variavel0=João Batista Aparecido - jbaparec@dem.feis.unesp.br Universidade Estadual Paulista Cássio Roberto Macedo Maia - cassio@dem.feis.unesp.br FEIS/UNESP Luiz Fernando Milanez - milanez@fem.unicamp.br UNICAMP Abstract. Laminar forced convection inside tubes of various cross-section shapes is of interest in the design of low Reynolds number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of simple geometries such as a circular tube, parallel plate or annular duct has been well studied in the literature and documented in various books, but for elliptical duct there are not much work done. The main assumptions used in this work are non-Newtonian fluid, laminar flow, constant physical properties, negligible axial heat diffusion (high Péclet number). Most of the previous research in elliptical ducts deal mainly with aspects of fully developed laminar flow forced convection such as velocity profile, maximum velocity, pressure drop and heat transfer quantities. In this work we examine heat transfer in hydrodynamically developed, thermally developing laminar forced convection flow of fluid inside elliptical tube, under a boundary condition of second kind. To solve the thermally developing problem we use the generalized integral transform technique (GITT) also known as Sturm-Liouville transform. Actually, such integral transform is a generalization of the finite Fourier transform where the sine and cosine functions are replaced by more general sets of orthogonal functions. The axes are algebraically transformed from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the elliptical duct wall. Then the GITT is applied to transform and solve the problem and to obtain the once unknown temperature field. Afterward it is possible to compute and present the quantities of practical interest, such as the bulk fluid temperature, the local Nusselt number and the average Nusselt number for various cross-section aspect ratios. Keywords. Non-Newtonian fluids, Forced convection, Integral Transform, Elliptical Tube.