How does temperature gradient affect the performance of pipelines carrying viscous crude oil?

Temperature gradient, which is the change in temperature along the length or across the cross-section of a pipeline, significantly affects the performance of pipelines carrying viscous crude oil primarily due to its impact on viscosity. Viscosity is a measure of a fluid's resistance to flow, and the viscosity of crude oil is highly temperature-dependent. As temperature decreases, the viscosity of crude oil increases, and as temperature increases, viscosity decreases. When a temperature gradient exists along the pipeline, the crude oil's viscosity will vary along the pipeline length. This leads to non-uniform flow behavior a....