The heterogeneous combustion and the combined hetero-/homogeneous combustion of deficient reactants with Lewis numbers (Le) larger than unity was investigated analytically and numerically in two geometrical configurations, the flat plate and the planar channel, under the condition of infinitely fast catalytic chemistry. Analytical results based on similarity solutions for the catalytic flat plate and on heat and mass transfer solutions for the channel were complemented by detailed 2-D numerical simulations. The larger than unity Lewis number led to the underadiabatic surface temperatures, which in turn gave rise to gas-phase regions with local energy excess. For the flat plate case, the maximum gas-phase energy excess was a non-monotonic function of the Lewis number. The peak occurred at Le = 6.5 with a corresponding energy excess 6.4% above the total energy of the fresh reactants. In channel-flow combustion, the maximum gas-phase energy excess was a monotonically increasing function of Lewis number, approaching asymptotically the considerably higher value of 20.8% as Le -> infinity. For current catalytic combustion methodologies, which include the fuel-lean hydrocarbon/air combustion (Lewis numbers of deficient hydrocarbon fuels up to similar to 3.2) and the fuel-rich hydrogen/air combustion (Lewis number of deficient oxygen similar to 2.3), the energy excess in the gas was significant and could reach up to 14%. Hetero-/homogeneous combustion simulations have shown that, upon homogeneous ignition, the gas-phase energy excess manifested itself with superadiabatic flame temperatures. However, the superadiabaticity in the gas was confined to the channel core, such that the surface temperature did not exceed the adiabatic equilibrium temperature. This behavior had key implications for the reactor thermal management and catalyst stability. Moreover, the gas-phase superadiabaticity led to peak prompt NOx values 30% higher than those achieved by a diffusionally neutral deficient reactant (Le = 1). (C) 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.