Heat Transfer between Flowing Liquids in Cylindrical Tubes
Prepared by C. Gruesbeck
Download the CDF file to view the simulation using the free Wolfram CDF player.
https://sites.google.com/a/learncheme.com/learncheme/simulations/cdf-files/HeatTransferBetweenFlowingLiquidsInCylindricalTubes.cdf?attredirects=0&d=1
This Demonstration shows the velocity and temperature profiles of two liquids at different initial temperatures flowing concurrently in laminar flow in a cylindrical tube and the surrounding cylindrical annulus.

The properties of the two liquids are assumed to be constant, and their velocity profiles are assumed to be independent of axial location. In the inlet region z < 0, the liquids in the annular and the tube regions have different uniform temperatures Tannulus and Ttube, respectively; in the region z > 0, the external annulus wall is thermally insulated and the wall of the circular tube is assumed to be thermally thin.

Similar arrangements occur in various industrial applications, including heat exchangers and tubular reactors. You can vary the ratio of the properties of the fluid in the cylinder to the fluid in the annulus, the relative dimension of the tubular to axial radii and the pressure gradient in the two flow regions to see the temperature and velocities in the two flow regions.