The combined natural and forced convection in vertical concentric annuli at high Prandtl numbers is a common problem in engineering. The hydrodynamical and thermal flow state in annuli depends on the Grashof number. In this paper, first, mathematical models of the combined natural and forced convection in vertical concentric annuli at high Prandtl numbers are established. For diverse Grashof number ranges, integral and analytical methods are introduced to solve annuli's velocity and temperature profiles. Subsequently, a computational fluid dynamic simulation based on the finite volume method is carried out to verify the accuracy of the integral and analytical methods. Under various physical configurations, annuli's heat and mass transfer characteristics are accurately predicted. The relative error of the average fluid velocity is less than 4.4745%, and the relative error of the maximum temperature is less than 2.3719%. The integral and analytical methods perform much better in computation speed, increasing by 180 and 3000 times, respectively. Finally, based on the faster numerical computation scheme developed, local Nusselt number correlations suitable for different Grashof number ranges are proposed, considering different thermal and pressure boundary conditions.