Pressure drop correlation for laminar, mixed convection, aiding flow heat transfer in a vertical tube

Pressure drop is significantly affected by heat transfer in mixed convection situations. A semi-empirical correlation for pressure drop is developed from a theoretical base by first making use of the momentum integral solution to the heat and momentum equations for natural convection on a vertical surface. The boundary condition on the free-stream side of the boundary layer is changed to reflect the shear on that surface due to the forced convection, and empirical data are used to develop a formula useful in design and applications. The equation may be used with bulk fluid properties or film properties. The equation is valid for laminar, mixed convection conditions in vertical, internal, aiding flows with constant wall temperature boundary condition