THE GRAETZ PROBLEM FOR A FENE-P FLUID IN A PIPE

The development of the thermal boundary layer in a pipe for a FENE-P fluid is investigated using the method of separation of variables. The ensuing Sturm-Liouville problem is then solved for the eignevalues by means of an adequate solver, while the ordinary differential equations for the eigenfunctions and their derivatives are calculated with a fourth order Runge-Kutta method. Solutions are presented for two different boundary conditions and viscous dissipation effects are included: imposed wall temperature and imposed wall heat flux. The physical properties are considered to be independent of temperature, the fluid dynamics is fully-developed and axial conduction is neglected. Results are presented for the Nusselt number and normalized temperature as a function of the Brinkman number, which quantifies the intensity of viscous dissipation, and of numbers accounting for elastic effects, such as the Weissenberg number and the extensibility parameter.