This paper includes the Artificial Neural Network (ANN) solution as one of the numerical analyses to investigate the buoyancy and property variation effects calculating Nusselt numbers during the upward and downward flow of water in a smooth pipe. Available data in the literature (Parlatan et al.) has been used in the analyses to show ANN's success ratio of predictability on the measured pipe length's averaged Nusselt numbers (Nu(avg)) and forced convection's Nusselt numbers (Nu(o)) Mixed convective flow conditions were valid for Reynolds numbers ranging from 4000 to 9000 with Bond numbers smaller than 1.3. Dimensionless values of Reynolds number, Grashof number, Prandtl number, Bond number, Darcy friction factor, isothermal friction factor in forced convection, ratio of dynamic viscosities, and a Parlatan et al.'s friction factor were the inputs while Nu(av)(g) and Nu(o) were the outputs of ANN analyses. All data was properly separated for test/training/validation processes. The ANNs performances were determined by way of relative error criteria with the practice of unknown test sets. As a result of analyses, outputs were predicted within the deviation of +/- 5% accurately, new correlations were proposed using the inputs, and importance of inputs on the outputs were emphasized according to dependency analyses showing the importance of buoyancy influence (Gr(T)) and the effects of temperature-dependent viscosity variations under mixed convection conditions in aiding and opposing transition and turbulent flow of water in a test tube.