This study uses a methodology based on the calculus of variation to determine the heat transfer in passages with two-dimensional velocity fields such as rectangular channels and in the presence of axial conduction. The mathematical procedure is presented and the subsequent numerical computations provide the Nusselt number values. To verify the accuracy of this numerical procedure, the Nusselt number values are acquired for parallel-plate channels and circular pipes and compared with similar data from the Graetz-type exact analyses. Then, rectangular passages are selected to show the capability and a square duct is used to study the domain of accuracy for this procedure. The results for small Peclet numbers lead to a simple correlation for determination of the bulk temperature and they compare well with those obtained from an asymptotic solution.

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