Numerical Modeling of Non-Isothermal Laminar Flow and Heat Transfer of Paraffinic Oil with Yield Stress in a Pipe

This paper presents the results of a study on the non-isothermal laminar flow and heat transfer of oil with Newtonian and viscoplastic rheologies. Heat exchange with the surrounding environment leads to the formation of a near-wall zone of viscoplastic fluid. As the flow proceeds, the transformation of a Newtonian fluid to a viscoplastic state occurs. The rheology of the Shvedoff–Bingham fluid as a function of temperature is represented by the effective molecular viscosity apparatus. A numerical solution to the system of equations of motion and heat transfer was obtained using the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The calculated data are obtained at Reynolds number Re from 523 to 1046, Bingham number Bn from 8.51 to 411.16, and Prandl number Pr = 45. The calculations’ novelty lies in the appearance of a “stagnation zone” in the near-wall zone and the pipe cross-section narrowing. The near-wall “stagnation zone” is along the pipe’s radius from r/R = 0.475 to r/R = 1 at Re = 523, Bn = 411.16, Pr = 45, u1 = 0.10 m/s, t1 = 25 °C, and tw = 0 °C. The influence of the heat of phase transition of paraffinic oil on the development of flow and heat transfer characteristics along the pipe length is demonstrated.