Hybrid analytical-numerical solution for thermal problems inside circular sector ducts

Abstract

In this work, the forced convection heat transfer was calculated for hydrodynamically fully developed and thermally non-developed Newtonian laminar flow with uniform temperature entrance profile inside circular sector ducts under boundary condition of constant surface temperature (Dirichlet condition). In order to facilitate the analytical treatment and the application of the boundary conditions, a Conformal Transform was employed to change the domain into a more suitable coordinate system. Thereafter, Generalized Integral Transform Technique – GITT was applied on the energy equation to obtain the temperature field. Numerical results were obtained for bulk mean temperature, local and average Nusselt number, and thermal entry length considering several geometric configurations. These results were compared, as much as possible, to those available in the literature and they presented a good agreement.