Numerical investigation of isothermal and non-isothermal viscoelastic flow in lid-driven polar cavity

Abstract

The isothermal and non-isothermal viscoelastic ow of Phan-Thien-Tanner (PTT) uids is considered in lid-driven polar cavity geometry, with stationary and oscillatory lid motion, using a numerical solution method with parameter continuation technique. Thermoelastic e ects, in terms of elastic/elongational e ects and viscous dissipation, are demonstrated by the changes in vortical structure, temperature/stress distributions and heat transfer characteristics in the curved cavity. Central vortex location shifts are observed under elastic and elongational (strain hardening and strain softening/shear thinning) e ects for isothermal and non-isothermal conditions. The growth in size and strength of a secondary vortex is denoted in the downstream stationary corner of the cavity for the viscoelastic uid under strain hardening e ects which also introduce an increase in stress gradients. Decrease in both stress values and their gradients are observed under viscous dissipation. The changes in temperature eld and heat transfer properties are revealed. The oscillatory response of the viscoelastic Phan-Thien-Tanner model for isothermal and non-isothermal cases is examined. The Fourier transform rheology technique is used to understand the frequency spectrum of the response. The results are shown as phase diagrams and Fourier spectrums of the time variations of the shear stress, rst normal stress di erence, and dimensionless Nusselt modulus, which is an indication of the heat transfer rate.