The paper is concerned with the steady-state convective diffusion to a heat-conducting reacting sphere in a laminar translational and shear flow, with a nonisothermal chemical reaction proceeding on its surface at the rate arbitrarily dependent on temperature and concentrations. It is shown that for the integral heat and mass fluxes of reacting components to a particle (i.e. mean Nusselt, Nu, and Sherwood, Sh m , numbers) to be determined at small Peclet numbers, it suffices to solve the following universal algebraic (transcendental) system of equations Sh m=ƒ( N u Nu infin; , Sh 1 Sh 1∞ ,…, Sh M Sh M∞ ) , Nu= Σ m=1 M h mSH m , which is appreciably simpler than the initial system of partial differential equations. The system suggested makes it possible to obtain for the Sherwood and Nusselt numbers the first four (shear flow), and the first three (translational flow), terms of the corresponding asymptotic expansion in small Peclet numbers. An irreversible isothermal 2nd-order reaction and a successive stepwise 1st-order reaction have been studied. The case of nonisothermal surface reaction, which proceeds following the Arrhenius law with one reacting component present in the flow, has been studied in detail. Adsorption on the particle surface, the rate of which is governed by the Langmuir kinetics, is analyzed. Based on comparison with the earlier results for isothermal reactions at moderate and large Peclet numbers, it is shown that with a suitable choice of the governing parameters Sh m∞ ( Nu ∞) the suggested algebraic system can also be successfully applied for approximate determination of the mean Sherwood numbers within the whole range of Peclet numbers. The results obtained enable investigation of the inverse mass and heat transfer problem for reacting particles in the flow, i.e. allow one to explicitly determine the dependence of the surface reaction rate on concentrations from the available integral fluxes that can be determined experimentally.