Analytical and numerical solutions of forced convection in ducts with a boundary condition of the third kind

Forced convection inside ducts, such as circular pipes, parallel plates, rectangular ducts, isosceles triangular ducts, and hexagonal ducts is often encountered in heat exchange equipment. In most cases, the heat transfer of ambient fluid to the duct occurs in addition to the heat transfer inside the duct. This is approximated by the third kind of thermal boundary condition when one predicts the forced convection inside the duct. The present research provides an analytical/numerical solution of the heat transfer of the fluid inside the circular pipe and the above mentioned non-circular ducts subjected to the third kind of boundary condition. The slug flow and the fully developed flow inside the ducts are considered. The effects of the Biot number on the temperature profile of the fluid and the Nusselt number are investigated for each duct. It was found that the Biot number has significant effects on both the temperature distribution and the Nusselt number. It would be inappropriate to simply use the solutions for the first and second boundary conditions to predict the forced convection heat transfer inside the duct that is subjected to the third kind of boundary condition.