In spite of the growing shortage of fossil fuels, combustion technology will be required throughout the foreseeable future. This cursory survey of the current state of the art shows that the fluid mechanics of combustion is still at a primitive stage of development. This situation is largely due to the complexity of the industrial combustion process, which usually involves the interdependent phenomena of three-dimensional two-phase flow fields, turbulent mixing, chemical kinetics, evaporation and heat transfer, all occurring simultaneously. Fortunately, experimental information on the effect of fluctuations in velocity, temperature, pressure and concentration on these physical and chemical processes is starting to become available. Similarly, comprehensive theoretical models are emerging, but require experimental data, presently unavailable, in order to test critically their validity. Various unresolved scientific problems are identified and some guidelines to their solution are set forth. It is easy to justify the cost of work in this field, since astronomical sums of money may be saved by very modest improvements in the efficiency of combustion systems.

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