Transport phenomena as they apply to throughflow calculations in axial-flow compressors are reviewed. An historical background is presented. Then the debate raised by the Adkins and Smith versus the Gallimore and Cumpsty approaches to radial transport is discussed. This debate was resolved in that it was finally concluded that both turbulent transport and convective secondary flows play a role in spanwise transport. Other major related efforts mentioned are those of Hirsch and his colleagues and Papailiou and his colleagues. Readers are encouraged to reconsider exploitation of the work of Kerrebrock and Mikolajczak concerning circumferential transport. Comments on future trends are offered.

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