A Solution for the Temperature Distribution in a Pipe Wall Subjected to Internally Stratified Flow

Stratified flow in a pipe is a phenomenon in which two distinct fluids flow simultaneously through a pipe with little or no mixing. Under certain conditions the flow stratification will result in a dramatic temperature variation within the pipe wall. This paper presents a solution for the temperature distribution in a pipe wall subjected to internally stratified flow by solving Laplace’s equation in cylindrical coordinates using a finite Fourier cosine transform. The top and bottom sections are treated separately and coupled by boundary conditions at the interface. A one-dimensional approximation for the temperature distribution in the pipe at the interface is developed to uncouple the top and bottom sections, thereby avoiding the necessity for simultaneous solution of two partial differential equations. Results from the solution for a case study of a particular physical situation were compared to the solution obtained using the ANSYS finite element computer program. The solution agreed with the finite element solution to within approximately 2.4 percent throughout the pipe wall and was within 0.4 percent for most of the pipe.