Gas flow rates can be measured with a hot-wire anemometer which employs a fine wire mounted transversely to the gas flow. The wire is heated by an electrical current and the temperature rise, which depends inversely on the flow rate, is determined by the resistance change of the wire. In the optical fiber anemometer the fine wire is replaced by a short segment of gold-coated single-mode optical fiber which forms one arm of an all-fiber Mach-Zehnder interferometer. The gold coating is 0.1 pm thick and covers a 1 cm length of the unjacketed silica fiber; this coated section is mounted transversely within a 1 cm diameter tube through which nitrogen gas flows. The fiber is heated by applying a 5 sec voltage pulse to the gold coating. The increase in the temperature results in an increase in both the length and refractive index of the fiber core, and a corresponding increase in the phase of the light propagating through the sensing arm of the interferometer. The magnitude of this phase change, which is determined by fringe counting, is used to determine the temperature change and hence the flow rate. Convective heat transfer coefficients were determined for the low flow rates (0-2 m/sec) employed in these experiments. The experimental results are in excellent agreement with previous experimental results on low-velocity forced convection. In general the device can measure gas flows with greater precision than a conventional hot-wire device.