An estimation of the local Nusselt number distribution for a flat and a ribbed surface from transient liquid crystal images is presented. Liquid crystal thermography generates color images of the time-varying surface temperature field, when an initially heated surface is subjected to cooling in forced flow. The inverse technique compares the approximate numerical solution with the transient experimental temperature distribution, and enforces the applicable physical laws in such a way that a globally correct Nusselt number distribution is predicted. The related optimization problem has been solved by a conjugate gradient method, with a stabilization scheme based on additional experimental data. The partial differential equations arising at the intermediate stages have been solved numerically using the finite difference technique. Predictions of the local Nusselt number have been compared with the full numerical solution based on unsteady incompressible laminar flow, as well as the one-dimensional semi-infinite solid approximation applied to experimental data. Reynolds numbers considered in the study are 160 and 260, based on the rib height. Results show that the inverse technique is capable of resolving sharp as well as gradual changes in the heat transfer rates for the flat plate and the rib geometries. The peak in the Nusselt number distribution for flow past a rib is seen to fall at a location where the flow reattaches with the flat surface. The inverse technique is robust with respect to signal length, and within limits it is insensitive to noise in the experimental data.