Convective heat transfer in non-MHD laminar flow through rectangular channels in the first wall and limiter/divertor plates of fusion reactors has been analyzed numerically. Even for uniform heat flux, the Nusselt number (Nu) is not constant along the face of a rectangular channel, because the velocity is much smaller near a corner. For uniform heat flux, Nu varies by 67% from the center of a side to the corner (6.7 to 2.2). Therefore, the corners of a rectangular channel are possible hot-spot areas of concern for thermal-hydraulic designs. In addition, the surface heat flux on coolant channels in the plasma-facing components varies circumferentially. This nonuniformity of surface heat flux also affects the Nu. At the center of a side, Nu can be reduced from 6.7 to 2.8, i.e. by about 58%. For large nonuniformity of surface heat flux, the Nu at some locations can become infinity or negative; infinity, when the coolant/wall interface temperature becomes equal to the coolant bulk temperature and, negative, when the bulk temperature becomes larger than the interface temperature at these locations. The entry length is also increased due to the nonuniformity of surface heat flux. This increase can be as much as 4 times the entry length for uniform heat flux. For safe thermal-hydraulic designs of the first wall and limiter/divertor plates of fusion reactors, these effects must be taken into consideration.