Metallic catalytic converters are composed of monoliths through which pass hundreds or thousands of parallel channels. Their mode of manufacture is such that each channel has the cross-section of a sinusoidal curve closed off by a nearly straight edge. During the operation of such converters, heat generated at the channel walls is transferred to the gases flowing through the channels. To understand the overall heat transfer characteristics of the monolith, it is necessary to understand the heat transfer rate between the channel walls and the fluid contained within them. With the use of the computational fluid dynamics package FIDAP, a three-dimensional model of a single channel was used to determine the local Nusselt number (Nu) versus Graetz number (Gz) correlation for heat transfer between the fluid and the walls of the channel. Flow through the channel was laminar and developing from a flat velocity profile at the channel inlet to the fully developed flow towards the outlet. Three different models were developed which corresponded to sinusoid height to width aspect ratios of 5 : 2, 3 : 2, and 1 : 1, respectively. The Nu vs. Gz correlations for the straight edge, curved sinusoidal edge and entire perimeter were calculated and are reported.