An IBM PC was used to obtain finite-difference solutions to a complex heat transfer and fluid flow problem in which the solution domain contained nearly 6000 grid points. The investigated problem was the abrupt, asymmetric enlargement of a parallel-plate channel. The enlargement lakes the form of a backward-facing step, the presence of which causes separation of the flow. Heat transfer occurred at the channel wall which extended downstream from the foot of the step. The present velocity solutions were shown to be at least as accurate as prior numerical solutions and served to extend the range of investigated enlargements. The variation of the local Nusselt number with the Reynolds number took on different forms at various axial distances from the enlargement step. In a region extending downstream from the step, the Nusselt number actually decreased monotonically with increasing Reynolds number. Farther downstream, the Nusselt-Reynolds variation was monotonically increasing, while still farther downstream, the Nusselt number was independent of the Reynolds number.