On the laminar forced convection with non-linear viscoelastic fluids in concentric and eccentric cylindrical annuli

Forced convection of non-linear viscoelastic fluids described by the Modified Phan Thien Tanner model (MPTT) is studied for laminar, pressure gradient driven flow through concentric and eccentric horizontal annuli with constant and equal peripheral wall temperatures. An analytical solution, including viscous dissipation, is developed using a double asymptotic expansion in the Weissenberg number and a mapping parameter that transforms circular cross-sections into annular geometries of varying eccentricity while satisfying simultaneously the no-slip and thermal boundary conditions. At leading order, solutions are obtained for concentric annuli, with higher-order corrections capturing eccentricity effects. In concentric tubes, elasticity alone enhances heat transfer compared to Newtonian fluids. In eccentric tubes, symmetry breaking induces secondary transversal flows driven by unbalanced normal stress differences. For small Weissenberg numbers, the weak vortical motion cannot counteract the reduction in heat transfer caused by eccentricity. Consequently, maximum heat transfer occurs in concentric geometries, while increasing eccentricity progressively diminishes it, consistent with Newtonian trends. However, as elasticity increases, the difference is reduced. The influence of eccentricity, elasticity, and the Brinkman number on vortical structures and Nusselt numbers is examined under both double-heating (walls hotter than the fluid) and double-cooling (walls cooler than the fluid). © 2025 Elsevier Ltd