Numerical study of heat transfer in fully developed laminar flow inside a circular tube

This numerical study is aimed at investigating the convective heat transfer and flow fluid inside a horizontal circular tube in a fully developed laminar flow regime under a constant wall temperature boundary condition, commonly called the Graetz problem; our goal is to get the steady temperature distribution in the fluid. The complexity of the partial differential equation that describes the temperature field with the associated linear or non-linear boundary conditions is simplified by means of numerical methods using current computational tools. The simplified energy equation is solved numerically by the orthogonal collocation method followed by the finite difference method (Crank-Nicholson method). The calculations were effected through a FORTRAN computer program, and the results show that the orthogonal collocation method gives better results than the Crank-Nicholson method. In addition, the numerical results were compared to the experimental values obtained on the same tube diameter. It is important to note that the numerical results are in good agreement with the published experimental data.