A method of combusting a catalyzed hydrocarbon fuel comprising providing a first fluid and a second fluid, at least one of said fluids comprising a mixture of a hydrocarbon fuel with an air stream, passing the first fluid into one or more catalytic tubes of a catalytic reactor, and passing the second fluid adjacent the catalytic tubes in a chamber of a catalytic reactor. A varying tube cross section to modify the flow of one of the fluids is provided for at least a portion of the tube. The flow of the first fluid leaving the catalytic tubes is mixed with the second fluid and combusted.