Analysis of the effect of normal stress differences on heat transfer in creeping viscoelastic Dean flow

In this paper, the convective heat transfer in viscoelastic creeping flow in a curved circular pipe is investigated analytically. The flow and heat transfer is assumed to be fully-developed and a constant heat flux at the walls is imposed as the boundary condition. The second order constitutive equation is used to simulate the low speed flow of viscoelastic fluids. The closed form of temperature distributions for H2 boundary condition is obtained using a perturbation method. For this reason, the pipe curvature ratio is used as the perturbation parameter for both flow field and temperature distribution. The solutions are obtained for two types of material models based on hypergeometric functions. Owing to the singularity situation, analyzing the effect of second normal stress difference on Dean flow is very complex. The current article therefore focuses on studying analytically the opposite effect of the first and negative second normal stress differences on convective heat transfer in viscoelastic Dean flow. The current study finds applications in polymer processing and arterial biofluid dynamics.