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Numerical solutions are presented for the transient natural convection heattransfer problem in horizontal isothermal cylindrical annuli, enclosed in heatedinner and cooled outer cylinders. Solutions for laminar case were obtained withinGrashof number based on the inner diameter which varied from 1x102 to 1x105 inair. Both vorticity and energy equations were solved using alternating directionimplicit (ADI) method and stream function equation by successive over relaxation(SOR) method. The structure of fluid flow such as a velocity vector andtemperature distribution as well as Nusselt number were obtained and the effect ofdiameter ratio on them was examined. In addition, the Grashof number waschanged with the influence of variation in Prandtle number and diameter ratio. Ournumerical calculation are summarized by Nussult number vs. Grashof numbercurves with diameter ratios and Prandtl as a parameter, which serves as a guide tonatural convection heat transfer calculated from annulus. Good agreement withprevious data is obtained.