SINOPSIS

An analytical solution for the extended Graetz problem with axial heat conduction is presented. The method is applicable to a fully developed flow in a circular tube subject to more general, first-kind wall boundary conditions as a function of the axial distance. The solution is generated using a convenient complete basis for the set of square integrable functions in R, orthogonal to the Hermite polynomials. Thus, the solution for the temperature profile is obtained by the infinite series of products of functions, resulting in the decomposition of the energy equation into a set of ordinary differential equations, each of which depends only upon the two previous equations. This fact allows the set to be solved successively. Representative curves illustrating the variations of the temperature surfaces, bulk temperature, heat flux, and Nusselt numbers with pertinent parameters are obtained.