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We consider two common heat transfer processes and perform a throughsensitivity study of the variables involved. We derive and discuss analyticalformulas for the heat transfer coefficient in function of film velocity, airtemperature and pipe diameter. The according plots relate to a qualitativeanalysis of the multi-variable function $h$, according to functionaloptimization. For each process, we provide with graphs and tables of theparameters of interest, such as the Reynolds number. This method of study andthe specific values can constitute a useful reference for didactic purposes.

Sensitivity studies of heat transfer: forced convection across a cylindrical pipe and duct flow