On the energetic balance for the flow of an Oldroyd-B fluid induced by a constantly accelerating plate

TL;DR

This paper derives exact and approximate formulas for energy dissipation, shear power, and boundary layer thickness in an Oldroyd-B fluid driven by a constantly accelerating plate, comparing with other fluid models.

Contribution

It provides a unified analysis of Oldroyd-B, Maxwell, Newtonian, and second grade fluids, highlighting their differences through asymptotic approximations.

Findings

Derived formulas for dissipation and boundary layer thickness

Established limiting cases for different fluid models

Highlighted unique features of Oldroyd-B fluid behavior

Abstract

Exact and approximate expressions are established for dissipation, the power of the shear stress at the wall and the boundary layer thickness corresponding to the motion of an Oldroyd-B fluid induced by a constantly accelerating plate. The similar expressions for Maxwell, Newtonian and second grade fluids, performing the same motion, are obtained as limiting cases of our general results. The specific features of the four models are emphasized by means of the asymptotic approximations.