Heat transport by laminar boundary layer flow with polymers

TL;DR

This paper investigates how polymers in a laminar boundary layer flow influence heat transport, revealing that polymers effectively increase viscosity near the wall, enhance drag, and reduce heat transfer.

Contribution

It introduces a numerical method to analyze polymer effects on boundary layer flow and demonstrates how polymers modify effective viscosity and heat transport.

Findings

Polymers create a space-dependent effective viscosity.

Effective viscosity increases near the wall and decreases far from it.

Polymers lead to enhanced drag and reduced heat transfer.

Abstract

Motivated by recent experimental observations, we consider a steady-state Prandtl-Blasius boundary layer flow with polymers above a slightly heated horizontal plate and study how the heat transport might be affected by the polymers. We discuss how a set of equations can be derived for the problem and how these equations can be solved numerically by an iterative scheme. By carrying out such a scheme, we find that the effect of the polymers is equivalent to producing a space-dependent effective viscosity that first increases from the zero-shear value at the plate then decreases rapidly back to the zero-shear value far from the plate. We further show that such an effective viscosity leads to an enhancement in the drag, which in turn leads to a reduction in heat transport.