Fully developed, constant properly, laminar flows of viscous power-law fluids in double-sine shaped ducts are considered. The double-sine cross section represents a limiting inter-plate channel geometry in plate heat exchangers with sinusoidally corrugated plates. The non-Newtonian fluid rheology is described by the power-law or Ostwald-de Waele model, and shear thinning (n < I) as well as shear thickening (n > I) flows are considered. Both fluid flow and convective heat transfer problems under (T) and (HI) thermal boundary conditions are analyzed. Analytical solutions based on the Galerkin integral method are presented for a; wide range of flow behavior index (0.15 less than or equal to n less than or equal to 2.5) and duct aspect ratio (0.25 less than or equal to gamma less than or equal to 4.0). The effects of fluid rheology (pseudoplasticity or dilatancy), duct geometry, and thermal boundary conditions on the velocity and temperature field, are delineated. Also, isothermal friction factor and Nusselt number results for various conditions are presented, and strategies for predicting fRe and Nu are evaluated.