variavel0=André Fonseca Mendes - Chemical and Food Engineering Department - UFPA Nielson Fernando da Paixão Ribeiro - Chemical and Food Engineering Department - UFPA Emanuel Negrão Macêdo - enegrao@ufpa.br Chemical and Food Engineering Department - UFPA João Nazareno Nonato Quaresma - quaresma@ufpa.br Chemical and Food Engineering Department - UFPA Abstract. The Integral Transform Method is employed in the solution of thermally developing flow of Phan-Thien-Tanner (PTT) fluids in ducts. In the analysis of the problem, it is considered a thermal boundary condition of prescribed heat flux at the duct walls and, in addition, viscous dissipation effects are also taken into account. Numerical results for Nusselt numbers are computed in the thermal entry region as functions of the Brinkman number and parameters of PTT model. Critical comparisons with previous results in the literature are performed, which show the consistency of the final results. Keywords. Integral Transform Method, Phan-Thien-Tanner (PTT) Model, Thermally Developing Duct Flow.