In this paper, a numerical study on the flow of an array of alternating horizontal or vertical oval cross-section pipes placed in a cross stream, resembling that encountered in a real cross-flow heat exchanger, is presented. The results include temperature contours and velocity vectors on the surface of the pipe and at several selected cross-sections, the local and sectional averaged Nusselt number distributions, and the overall Nusselt number variations versus the internal and external flow Reynolds numbers. The computation shows that the wall temperature varies dramatically along both the circumferential and the axial directions of the pipe, and is far different from a constant wall temperature distribution assumed in most previous studies. In general, the portion of the pipe with external wall facing forwards the cross-flow stream has lower temperature and higher local heat-transfer rate than the portion with wall facing backwards the cross-flow stream. At the maximum external flow Reynolds number, Re = 40, considered in this paper, the magnitude of pipe's overall Nusselt number is about one-sixth the magnitude of that calculated based on the ideal constant wall temperature assumption.