The forced convective cooling of an optical fiber during the drawing process can be controlled by using a heat exchange channel with the cooling gas moving in the same or opposite direction as the fiber. In this paper, transport processes associated with the cooling of a heated optical fiber moving in a channel are numerically investigated, assuming a transient, axisymmetric circumstance with laminar fluid flow. Three different flow circumstances, involving uniform flow at the inlet in the same or in the opposite direction as the movement of the optical fiber as well as peripheral flow entrance, are considered in this study. The governing full, elliptic, equations are solved, employing finite volume methods. The transport in the fiber is coupled with that in the fluid, through the boundary conditions. A vorticity-stream function formulation is employed to solve the transport in the fluid and the fiber. Variable properties are also considered, linearizing the non-linear terms in the diffusion equations by extrapolating the property values obtained for the previous time step. The effects of several relevant parameters like the fiber speed, free-stream velocity, the channel width, wall thermal conditions and the fluid on the local Nusselt number, temperature distribution and the flow field are investigated. The effect of radiative heat transfer from the fiber is also considered. It is found that the effect of channel width on the heat transfer is quite significant for narrow channels. But as the channel width increases, the resulting heat transfer approaches the characteristics of a fiber moving in a free fluid stream, as expected. For the opposing and peripheral flow circumstance, a recirculating region arises within the fluid close to the moving fiber, causing a decrease in the heat transfer rate. The temperature of the fiber at the outlet of a channel of fixed length can be controlled quite accurately by varying a number of parameters. Validation of the numerical results obtained is carried out by comparison with earlier experimental results and a fairly good agreement is observed.