Cartesian Graetz problem with boundary condition of the third kind: A semi-analytical solution

Abstract

A semi-analytical analysis to the Cartesian Graetz problem with boundary condition of the third kind is carried out using a spectral method that considers a Fourier series expansion for the temperature field, in this way the energy equation is reduced to a system of first-order ordinary differential equations, which is trivially solved by standard methods. The results obtained were parameterized with the Biot number and show interesting variations for different values of the Biot number near the thermal entrance location. The semi-analytical method presented in this work is a good calculation alternative for problems of this type, providing good numerical precision and allowing solutions to be found in a very simple way and with low computational cost, in particular, the method provides very accurate solutions for the temperature field in regions very close to the channel entrance.