Is there correlation which can calculation convective heat transfer coefficient in vertical upward flow ( for single phase water and conventional pipe) ?
The answer depends on the conditions. Normally, gravity does not matter, so flow direction is irrelevant. However, if the velocity is low and/or buoyancy is strong, free convection effect may come into play. The contribution of the free convection flow may assist or oppose the forced convective contribution. However, for water, free convection effects are usually negligible, and you may use any suitable forced convection correlation independent of the flow direction. [Sidenote: There is some evidence that the heat flux direction may have some influence in the laminar/turbulent transition in vertical flows, but this only applies to Re-numbers around 2 000- 3 000]