Viscoelastic dream pipe with triangular pressure gradient wave form for substantial enhancement of heat transfer

Abstract

A theoretical investigation is carried out to analyse the combined effects of oscillation and conjugation on the enhancement of heat transfer in laminar flow of viscoelastic fluids (CPyCl/NaSal) flowing in a circular tube with thermally conducting walls. The fluid flow is induced by a triangular pressure gradient wave form. Closed-form solutions for the momentum and heat equations are presented. The effects of influential parameters such as the wall thermal conductivity (ks), wall thickness (ε), fluid thickness, Womersley number (α), Deborah number and Prandtl number on the effective thermal diffusivity (κe) are examined. Several maxima occur in κe where the fluid flow exhibits a resonant behavior. In the viscous regime, κe increases with increasing ks and ϵ only up to the optimum value of α. In the elastic regime, the effect of conjugation on κe is saturated. The highest heat flux is achieved by the viscoelastic fluids with sinusoidal pressure gradient wave form when the walls are thermally insulated and this maximum heat flux (6.53 × 1011 W/m2) is 2968 times higher than the next highest value (2.2 × 108 W/m2) achieved by the Newtonian fluids with triangular pressure gradient wave form with thermally conducting walls. The present study demonstrates that viscoelastic fluids are preferable to Newtonian fluids and further triangular pressure gradient wave form is preferable when the walls are thermally conducting and sinusoidal pressure gradient wave form is preferable when the walls are thermally insulated.