This paper reports the results of experimental and numerical investigations of optimal heat distribution among the protruding heat sources under laminar conjugate mixed convection heat transfer in a vertical duct. A printed circuit board with 15 heat sources forms a wall of a duct. Three-dimensional governing equations of flow and heat transfer were solved in the flow domain along with the energy equation in the solid domain using FLUENT 6.3 . A database of temperatures of each of the heat sources for different heat distributions is generated numerically. Artificial neural networks (ANNs) were used as a forward model to replace the time consuming complex computational fluid dynamics (CFD) simulations. The functional relationship between heat input distribution and the corresponding temperatures of the heat sources obtained by training the network is used to drive a genetic algorithm based optimization procedure to determine the optimal heat distribution. The optimal distribution here refers to the apportioning of a fixed quantity of heat among 15 heat sources, keeping the maximum of the temperatures of the heat sources to a minimum. Furthermore, the heat distribution corresponding to a set of specified target temperatures of the heat sources is obtained using a network that is trained and tested with a database of temperatures of the heat sources generated using FLUENT 6.3 in the range of total heat dissipation of 5–25 W. Using this network, it was possible to maximize the total heat dissipation from the heat sources for a given target temperature directly. In order to validate the optimization method, a low speed vertical wind tunnel has been used to carry out the mixed convection experiments for different combinations of heat distribution and also for the optimal heat distribution, and the temperatures of the heat sources were measured. The results of the numerical simulations, ANN, and the corresponding experimental results are in good agreement.