Drag reduction in heavy oil transport systems is a key for high-efficiency oil transfer and, thus, for energy conservation. fit this paper, we investigated the influence of viscosity, velocity, and velocity-gradient fields on drag resistance in fluid flow with variable viscosity in terms of the field synergy. The theoretical analysis indicates that the drag during varying viscosity fluid flow processes depends upon not only the synergy between the, velocity and its gradient over the entire flow domain but also the viscosity and velocity gradient,it the boundary, That is, for a given now rate or inlet velocity, simultaneously reducing the fluid flow field synergy number over the entire flow domain and decreasing the fluid viscosity and the velocity gradient at the boundary will lead to a smaller flow resistance. In addition, starting from the basic governing equation and via the calculus of variations, we derived Euler's equation, essentially the momentum equation with a special additional volume force, using the criterion of the minimum viscous dissipation rate to optimize the flow processes for varying viscosity fluid. For fixed Row rate or Inlet velocity, solving Euler's equation will result in the optimal velocity and viscosity Fields, leading to the minimized now resistance. Finally, a thermal insulating transport process for heavy oil was taken as a testing case to demonstrate the application of the theory. The results show that generating longitudinal vortexes to enhance the transfer performance of heavy oil will facilitate the flow drag reduction. For instance, when the inlet heavy oil velocity and the external effective heat-transfer coefficient are 0.01 in/s and 2 W m(-2) K-1, respectively.. the total viscous dissipation rate with a certain presence of longitudinal vortexes is decreased by 19% compared to the. result without the vortexes.