A mathematical model of the movement and heat transfer of a turbulent non-isothermal non-Newtonian fluid through a pipe wall with a cold surrounding space has been developed and simulated numerically. Fluid turbulence is described in the framework of the isotropic two-parameter k– $\tilde{\epsilon }$ model. The Newtonian properties of the fluid in the initial cross-sections of the pipe transformed gradually into a viscoplastic non-Newtonian Bingham-Schwedoff fluid state due to heat transfer through the pipe wall between the heated fluid and a cold environment. The value of its streamwise velocity in the axial zone increased significantly when the fluid moved along the pipe. On the contrary, it decreased in the near-wall zone and the height of the region with a zero fluid velocity increased. This occurred due to the viscoplastic properties of a non-Newtonian fluid. The height of the region with a zero fluid velocity in the pipe increased gradually as the non-Newtonian fluid (waxy crude oil) moved through the pipe. A noticeable increase in the level of turbulent kinetic energy in the axial zone of the pipe and its noticeable decrease in its near-wall region were observed. A significant increase in the average dynamic viscosity and yield stress in the near-wall part of the pipe was shown. The boundary of the area of existence of Newtonian properties of fluid was determined. The height of the region with a zero fluid velocity in the pipe increased gradually as waxy crude oil moved through the pipe and reached y/R ≈ 0.1 at x/D = 15.

已经开发并数值模拟了湍流非等温非牛顿流体通过具有冷周围空间的管壁的运动和传热的数学模型。流体湍流在各向同性两参数k的框架中描述-$\stackrel{～}{\epsilon }$模型。由于加热流体和冷环境之间通过管壁的热传递，管道初始横截面中流体的牛顿特性逐渐转变为粘塑性非牛顿宾汉-施韦多夫流体状态。当流体沿管道移动时，其轴向区的流向速度值显着增加。相反，在近壁区，它减小，零流体速度区域的高度增加。这是由于非牛顿流体的粘塑性。随着非牛顿流体（含蜡原油）通过管道，管道中流体速度为零的区域的高度逐渐增加。观察到管道轴向区域的湍动能水平显着增加，而其近壁区域则显着降低。显示出管道近壁部分的平均动态粘度和屈服应力显着增加。确定了流体的牛顿性质存在区域的边界。管内流体速度为零的区域的高度随着含蜡原油在管内移动并到达y / R  ≈ 0.1 在x / D  = 15。