Analytical solution for thermally developing laminar core-annular flow with two immiscible liquids considering axial diffusion in semi-infinite ducts

Abstract

Flows involving core-annular immiscible liquids provide a wide range of useful engineering applications, such as transportation of heavy oils and cooling processes. The present article considers an analytical solution for the internal convection heat transfer in hydrodynamically developed and thermally developing laminar core-annular liquid–liquid immiscible flows in circular ducts. The axial diffusion is considered in the model and the problem is investigated for semi-infinite domain under convective boundary condition on duct walls and prescribed inlet flow temperature. The steady-state problem is solved through the generalized integral transform technique (GITT) with a single domain approach, in which, the coupled ODE system arising from the GITT is analytically solved using the matrix exponential method. Moreover, integral balance is used to compute the Nusselt number. The convergence process of the local Nusselt number is shown in different flow regions and the results are presented for multiple flow parameters. The effects of the boundary conditions, flow properties, and other parameters are discussed. An analysis of axial diffusion effects is performed, which confirms that it can interfere with the local Nusselt number, especially for lower Péclet numbers.