (or temperature boundary layer), and under conditions of constant wall heat transfer rate (or constant wall mass transfer rate), the Nusselt number (Schmidt number) = 4.36. My question: 1) If the flow inside the circular tube is a fully developed laminar flow, and if the concentration boundary layer (or temperature boundary layer) is also fully developed, as well, and if the heat transfer (or mass transfer) rate through the tube wall is proportional to the temperature (or concentration) at the tube wall, what is the Nusselt number (or Schmid number)? 2) If the flow inside the circular tube is a fully developed laminar flow, while the concentration boundary layer (or temperature boundary layer) has not yet developed fully, and the heat transfer (or mass transfer) rate through the tube wall is proportional to the temperature (or concentration) at the tube wall surface, how does the Nusselt number (or Schmid number) change? This is one of the sub-projects of my doctoral thesis.