Heat transfer enhancement for electro-thermo-convection of FENE-P viscoelastic fluid in a square cavity

This study numerically investigates the heat transfer enhancement for viscoelastic electro-thermo-convection in a two-dimensional differentially heated cavity with injection from below. The flow motion is assumed to be incompressible, which is driven by the Coulomb force and the thermal buoyant force. The polymers are described by the FENE-P model which exhibits typical shear-thinning and elastic properties. Based on the extensibility parameter ($L$), the cases are divided into several scenarios, corresponding to weak elasticity with strong shear-thinning, moderate elasticity with moderate shear-thinning, and strong elasticity with weak shear-thinning, respectively. We find that the competition between the shear-thinning and elasticity dominates the flow state and heat transport. The shear-thinning effect tends to facilitate heat transfer, while its elastic properties tend to decrease it. In the scenario of weak elasticity with strong shear-thinning ($L^2=10$), the polymer additives significantly improve the heat transfer enhancement (HTE) of the electric field as the polymer viscosity ratio ($\beta$) decreases or Weissenberg number ($Wi$) increases, where the maximum HTE reaches around 92.1%. The amount of HTE first increases rapidly with $Wi$ but then remains almost constant once a critical $Wi$ is exceeded. However, the HTE significantly decreases in the scenario of strong elasticity with weak shear-thinning ($300\le L\le 1000$) since the elasticity dominates over the shear-thinning. These heat transfer performances are then corroborated with the boundary layer and kinetic energy budget analysis.